------------------------------------------------------------------------------------------------------------------------------- name: log: c:\acdbookrevision\webpage_finalize\racd06p1.txt log type: text opened on: 6 Jun 2013, 15:43:08 . . ********** OVERVIEW OF racd06p1.do ********** . . * STATA Program . * copyright C 2013 by A. Colin Cameron and Pravin K. Trivedi . * used for "Regression Analyis of Count Data" SECOND EDITION . * by A. Colin Cameron and Pravin K. Trivedi (2013) . * Cambridge University Press . . * Chapter 6.3 only . * 6.3 NMES DOCTOR VISITS . . * To run you need file . * racd06data1healthcare.dta . * and user-written Stata addon . * fmm . * in your directory . . ********** SETUP ********** . . set more off . version 11.2 . clear all . set mem 10m . * set linesize 82 . set scheme s1mono /* Graphics scheme */ . . ********** DATA DESCRIPTION . . * The data are extracted from the 1987-88 National Medical Expenditure Survey (NMES). . * The extract and analysis are in P. Deb and P.K. Trivedi (1997), . * Demand for Medical Care by the Elderly: A Finite Mixture Approach" . * Journal of Applied Econometrics, 12, 313-326. . . * See this article for more detailed discussion . * Also see racd06makedata1healthcare.do for further details . . ********** RESULTS HERE DIFFER IN SOME PLACES FROM THE BOOK . . * This Stata program reanalyzes the data given in the published paper by . * Deb and Trivedi (1997). Their results used quite different code written . * in a program other than Stata, and there is some difference in results. . . * Tables 6.1 and 6.2 generated here are the same as Deb and Trivedi (1997). . * For Tables 6.3 - 6.5 generatedhere there are differences for some of the . * many models estimated. The book reports the tables in the published article. . * For Tables 6.6 - 6.8 the diferences are small and the book reports . * the Stata output given below. . . * Using the results obtained below Table 6.4 in the book becomes . . * TABLE 6.4 RE-COMPUTED USING CODE WRITTEN IN STATA . . * NB1 or NB2 Model k lnL AIC BIC T_GOF . * ------------------------------------------------------------- . * NB1 NB 18 -12156 24348 24463 Not . * NB1 NBH 36 -12126 24325 24554 computed . * NB1 CFMNB-2 21 -12098 24238 24372 Not . * NB1 FMNB-2 37 -12092 24259 24495 computed . * NB1 CFMNB-3 24 -12096 24239 24392 Not . * NB1 FMNB-3 56 -12050 24210 24562 computed . * ------------------------------------------------------------- . * NB2 NB 18 -12202 24440 24555 Not . * NB2 NBH 36 -12108 24289 24519 computed . * NB2 CFMNB-2 21 -12149 24340 24474 Not . * NB2 FMNB-2 37 -12139 24352 24589 computed . * NB2 CFMNB-3 24 -12144 24336 24490 Not . * NB2 FMNB-3 56 -12080 24272 24630 computed . * ------------------------------------------------------------- . . ********** 6.3.1 NMES DOCTOR VISITS DATA: READ DATA AND SUMMARIZE . . use racd06data1healthcare.dta, clear . . *** TABLE 6.1: OFP Frequency distribution . generate OFPfreqs = OFP . replace OFPfreqs = 13 if OFPfreqs >= 13 (427 real changes made) . tabulate OFPfreqs OFPfreqs | Freq. Percent Cum. ------------+----------------------------------- 0 | 683 15.50 15.50 1 | 481 10.92 26.42 2 | 428 9.71 36.13 3 | 420 9.53 45.67 4 | 383 8.69 54.36 5 | 338 7.67 62.03 6 | 268 6.08 68.11 7 | 217 4.93 73.04 8 | 188 4.27 77.30 9 | 171 3.88 81.18 10 | 128 2.91 84.09 11 | 115 2.61 86.70 12 | 86 1.95 88.65 13 | 500 11.35 100.00 ------------+----------------------------------- Total | 4,406 100.00 . . *** TABLE 6.2: Variable descriptions and summary statistics . describe Contains data from racd06data1healthcare.dta obs: 4,406 vars: 23 7 Jun 2011 10:39 size: 405,352 ------------------------------------------------------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------------------------------------------------------- OFP float %9.0g Number of physician office visits OFNP float %9.0g Number of non-physician office visits OPP float %9.0g Number of physician outpatient visits OPNP float %9.0g Number of non-physician outpatient visits EMR float %9.0g Number of emergency room visits HOSP float %9.0g Number hospitalizations EXCLHLTH float %9.0g Equals 1 if self perceived health is excellent POORHLTH float %9.0g Equals 1 if self perceived health is poor NUMCHRON float %9.0g Number of chronic conditions ADLDIFF float %9.0g Equals 1 if the person has a condition that limits activities of daily living NOREAST float %9.0g Equals 1 if the person lives in northeastern U.S. MIDWEST float %9.0g Equals 1 if the person lives in the midwestern U.S. WEST float %9.0g Equals 1 if the person lives in the western U.S. AGE float %9.0g Age in years (divided by 10) BLACK float %9.0g Equals 1 if the person is African American MALE float %9.0g Equals 1 if the person is male MARRIED float %9.0g Equals 1 if the person is married SCHOOL float %9.0g Number of years of education FAMINC float %9.0g Family income in $10,000 EMPLOYED float %9.0g Equals 1 if the person is employed PRIVINS float %9.0g Equals 1 if the person is covered by private health insurance MEDICAID float %9.0g Equals 1 if the person is covered by Medicaid OFPfreqs float %9.0g ------------------------------------------------------------------------------------------------------------------------------- Sorted by: Note: dataset has changed since last saved . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- OFP | 4406 5.774399 6.759225 0 89 OFNP | 4406 1.618021 5.317056 0 104 OPP | 4406 .7507944 3.652759 0 141 OPNP | 4406 .5360872 3.879506 0 155 EMR | 4406 .2635043 .7036586 0 12 -------------+-------------------------------------------------------- HOSP | 4406 .2959601 .7463978 0 8 EXCLHLTH | 4406 .0778484 .2679633 0 1 POORHLTH | 4406 .1257376 .3315911 0 1 NUMCHRON | 4406 1.541988 1.349632 0 8 ADLDIFF | 4406 .2040399 .4030441 0 1 -------------+-------------------------------------------------------- NOREAST | 4406 .1899682 .3923203 0 1 MIDWEST | 4406 .2625965 .4400949 0 1 WEST | 4406 .1811167 .3851585 0 1 AGE | 4406 7.402406 .6334051 6.6 10.9 BLACK | 4406 .117113 .3215914 0 1 -------------+-------------------------------------------------------- MALE | 4406 .4035406 .4906631 0 1 MARRIED | 4406 .5460735 .4979292 0 1 SCHOOL | 4406 10.29029 3.738736 0 18 FAMINC | 4406 2.527132 2.924648 -1.0125 54.8351 EMPLOYED | 4406 .1032683 .3043435 0 1 -------------+-------------------------------------------------------- PRIVINS | 4406 .7764412 .4166769 0 1 MEDICAID | 4406 .0912392 .2879817 0 1 OFPfreqs | 4406 5.008171 4.256362 0 13 . . tabulate OFP Number of | physician | office | visits | Freq. Percent Cum. ------------+----------------------------------- 0 | 683 15.50 15.50 1 | 481 10.92 26.42 2 | 428 9.71 36.13 3 | 420 9.53 45.67 4 | 383 8.69 54.36 5 | 338 7.67 62.03 6 | 268 6.08 68.11 7 | 217 4.93 73.04 8 | 188 4.27 77.30 9 | 171 3.88 81.18 10 | 128 2.91 84.09 11 | 115 2.61 86.70 12 | 86 1.95 88.65 13 | 73 1.66 90.31 14 | 76 1.72 92.03 15 | 53 1.20 93.24 16 | 47 1.07 94.30 17 | 48 1.09 95.39 18 | 30 0.68 96.07 19 | 24 0.54 96.62 20 | 16 0.36 96.98 21 | 18 0.41 97.39 22 | 16 0.36 97.75 23 | 10 0.23 97.98 24 | 12 0.27 98.25 25 | 3 0.07 98.32 26 | 9 0.20 98.52 27 | 7 0.16 98.68 28 | 4 0.09 98.77 29 | 3 0.07 98.84 30 | 4 0.09 98.93 31 | 4 0.09 99.02 32 | 1 0.02 99.05 33 | 1 0.02 99.07 34 | 2 0.05 99.11 35 | 1 0.02 99.14 36 | 1 0.02 99.16 37 | 3 0.07 99.23 38 | 2 0.05 99.27 39 | 5 0.11 99.39 40 | 2 0.05 99.43 41 | 1 0.02 99.46 42 | 4 0.09 99.55 43 | 2 0.05 99.59 44 | 1 0.02 99.61 47 | 1 0.02 99.64 48 | 1 0.02 99.66 49 | 1 0.02 99.68 50 | 1 0.02 99.70 51 | 1 0.02 99.73 53 | 2 0.05 99.77 55 | 1 0.02 99.80 56 | 1 0.02 99.82 58 | 2 0.05 99.86 61 | 1 0.02 99.89 63 | 1 0.02 99.91 65 | 1 0.02 99.93 66 | 1 0.02 99.95 68 | 1 0.02 99.98 89 | 1 0.02 100.00 ------------+----------------------------------- Total | 4,406 100.00 . * OFP histogram . * histogram OFP if OFP < 45, discrete fraction scale(1.2) . . * Global for the regressors . global XLIST EXCLHLTH POORHLTH NUMCHRON ADLDIFF NOREAST MIDWEST WEST AGE /// > BLACK MALE MARRIED SCHOOL FAMINC EMPLOYED PRIVINS MEDICAID . . *********** 6.3.4 MODEL SELECTION AND COMPARISON (NB, Hurdle, FM) for Tables 6.3-6.5 . . * Poisson . poisson OFP $XLIST, vce(robust) Iteration 0: log pseudolikelihood = -18134.655 Iteration 1: log pseudolikelihood = -18134.567 Iteration 2: log pseudolikelihood = -18134.567 Poisson regression Number of obs = 4406 Wald chi2(16) = 570.03 Prob > chi2 = 0.0000 Log pseudolikelihood = -18134.567 Pseudo R2 = 0.0868 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.3862208 .0786163 -4.91 0.000 -.540306 -.2321356 POORHLTH | .2873922 .0576105 4.99 0.000 .1744776 .4003068 NUMCHRON | .1639607 .0122684 13.36 0.000 .139915 .1880064 ADLDIFF | .0934088 .051097 1.83 0.068 -.0067395 .1935571 NOREAST | .1075677 .0492905 2.18 0.029 .01096 .2041754 MIDWEST | -.0105486 .0447331 -0.24 0.814 -.0982239 .0771267 WEST | .1238461 .0475824 2.60 0.009 .0305862 .217106 AGE | -.0552906 .0289719 -1.91 0.056 -.1120745 .0014933 BLACK | -.0655474 .0637323 -1.03 0.304 -.1904604 .0593656 MALE | -.0713668 .0379348 -1.88 0.060 -.1457176 .002984 MARRIED | -.0407636 .038426 -1.06 0.289 -.1160772 .0345499 SCHOOL | .0258206 .0055887 4.62 0.000 .0148668 .0367743 FAMINC | -.0023524 .0057808 -0.41 0.684 -.0136825 .0089776 EMPLOYED | .0527792 .0750458 0.70 0.482 -.0943078 .1998663 PRIVINS | .321541 .0513952 6.26 0.000 .2208082 .4222739 MEDICAID | .2886599 .0616569 4.68 0.000 .1678145 .4095052 _cons | 1.296604 .2334117 5.56 0.000 .8391257 1.754083 ------------------------------------------------------------------------------ . estimates store POISSON . . * NB1 . nbreg OFP $XLIST, vce(robust) dispersion(constant) Fitting Poisson model: Iteration 0: log pseudolikelihood = -18134.655 Iteration 1: log pseudolikelihood = -18134.567 Iteration 2: log pseudolikelihood = -18134.567 Fitting constant-only model: Iteration 0: log pseudolikelihood = -14552.718 Iteration 1: log pseudolikelihood = -12647.886 Iteration 2: log pseudolikelihood = -12493.025 Iteration 3: log pseudolikelihood = -12492.829 Iteration 4: log pseudolikelihood = -12492.829 Fitting full model: Iteration 0: log pseudolikelihood = -12492.829 Iteration 1: log pseudolikelihood = -12301.184 Iteration 2: log pseudolikelihood = -12157 Iteration 3: log pseudolikelihood = -12156.203 Iteration 4: log pseudolikelihood = -12156.202 Negative binomial regression Number of obs = 4406 Dispersion = constant Wald chi2(16) = 694.92 Log pseudolikelihood = -12156.202 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.2679127 .0506053 -5.29 0.000 -.3670973 -.1687281 POORHLTH | .1890825 .0460892 4.10 0.000 .0987494 .2794156 NUMCHRON | .1774737 .0102697 17.28 0.000 .1573455 .197602 ADLDIFF | .0054215 .0392485 0.14 0.890 -.0715041 .0823471 NOREAST | .0715408 .0389436 1.84 0.066 -.0047872 .1478688 MIDWEST | .0138372 .0339726 0.41 0.684 -.0527478 .0804222 WEST | .1049489 .0384155 2.73 0.006 .0296559 .180242 AGE | -.0032939 .0233938 -0.14 0.888 -.0491448 .042557 BLACK | -.1275746 .0520345 -2.45 0.014 -.2295604 -.0255888 MALE | -.1231018 .0295699 -4.16 0.000 -.1810578 -.0651458 MARRIED | .0221482 .0308756 0.72 0.473 -.0383668 .0826632 SCHOOL | .0212676 .0043099 4.93 0.000 .0128203 .0297149 FAMINC | -.000249 .0046019 -0.05 0.957 -.0092685 .0087705 EMPLOYED | -.0180486 .0483787 -0.37 0.709 -.112869 .0767719 PRIVINS | .3364587 .0436197 7.71 0.000 .2509656 .4219518 MEDICAID | .3180563 .0580432 5.48 0.000 .2042938 .4318189 _cons | .949961 .1900152 5.00 0.000 .577538 1.322384 -------------+---------------------------------------------------------------- /lndelta | 1.576208 .0405414 1.496748 1.655668 -------------+---------------------------------------------------------------- delta | 4.836581 .1960816 4.46714 5.236575 ------------------------------------------------------------------------------ . estimates store NB1 . scalar llNB1 = e(ll) . scalar kNB1 = e(k) . . * NB2 . nbreg OFP $XLIST, vce(robust) Fitting Poisson model: Iteration 0: log pseudolikelihood = -18134.655 Iteration 1: log pseudolikelihood = -18134.567 Iteration 2: log pseudolikelihood = -18134.567 Fitting constant-only model: Iteration 0: log pseudolikelihood = -12492.848 Iteration 1: log pseudolikelihood = -12492.829 Iteration 2: log pseudolikelihood = -12492.829 Fitting full model: Iteration 0: log pseudolikelihood = -12234.27 Iteration 1: log pseudolikelihood = -12202.779 Iteration 2: log pseudolikelihood = -12202.168 Iteration 3: log pseudolikelihood = -12202.168 Negative binomial regression Number of obs = 4406 Dispersion = mean Wald chi2(16) = 539.90 Log pseudolikelihood = -12202.168 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.3845558 .0781452 -4.92 0.000 -.5377175 -.2313941 POORHLTH | .3226979 .0561814 5.74 0.000 .2125843 .4328115 NUMCHRON | .1897393 .013172 14.40 0.000 .1639228 .2155559 ADLDIFF | .0967679 .0506209 1.91 0.056 -.0024473 .1959832 NOREAST | .1112554 .0505925 2.20 0.028 .0120959 .2104148 MIDWEST | -.0011415 .0448927 -0.03 0.980 -.0891295 .0868466 WEST | .1368204 .0479385 2.85 0.004 .0428626 .2307782 AGE | -.0356419 .0310612 -1.15 0.251 -.0965208 .025237 BLACK | -.0661781 .066558 -0.99 0.320 -.1966295 .0642732 MALE | -.0750747 .0397817 -1.89 0.059 -.1530453 .002896 MARRIED | -.0355702 .0411729 -0.86 0.388 -.1162677 .0451272 SCHOOL | .0273927 .005449 5.03 0.000 .0167128 .0380726 FAMINC | -.0016692 .0055387 -0.30 0.763 -.0125248 .0091864 EMPLOYED | .0255671 .0677192 0.38 0.706 -.10716 .1582943 PRIVINS | .3458812 .0547448 6.32 0.000 .2385834 .4531791 MEDICAID | .2761624 .0670752 4.12 0.000 .1446975 .4076273 _cons | 1.059449 .2630634 4.03 0.000 .5438547 1.575044 -------------+---------------------------------------------------------------- /lnalpha | -.1674192 .0333357 -.232756 -.1020824 -------------+---------------------------------------------------------------- alpha | .845845 .0281969 .7923469 .9029552 ------------------------------------------------------------------------------ . estimates store NB2 . scalar llNB2 = e(ll) . scalar kNB2 = e(k) . . ****** HURDLE MODELS - FIRST COMPONENT logit or NB1 or NB2 . . generate DOFP = OFP > 0 . . * Hurdle first component: logit . logit DOFP $XLIST, vce(robust) Iteration 0: log pseudolikelihood = -1900.3601 Iteration 1: log pseudolikelihood = -1728.708 Iteration 2: log pseudolikelihood = -1710.6166 Iteration 3: log pseudolikelihood = -1710.5266 Iteration 4: log pseudolikelihood = -1710.5266 Logistic regression Number of obs = 4406 Wald chi2(16) = 279.07 Prob > chi2 = 0.0000 Log pseudolikelihood = -1710.5266 Pseudo R2 = 0.0999 ------------------------------------------------------------------------------ | Robust DOFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.328511 .1422489 -2.31 0.021 -.6073137 -.0497083 POORHLTH | .0708379 .1687321 0.42 0.675 -.2598709 .4015467 NUMCHRON | .556512 .0527686 10.55 0.000 .4530873 .6599366 ADLDIFF | -.1881657 .1299432 -1.45 0.148 -.4428498 .0665183 NOREAST | .1292212 .1250505 1.03 0.301 -.1158732 .3743157 MIDWEST | .1008883 .1146354 0.88 0.379 -.1237929 .3255695 WEST | .2016633 .1336443 1.51 0.131 -.0602747 .4636014 AGE | .1904976 .0811478 2.35 0.019 .0314509 .3495443 BLACK | -.326972 .1334663 -2.45 0.014 -.5885612 -.0653829 MALE | -.4644473 .09852 -4.71 0.000 -.6575429 -.2713517 MARRIED | .2472641 .1039523 2.38 0.017 .0435213 .4510068 SCHOOL | .0542073 .0131949 4.11 0.000 .0283458 .0800688 FAMINC | .0067446 .0184979 0.36 0.715 -.0295106 .0429998 EMPLOYED | -.0123197 .145099 -0.08 0.932 -.2967086 .2720692 PRIVINS | .7624604 .1173052 6.50 0.000 .5325464 .9923745 MEDICAID | .5535139 .1812261 3.05 0.002 .1983173 .9087106 _cons | -1.475312 .6464112 -2.28 0.022 -2.742254 -.2083689 ------------------------------------------------------------------------------ . estimates store H1logit . scalar llH1logit = e(ll) . scalar kH1logit = e(k) . scalar nH = e(N) . . * Hurdle first component: NB1 . program lfNB1binary 1. version 10.1 2. args lnf theta1 a // theta1=x'b, a=alpha, lnf=lnf(y) 3. tempvar mu p0 4. local y $ML_y1 // Define y so program more readable 5. generate double `mu' = exp(`theta1') 6. generate double `p0' = (1/(1+`a'))^(`mu'/`a') 7. quietly replace `lnf' = ln(`p0') if $ML_y1 == 0 8. quietly replace `lnf' = ln(1-`p0') if $ML_y1 == 1 9. end . ml model lf lfNB1binary (DOFP = $XLIST) (), vce(robust) . ml maximize, nolog (4406 missing values generated) initial: log pseudolikelihood = - (could not be evaluated) feasible: log pseudolikelihood = -2047.454 rescale: log pseudolikelihood = -1900.5194 rescale eq: log pseudolikelihood = -1900.5194 Number of obs = 4406 Wald chi2(16) = 237.97 Log pseudolikelihood = -1723.7526 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust DOFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- eq1 | EXCLHLTH | -.1735103 .0722673 -2.40 0.016 -.3151516 -.031869 POORHLTH | .0204064 .0731079 0.28 0.780 -.1228824 .1636952 NUMCHRON | .206869 .0208221 9.94 0.000 .1660584 .2476796 ADLDIFF | -.1094521 .0581162 -1.88 0.060 -.2233577 .0044535 NOREAST | .061183 .0575746 1.06 0.288 -.0516612 .1740272 MIDWEST | .0515839 .0527429 0.98 0.328 -.0517903 .1549582 WEST | .117734 .0589905 2.00 0.046 .0021147 .2333534 AGE | .0615207 .0366497 1.68 0.093 -.0103113 .1333527 BLACK | -.1756703 .0670894 -2.62 0.009 -.3071631 -.0441776 MALE | -.2070004 .0451632 -4.58 0.000 -.2955186 -.1184822 MARRIED | .0970383 .048013 2.02 0.043 .0029346 .191142 SCHOOL | .0229889 .006056 3.80 0.000 .0111193 .0348585 FAMINC | .0033474 .0076281 0.44 0.661 -.0116033 .0182982 EMPLOYED | -.0316314 .0672774 -0.47 0.638 -.1634927 .1002299 PRIVINS | .3805973 .0583269 6.53 0.000 .2662786 .494916 MEDICAID | .277444 .0869749 3.19 0.001 .1069764 .4479116 _cons | -.2496048 .294187 -0.85 0.396 -.8262007 .3269912 -------------+---------------------------------------------------------------- eq2 | _cons | 1.000444 .0129819 77.06 0.000 .9750004 1.025888 ------------------------------------------------------------------------------ . estimates store H1NB1 . scalar llH1NB1 = e(ll) . scalar kH1NB1 = e(k) . . * Hurdle first component: NB2 . program lfNB2binary 1. version 10.1 2. args lnf theta1 a // theta1=x'b, a=alpha, lnf=lnf(y) 3. tempvar mu p0 4. local y $ML_y1 // Define y so program more readable 5. generate double `mu' = exp(`theta1') 6. generate double `p0' = (1/(1+`a'*`mu'))^(1/`a') 7. quietly replace `lnf' = ln(`p0') if $ML_y1 == 0 8. quietly replace `lnf' = ln(1-`p0') if $ML_y1 == 1 9. end . ml model lf lfNB2binary (DOFP = $XLIST) (), vce(robust) . ml maximize, nolog (4406 missing values generated) initial: log pseudolikelihood = - (could not be evaluated) feasible: log pseudolikelihood = -2151.5981 rescale: log pseudolikelihood = -2021.8161 rescale eq: log pseudolikelihood = -1978.5291 (7 missing values generated) (9 missing values generated) (13 missing values generated) (19 missing values generated) (26 missing values generated) Number of obs = 4406 Wald chi2(16) = 9.83 Log pseudolikelihood = -1708.5461 Prob > chi2 = 0.8756 ------------------------------------------------------------------------------ | Robust DOFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- eq1 | EXCLHLTH | -.628034 .3803345 -1.65 0.099 -1.373476 .117408 POORHLTH | .1488019 .344439 0.43 0.666 -.5262862 .82389 NUMCHRON | 1.164465 .4986804 2.34 0.020 .1870697 2.141861 ADLDIFF | -.2973999 .2614204 -1.14 0.255 -.8097745 .2149747 NOREAST | .2504665 .2596285 0.96 0.335 -.2583961 .7593291 MIDWEST | .1959491 .2410242 0.81 0.416 -.2764497 .6683479 WEST | .3734146 .3094784 1.21 0.228 -.2331519 .9799811 AGE | .4152715 .2466855 1.68 0.092 -.0682232 .8987662 BLACK | -.5815625 .3121817 -1.86 0.062 -1.193427 .0303023 MALE | -.8978032 .4011254 -2.24 0.025 -1.683994 -.1116119 MARRIED | .5236183 .3242043 1.62 0.106 -.1118105 1.159047 SCHOOL | .1078683 .0504125 2.14 0.032 .0090617 .2066749 FAMINC | .0130891 .0390349 0.34 0.737 -.0634178 .089596 EMPLOYED | .0339144 .290824 0.12 0.907 -.5360901 .6039189 PRIVINS | 1.410326 .53617 2.63 0.009 .3594523 2.4612 MEDICAID | .9886617 .4573735 2.16 0.031 .0922261 1.885097 _cons | -2.86773 1.681691 -1.71 0.088 -6.163784 .4283238 -------------+---------------------------------------------------------------- eq2 | _cons | 2.452479 1.112621 2.20 0.028 .2717811 4.633177 ------------------------------------------------------------------------------ . estimates store H1NB2 . scalar llH1NB2 = e(ll) . scalar kH1NB2 = e(k) . . ****** HURDLE MODELS - SECOND COMPONENT NB1 or NB2 . . * Hurdle second component: NB1 . ztnb OFP $XLIST if OFP>0, dispersion(constant) vce(robust) Fitting Zero-truncated poisson model: Iteration 0: log pseudolikelihood = -14579.565 Iteration 1: log pseudolikelihood = -14579.287 Iteration 2: log pseudolikelihood = -14579.287 Fitting constant-only model: Iteration 0: log pseudolikelihood = -11831.171 Iteration 1: log pseudolikelihood = -10932.093 Iteration 2: log pseudolikelihood = -10603.329 Iteration 3: log pseudolikelihood = -10589.675 Iteration 4: log pseudolikelihood = -10589.642 Iteration 5: log pseudolikelihood = -10589.642 (683 missing values generated) Fitting full model: Iteration 0: log pseudolikelihood = -10589.642 Iteration 1: log pseudolikelihood = -10455.669 Iteration 2: log pseudolikelihood = -10402.952 Iteration 3: log pseudolikelihood = -10402.502 Iteration 4: log pseudolikelihood = -10402.5 Iteration 5: log pseudolikelihood = -10402.5 Zero-truncated negative binomial regression Number of obs = 3723 Dispersion = constant Wald chi2(16) = 430.42 Log likelihood = -10402.5 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.4273102 .0944306 -4.53 0.000 -.6123908 -.2422296 POORHLTH | .2708583 .0512404 5.29 0.000 .170429 .3712875 NUMCHRON | .1533033 .0121155 12.65 0.000 .1295574 .1770492 ADLDIFF | .0812708 .0476659 1.71 0.088 -.0121527 .1746943 NOREAST | .0834631 .0506103 1.65 0.099 -.0157312 .1826574 MIDWEST | -.0168203 .0450092 -0.37 0.709 -.1050368 .0713961 WEST | .0963784 .0499589 1.93 0.054 -.0015392 .1942961 AGE | -.0604462 .0297356 -2.03 0.042 -.1187268 -.0021656 BLACK | -.0505329 .0657304 -0.77 0.442 -.1793622 .0782963 MALE | -.0478359 .0391429 -1.22 0.222 -.1245546 .0288827 MARRIED | -.0420995 .0400434 -1.05 0.293 -.1205832 .0363842 SCHOOL | .0182904 .0059409 3.08 0.002 .0066464 .0299343 FAMINC | -.001976 .0067402 -0.29 0.769 -.0151865 .0112345 EMPLOYED | -.0126104 .0708615 -0.18 0.859 -.1514964 .1262756 PRIVINS | .2467514 .0571132 4.32 0.000 .1348116 .3586912 MEDICAID | .3000174 .0672999 4.46 0.000 .1681121 .4319227 _cons | 1.524488 .2401803 6.35 0.000 1.053743 1.995233 -------------+---------------------------------------------------------------- /lndelta | 1.53823 .0547167 1.430987 1.645473 -------------+---------------------------------------------------------------- delta | 4.656342 .2547795 4.182827 5.18346 ------------------------------------------------------------------------------ . estimates store H2NB1 . scalar llH2NB1 = e(ll) . scalar kH2NB1 = e(k) . . * Hurdle second component: NB2 . ztnb OFP $XLIST if OFP>0, dispersion(mean) vce(robust) Fitting Zero-truncated poisson model: Iteration 0: log pseudolikelihood = -14579.565 Iteration 1: log pseudolikelihood = -14579.287 Iteration 2: log pseudolikelihood = -14579.287 Fitting constant-only model: Iteration 0: log pseudolikelihood = -10629.691 Iteration 1: log pseudolikelihood = -10591.459 Iteration 2: log pseudolikelihood = -10589.644 Iteration 3: log pseudolikelihood = -10589.642 Iteration 4: log pseudolikelihood = -10589.642 Fitting full model: Iteration 0: log pseudolikelihood = -10421.041 Iteration 1: log pseudolikelihood = -10400.551 Iteration 2: log pseudolikelihood = -10399.965 Iteration 3: log pseudolikelihood = -10399.965 Zero-truncated negative binomial regression Number of obs = 3723 Dispersion = mean Wald chi2(16) = 366.15 Log likelihood = -10399.965 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.3775072 .08729 -4.32 0.000 -.5485924 -.206422 POORHLTH | .332509 .056758 5.86 0.000 .2212654 .4437527 NUMCHRON | .1429373 .0134919 10.59 0.000 .1164936 .169381 ADLDIFF | .1290356 .0516041 2.50 0.012 .0278934 .2301778 NOREAST | .1040669 .0527816 1.97 0.049 .0006169 .2075169 MIDWEST | -.0163183 .0475077 -0.34 0.731 -.1094317 .076795 WEST | .1232471 .0504032 2.45 0.014 .0244586 .2220356 AGE | -.0753009 .0322667 -2.33 0.020 -.1385425 -.0120593 BLACK | .0016163 .0700154 0.02 0.982 -.1356115 .138844 MALE | .0041276 .0421946 0.10 0.922 -.0785722 .0868275 MARRIED | -.0920324 .0437363 -2.10 0.035 -.1777539 -.006311 SCHOOL | .0216107 .0056617 3.82 0.000 .0105139 .0327074 FAMINC | -.0022357 .0058904 -0.38 0.704 -.0137807 .0093093 EMPLOYED | .0296558 .0739422 0.40 0.688 -.1152683 .1745798 PRIVINS | .227151 .0566744 4.01 0.000 .1160712 .3382307 MEDICAID | .1847926 .0664584 2.78 0.005 .0545365 .3150487 _cons | 1.630983 .2692161 6.06 0.000 1.103329 2.158636 -------------+---------------------------------------------------------------- /lnalpha | -.2959886 .0542084 -.4022352 -.189742 -------------+---------------------------------------------------------------- alpha | .7437959 .04032 .6688234 .8271725 ------------------------------------------------------------------------------ . estimates store H2NB2 . scalar llH2NB2 = e(ll) . scalar kH2NB2 = e(k) . . * Combine two parts: NB1 and NB1 . scalar llHNB1 = llH1NB1 + llH2NB1 . scalar kHNB1 = kH1NB1 + kH2NB1 . scalar AICHNB1 = -2*llHNB1 + 2*kHNB1 . scalar BICHNB1 = -2*llHNB1 + ln(nH)*kHNB1 . . * Combine two parts: NB2 and NB2 . scalar llHNB2 = llH1NB2 + llH2NB2 . scalar kHNB2 = kH1NB2 + kH2NB2 . scalar AICHNB2 = -2*llHNB2 + 2*kHNB2 . scalar BICHNB2 = -2*llHNB2 + ln(nH)*kHNB2 . . * Combine two parts: logit and NB1 . scalar llHNB1log = llH1logit + llH2NB1 . scalar kHNB1log = kH1logit + kH2NB1 . scalar AICHNB1log = -2*llHNB1log + 2*kHNB1log . scalar BICHNB1log = -2*llHNB1log + ln(nH)*kHNB1log . . * Combine two parts: logit and NB2 . scalar llHNB2log = llH1logit + llH2NB2 . scalar kHNB2log = kH1logit + kH2NB2 . scalar AICHNB2log = -2*llHNB2log + 2*kHNB2log . scalar BICHNB2log = -2*llHNB2log + ln(nH)*kHNB2log . . ****** FINITE MIXTURE MODELS - constrained and unconstrained . . **** NB1 Finite Mixtures Models . . * Finite mixtures NB1 - 2 components unconstrained . fmm OFP $XLIST, components(2) mixtureof(negbin1) vce(robust) Fitting Negative Binomial-1 model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Iteration 0: log likelihood = -14552.718 Iteration 1: log likelihood = -12647.886 Iteration 2: log likelihood = -12493.025 Iteration 3: log likelihood = -12492.829 Iteration 4: log likelihood = -12492.829 Iteration 0: log likelihood = -12492.829 Iteration 1: log likelihood = -12301.184 Iteration 2: log likelihood = -12157 Iteration 3: log likelihood = -12156.203 Iteration 4: log likelihood = -12156.202 Fitting 2 component Negative Binomial-1 model: Iteration 0: log pseudolikelihood = -12156.74 (not concave) Iteration 1: log pseudolikelihood = -12155.694 (not concave) Iteration 2: log pseudolikelihood = -12134.293 (not concave) Iteration 3: log pseudolikelihood = -12108.437 (not concave) Iteration 4: log pseudolikelihood = -12100.205 Iteration 5: log pseudolikelihood = -12095.077 Iteration 6: log pseudolikelihood = -12093.661 Iteration 7: log pseudolikelihood = -12092.693 Iteration 8: log pseudolikelihood = -12092.43 Iteration 9: log pseudolikelihood = -12092.429 Iteration 10: log pseudolikelihood = -12092.429 2 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(32) = 805.15 Log pseudolikelihood = -12092.429 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.2290118 .0595272 -3.85 0.000 -.3456829 -.1123407 POORHLTH | .1499097 .058625 2.56 0.011 .0350068 .2648126 NUMCHRON | .1836232 .0145712 12.60 0.000 .1550641 .2121823 ADLDIFF | -.0520085 .0510709 -1.02 0.309 -.1521055 .0480886 NOREAST | .0546492 .0542024 1.01 0.313 -.0515856 .1608839 MIDWEST | .0191861 .045583 0.42 0.674 -.0701549 .1085271 WEST | .0944858 .047379 1.99 0.046 .0016248 .1873469 AGE | .0148273 .0308493 0.48 0.631 -.0456361 .0752908 BLACK | -.1799111 .0898293 -2.00 0.045 -.3559734 -.0038489 MALE | -.1377495 .0363032 -3.79 0.000 -.2089023 -.0665966 MARRIED | .0513625 .037287 1.38 0.168 -.0217187 .1244436 SCHOOL | .0133302 .0067885 1.96 0.050 .0000249 .0266354 FAMINC | .0007834 .0052861 0.15 0.882 -.0095773 .011144 EMPLOYED | -.0807253 .0543835 -1.48 0.138 -.1873149 .0258643 PRIVINS | .3593702 .0802377 4.48 0.000 .2021073 .5166331 MEDICAID | .4204549 .1516158 2.77 0.006 .1232933 .7176165 _cons | .7733975 .2661744 2.91 0.004 .2517052 1.29509 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.8178674 .3848952 -2.12 0.034 -1.572248 -.0634866 POORHLTH | .718358 .3416314 2.10 0.035 .0487726 1.387943 NUMCHRON | .1908478 .0934393 2.04 0.041 .0077101 .3739855 ADLDIFF | .549827 .2893593 1.90 0.057 -.0173069 1.116961 NOREAST | .2279207 .4032265 0.57 0.572 -.5623887 1.01823 MIDWEST | -.0123035 .4114692 -0.03 0.976 -.8187683 .7941612 WEST | .2660744 .2891064 0.92 0.357 -.3005636 .8327125 AGE | -.1334189 .237275 -0.56 0.574 -.5984694 .3316316 BLACK | .2680242 .7090175 0.38 0.705 -1.121625 1.657673 MALE | -.0228589 .1936876 -0.12 0.906 -.4024796 .3567618 MARRIED | -.242328 .1950364 -1.24 0.214 -.6245924 .1399364 SCHOOL | .1023137 .0435288 2.35 0.019 .0169988 .1876287 FAMINC | -.0011579 .0128741 -0.09 0.928 -.0263908 .0240749 EMPLOYED | .5400458 .441916 1.22 0.222 -.3260937 1.406185 PRIVINS | .227208 .6916896 0.33 0.743 -1.128479 1.582895 MEDICAID | -.6163631 1.171503 -0.53 0.599 -2.912467 1.679741 _cons | 1.554799 2.130245 0.73 0.465 -2.620405 5.730003 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.290933 .3660583 6.26 0.000 1.573471 3.008394 /lndelta1 | 1.259071 .059816 21.05 0.000 1.141834 1.376308 /lndelta2 | 2.441911 .4394107 5.56 0.000 1.580682 3.30314 ------------------------------------------------------------------------------ delta1 | 3.522148 .210681 3.132507 3.960255 delta2 | 11.49499 5.05102 4.858268 27.19791 pi1 | .9081233 .0305422 .8282779 .9529519 pi2 | .0918767 .0305422 .0470481 .1717221 ------------------------------------------------------------------------------ . estimates store FM2NB1 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- FM2NB1 | 4406 . -12092.43 37 24258.86 24495.31 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llFM2NB1 = e(ll) . scalar kFM2NB1 = e(rank) . . * Finite mixtures NB1 - 3 components unconstrained . * This has convergence problems - stop at exactly 20 iterations . fmm OFP $XLIST, components(3) mixtureof(negbin1) vce(robust) iter(20) Fitting 3 component Negative Binomial-1 model: Iteration 0: log pseudolikelihood = -12092.432 (not concave) Iteration 1: log pseudolikelihood = -12087.407 (not concave) Iteration 2: log pseudolikelihood = -12085.612 (not concave) Iteration 3: log pseudolikelihood = -12082.804 (not concave) Iteration 4: log pseudolikelihood = -12075.188 (not concave) Iteration 5: log pseudolikelihood = -12069.149 (not concave) Iteration 6: log pseudolikelihood = -12068.09 (not concave) Iteration 7: log pseudolikelihood = -12066.772 (not concave) Iteration 8: log pseudolikelihood = -12065.512 (not concave) Iteration 9: log pseudolikelihood = -12060.52 (not concave) Iteration 10: log pseudolikelihood = -12058.683 (not concave) Iteration 11: log pseudolikelihood = -12058.254 (not concave) Iteration 12: log pseudolikelihood = -12056.618 (not concave) Iteration 13: log pseudolikelihood = -12055.883 (not concave) Iteration 14: log pseudolikelihood = -12054.919 (not concave) Iteration 15: log pseudolikelihood = -12054.383 (not concave) Iteration 16: log pseudolikelihood = -12054.071 (not concave) Iteration 17: log pseudolikelihood = -12053.823 (not concave) Iteration 18: log pseudolikelihood = -12053.742 (not concave) Iteration 19: log pseudolikelihood = -12053.661 (not concave) Iteration 20: log pseudolikelihood = -12050.104 (not concave) convergence not achieved 3 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(48) = 1247.47 Log pseudolikelihood = -12050.104 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.2847297 .0657908 -4.33 0.000 -.4136773 -.1557821 POORHLTH | .2644781 .0529759 4.99 0.000 .1606473 .3683089 NUMCHRON | .1799031 .014409 12.49 0.000 .1516619 .2081442 ADLDIFF | .053308 .0499298 1.07 0.286 -.0445526 .1511686 NOREAST | .1245906 .0505973 2.46 0.014 .0254217 .2237595 MIDWEST | .0493078 .0439044 1.12 0.261 -.0367432 .1353588 WEST | .0729 .0474079 1.54 0.124 -.0200178 .1658179 AGE | .011974 .0300999 0.40 0.691 -.0470208 .0709687 BLACK | -.0585806 .0654226 -0.90 0.371 -.1868066 .0696455 MALE | -.177515 .0380627 -4.66 0.000 -.2521166 -.1029134 MARRIED | .0728448 .0397754 1.83 0.067 -.0051135 .1508031 SCHOOL | .0151465 .0069541 2.18 0.029 .0015167 .0287764 FAMINC | -.0004394 .0057157 -0.08 0.939 -.0116419 .0107632 EMPLOYED | -.0286309 .0637433 -0.45 0.653 -.1535655 .0963037 PRIVINS | .3459514 .0595861 5.81 0.000 .2291648 .4627381 MEDICAID | .4240416 .0713109 5.95 0.000 .2842748 .5638083 _cons | .7426774 .2777734 2.67 0.008 .1982515 1.287103 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.9974141 .4282742 -2.33 0.020 -1.836816 -.1580121 POORHLTH | .5846596 .2651793 2.20 0.027 .0649177 1.104402 NUMCHRON | .1769607 .1041399 1.70 0.089 -.0271496 .3810711 ADLDIFF | .448495 .2080451 2.16 0.031 .0407342 .8562558 NOREAST | .2245126 .2605289 0.86 0.389 -.2861146 .7351398 MIDWEST | -.0505727 .3029227 -0.17 0.867 -.6442902 .5431448 WEST | .1484823 .2189396 0.68 0.498 -.2806314 .577596 AGE | -.1251731 .1927655 -0.65 0.516 -.5029865 .2526404 BLACK | .2637915 .358101 0.74 0.461 -.4380735 .9656565 MALE | .0554094 .194355 0.29 0.776 -.3255193 .4363381 MARRIED | -.2075961 .1736381 -1.20 0.232 -.5479205 .1327282 SCHOOL | .099339 .0401715 2.47 0.013 .0206043 .1780737 FAMINC | -.0042642 .0126222 -0.34 0.735 -.0290033 .0204749 EMPLOYED | .607846 .2500944 2.43 0.015 .11767 1.098022 PRIVINS | .3530138 .4199824 0.84 0.401 -.4701366 1.176164 MEDICAID | -.1285387 .3579497 -0.36 0.720 -.8301073 .5730299 _cons | 1.676785 2.157238 0.78 0.437 -2.551324 5.904895 -------------+---------------------------------------------------------------- component3 | EXCLHLTH | .3723387 .2164584 1.72 0.085 -.051912 .7965894 POORHLTH | -2.194719 .5271828 -4.16 0.000 -3.227978 -1.16146 NUMCHRON | .3508214 .0777601 4.51 0.000 .1984144 .5032283 ADLDIFF | -1.355868 .3826845 -3.54 0.000 -2.105916 -.6058207 NOREAST | -.5435457 .2149249 -2.53 0.011 -.9647908 -.1223006 MIDWEST | -.2251766 .2171605 -1.04 0.300 -.6508033 .20045 WEST | .4840844 .1972072 2.45 0.014 .0975655 .8706033 AGE | .0533227 .1025373 0.52 0.603 -.1476466 .2542921 BLACK | -3.25453 .7336345 -4.44 0.000 -4.692427 -1.816633 MALE | .3658342 .1861978 1.96 0.049 .0008932 .7307752 MARRIED | -.4666917 .2716674 -1.72 0.086 -.99915 .0657665 SCHOOL | -.004687 .0201037 -0.23 0.816 -.0440896 .0347155 FAMINC | .0136748 .0086725 1.58 0.115 -.0033229 .0306725 EMPLOYED | -.6308724 .3449775 -1.83 0.067 -1.307016 .045271 PRIVINS | .1938224 .1688086 1.15 0.251 -.1370363 .5246811 MEDICAID | -2.297179 .6981917 -3.29 0.001 -3.66561 -.9287486 _cons | .743128 .76738 0.97 0.333 -.7609092 2.247165 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.216945 .1806036 12.28 0.000 1.862969 2.570922 /imlogitpi2 | -.2940686 .4102834 -0.72 0.474 -1.098209 .5100721 /lndelta1 | 1.233421 .0552554 22.32 0.000 1.125123 1.34172 /lndelta2 | 2.347295 .3109255 7.55 0.000 1.737892 2.956698 /lndelta3 | -29.17698 . . . . . ------------------------------------------------------------------------------ Warning: convergence not achieved delta1 | 3.432954 .1896894 3.080594 3.825617 delta2 | 10.45725 3.251425 5.685348 19.23436 delta3 | 2.13e-13 . . . pi1 | .8402463 .027901 .7777619 .8876992 pi2 | .0682161 .0248135 .0329408 .1359559 pi3 | .0915376 .0149043 .0623258 .1207495 ------------------------------------------------------------------------------ . estimates store FM3NB1 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- FM3NB1 | 4406 . -12050.1 55 24210.21 24561.7 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llFM3NB1 = e(ll) . scalar kFM3NB1 = e(rank) . . * Constrained Finite mixtures NB1 - 2 components only intercept varies . local i 1 . foreach var of varlist $XLIST { 2. constraint `i' [component1]`var' = [component2]`var' 3. local i = `i' + 1 4. } . fmm OFP $XLIST, components(2) mixtureof(negbin1) constraints(1/`i') Fitting Negative Binomial-1 model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Iteration 0: log likelihood = -14552.718 Iteration 1: log likelihood = -12647.886 Iteration 2: log likelihood = -12493.025 Iteration 3: log likelihood = -12492.829 Iteration 4: log likelihood = -12492.829 Iteration 0: log likelihood = -12492.829 Iteration 1: log likelihood = -12301.184 Iteration 2: log likelihood = -12157 Iteration 3: log likelihood = -12156.203 Iteration 4: log likelihood = -12156.202 Fitting 2 component Negative Binomial-1 model: Iteration 0: log likelihood = -12156.74 (not concave) Iteration 1: log likelihood = -12154.44 (not concave) Iteration 2: log likelihood = -12133.932 (not concave) Iteration 3: log likelihood = -12117.481 Iteration 4: log likelihood = -12101.87 Iteration 5: log likelihood = -12098.326 Iteration 6: log likelihood = -12097.883 Iteration 7: log likelihood = -12097.851 Iteration 8: log likelihood = -12097.85 2 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(16) = 787.57 Log likelihood = -12097.85 Prob > chi2 = 0.0000 ( 1) [component1]EXCLHLTH - [component2]EXCLHLTH = 0 ( 2) [component1]POORHLTH - [component2]POORHLTH = 0 ( 3) [component1]NUMCHRON - [component2]NUMCHRON = 0 ( 4) [component1]ADLDIFF - [component2]ADLDIFF = 0 ( 5) [component1]NOREAST - [component2]NOREAST = 0 ( 6) [component1]MIDWEST - [component2]MIDWEST = 0 ( 7) [component1]WEST - [component2]WEST = 0 ( 8) [component1]AGE - [component2]AGE = 0 ( 9) [component1]BLACK - [component2]BLACK = 0 (10) [component1]MALE - [component2]MALE = 0 (11) [component1]MARRIED - [component2]MARRIED = 0 (12) [component1]SCHOOL - [component2]SCHOOL = 0 (13) [component1]FAMINC - [component2]FAMINC = 0 (14) [component1]EMPLOYED - [component2]EMPLOYED = 0 (15) [component1]PRIVINS - [component2]PRIVINS = 0 (16) [component1]MEDICAID - [component2]MEDICAID = 0 ------------------------------------------------------------------------------ OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.281483 .0570791 -4.93 0.000 -.393356 -.16961 POORHLTH | .2108138 .041379 5.09 0.000 .1297124 .2919152 NUMCHRON | .1804335 .0096188 18.76 0.000 .161581 .1992861 ADLDIFF | .0130707 .0364905 0.36 0.720 -.0584493 .0845907 NOREAST | .0758954 .0377644 2.01 0.044 .0018786 .1499122 MIDWEST | .0104492 .0343951 0.30 0.761 -.0569639 .0778623 WEST | .1054022 .0381062 2.77 0.006 .0307154 .180089 AGE | .0005364 .0226922 0.02 0.981 -.0439395 .0450123 BLACK | -.1273596 .0485914 -2.62 0.009 -.222597 -.0321223 MALE | -.1253071 .0296905 -4.22 0.000 -.1834995 -.0671148 MARRIED | .0187 .0308608 0.61 0.545 -.0417861 .0791862 SCHOOL | .0207761 .0041285 5.03 0.000 .0126843 .0288679 FAMINC | .0002684 .0046869 0.06 0.954 -.0089176 .0094545 EMPLOYED | -.0347508 .0473112 -0.73 0.463 -.1274789 .0579774 PRIVINS | .3281347 .0411701 7.97 0.000 .2474428 .4088265 MEDICAID | .3397552 .0534812 6.35 0.000 .234934 .4445764 _cons | .8875917 .1834918 4.84 0.000 .5279544 1.247229 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.281483 .0570791 -4.93 0.000 -.393356 -.16961 POORHLTH | .2108138 .041379 5.09 0.000 .1297124 .2919152 NUMCHRON | .1804335 .0096188 18.76 0.000 .161581 .1992861 ADLDIFF | .0130707 .0364905 0.36 0.720 -.0584493 .0845907 NOREAST | .0758954 .0377644 2.01 0.044 .0018786 .1499122 MIDWEST | .0104492 .0343951 0.30 0.761 -.0569639 .0778623 WEST | .1054022 .0381062 2.77 0.006 .0307154 .180089 AGE | .0005364 .0226922 0.02 0.981 -.0439395 .0450123 BLACK | -.1273596 .0485914 -2.62 0.009 -.222597 -.0321223 MALE | -.1253071 .0296905 -4.22 0.000 -.1834995 -.0671148 MARRIED | .0187 .0308608 0.61 0.545 -.0417861 .0791862 SCHOOL | .0207761 .0041285 5.03 0.000 .0126843 .0288679 FAMINC | .0002684 .0046869 0.06 0.954 -.0089176 .0094545 EMPLOYED | -.0347508 .0473112 -0.73 0.463 -.1274789 .0579774 PRIVINS | .3281347 .0411701 7.97 0.000 .2474428 .4088265 MEDICAID | .3397552 .0534812 6.35 0.000 .234934 .4445764 _cons | 1.071645 .2005703 5.34 0.000 .6785343 1.464756 -------------+---------------------------------------------------------------- /imlogitpi1 | 1.531575 .307835 4.98 0.000 .9282298 2.134921 /lndelta1 | 1.075926 .0859428 12.52 0.000 .9074815 1.244371 /lndelta2 | 2.955879 .2237016 13.21 0.000 2.517432 3.394326 ------------------------------------------------------------------------------ delta1 | 2.932708 .2520452 2.478074 3.470751 delta2 | 19.21861 4.299233 12.39672 29.79456 pi1 | .8222367 .0449942 .716716 .8942513 pi2 | .1777633 .0449942 .1057487 .283284 ------------------------------------------------------------------------------ . estimates store CFM2NB1 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- CFM2NB1 | 4406 . -12097.85 21 24237.7 24371.91 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llCFM2NB1 = e(ll) . * e(rank) gives number of parameters (e(k)) minus number of constraints . scalar kCFM2NB1 = e(rank) . . * Constrained Finite mixtures NB1 - 3 components only intercept varies . * This needs to directly follow the constrained 2 components case . * Note the constraints 1=2 are remembered so only need to add constraints that 2=3 . foreach var of varlist $XLIST { 2. constraint `i' [component2]`var' = [component3]`var' 3. local i = `i' + 1 4. } . * This ultimately converges . fmm OFP $XLIST, components(3) mixtureof(negbin1) constraints(1/`i') Fitting 3 component Negative Binomial-1 model: Iteration 0: log likelihood = -12097.86 (not concave) Iteration 1: log likelihood = -12097.854 (not concave) Iteration 2: log likelihood = -12097.853 (not concave) Iteration 3: log likelihood = -12097.849 (not concave) Iteration 4: log likelihood = -12097.849 (not concave) Iteration 5: log likelihood = -12097.848 (not concave) Iteration 6: log likelihood = -12097.842 (not concave) Iteration 7: log likelihood = -12097.836 (not concave) Iteration 8: log likelihood = -12097.828 (not concave) Iteration 9: log likelihood = -12097.814 (not concave) Iteration 10: log likelihood = -12097.798 (not concave) Iteration 11: log likelihood = -12097.791 (not concave) Iteration 12: log likelihood = -12097.776 (not concave) Iteration 13: log likelihood = -12097.769 (not concave) Iteration 14: log likelihood = -12097.758 (not concave) Iteration 15: log likelihood = -12097.751 (not concave) Iteration 16: log likelihood = -12097.748 (not concave) Iteration 17: log likelihood = -12097.746 (not concave) Iteration 18: log likelihood = -12097.744 (not concave) Iteration 19: log likelihood = -12097.742 (not concave) Iteration 20: log likelihood = -12097.739 (not concave) Iteration 21: log likelihood = -12097.737 (not concave) Iteration 22: log likelihood = -12097.735 (not concave) Iteration 23: log likelihood = -12097.734 (not concave) Iteration 24: log likelihood = -12097.732 (not concave) Iteration 25: log likelihood = -12097.73 (not concave) Iteration 26: log likelihood = -12097.729 (not concave) Iteration 27: log likelihood = -12097.727 (not concave) Iteration 28: log likelihood = -12097.725 (not concave) Iteration 29: log likelihood = -12097.724 (not concave) Iteration 30: log likelihood = -12097.722 (not concave) Iteration 31: log likelihood = -12097.72 (not concave) Iteration 32: log likelihood = -12097.718 (not concave) Iteration 33: log likelihood = -12097.714 (not concave) Iteration 34: log likelihood = -12097.688 (not concave) Iteration 35: log likelihood = -12097.636 (not concave) Iteration 36: log likelihood = -12097.615 (not concave) Iteration 37: log likelihood = -12097.593 (not concave) Iteration 38: log likelihood = -12097.468 Iteration 39: log likelihood = -12097.122 Iteration 40: log likelihood = -12096.439 Iteration 41: log likelihood = -12096.131 Iteration 42: log likelihood = -12095.88 (not concave) Iteration 43: log likelihood = -12095.867 Iteration 44: log likelihood = -12095.717 (not concave) Iteration 45: log likelihood = -12095.659 (not concave) Iteration 46: log likelihood = -12095.648 (not concave) Iteration 47: log likelihood = -12095.638 (not concave) Iteration 48: log likelihood = -12095.63 Iteration 49: log likelihood = -12095.519 Iteration 50: log likelihood = -12095.484 Iteration 51: log likelihood = -12095.483 3 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(16) = 641.28 Log likelihood = -12095.483 Prob > chi2 = 0.0000 ( 1) [component1]EXCLHLTH - [component2]EXCLHLTH = 0 ( 2) [component1]POORHLTH - [component2]POORHLTH = 0 ( 3) [component1]NUMCHRON - [component2]NUMCHRON = 0 ( 4) [component1]ADLDIFF - [component2]ADLDIFF = 0 ( 5) [component1]NOREAST - [component2]NOREAST = 0 ( 6) [component1]MIDWEST - [component2]MIDWEST = 0 ( 7) [component1]WEST - [component2]WEST = 0 ( 8) [component1]AGE - [component2]AGE = 0 ( 9) [component1]BLACK - [component2]BLACK = 0 (10) [component1]MALE - [component2]MALE = 0 (11) [component1]MARRIED - [component2]MARRIED = 0 (12) [component1]SCHOOL - [component2]SCHOOL = 0 (13) [component1]FAMINC - [component2]FAMINC = 0 (14) [component1]EMPLOYED - [component2]EMPLOYED = 0 (15) [component1]PRIVINS - [component2]PRIVINS = 0 (16) [component1]MEDICAID - [component2]MEDICAID = 0 (17) [component2]EXCLHLTH - [component3]EXCLHLTH = 0 (18) [component2]POORHLTH - [component3]POORHLTH = 0 (19) [component2]NUMCHRON - [component3]NUMCHRON = 0 (20) [component2]ADLDIFF - [component3]ADLDIFF = 0 (21) [component2]NOREAST - [component3]NOREAST = 0 (22) [component2]MIDWEST - [component3]MIDWEST = 0 (23) [component2]WEST - [component3]WEST = 0 (24) [component2]AGE - [component3]AGE = 0 (25) [component2]BLACK - [component3]BLACK = 0 (26) [component2]MALE - [component3]MALE = 0 (27) [component2]MARRIED - [component3]MARRIED = 0 (28) [component2]SCHOOL - [component3]SCHOOL = 0 (29) [component2]FAMINC - [component3]FAMINC = 0 (30) [component2]EMPLOYED - [component3]EMPLOYED = 0 (31) [component2]PRIVINS - [component3]PRIVINS = 0 (32) [component2]MEDICAID - [component3]MEDICAID = 0 ------------------------------------------------------------------------------ OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.2859587 .0584868 -4.89 0.000 -.4005907 -.1713268 POORHLTH | .2244097 .0445029 5.04 0.000 .1371855 .3116338 NUMCHRON | .1873671 .0102801 18.23 0.000 .1672185 .2075157 ADLDIFF | .020037 .0376594 0.53 0.595 -.0537741 .0938481 NOREAST | .0826042 .0392089 2.11 0.035 .0057561 .1594523 MIDWEST | .0108504 .0352983 0.31 0.759 -.0583331 .0800338 WEST | .1035372 .0397691 2.60 0.009 .0255912 .1814832 AGE | .001084 .0235608 0.05 0.963 -.0450943 .0472623 BLACK | -.1307365 .0502246 -2.60 0.009 -.2291749 -.032298 MALE | -.1271959 .030551 -4.16 0.000 -.1870747 -.0673171 MARRIED | .0192235 .0319836 0.60 0.548 -.0434633 .0819103 SCHOOL | .0222097 .0043064 5.16 0.000 .0137693 .0306501 FAMINC | -.0000323 .0048077 -0.01 0.995 -.0094552 .0093907 EMPLOYED | -.0292248 .0482797 -0.61 0.545 -.1238513 .0654016 PRIVINS | .3366376 .0431284 7.81 0.000 .2521076 .4211677 MEDICAID | .3541806 .0565374 6.26 0.000 .2433694 .4649918 _cons | .8267899 .1920252 4.31 0.000 .4504275 1.203152 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.2859587 .0584868 -4.89 0.000 -.4005907 -.1713268 POORHLTH | .2244097 .0445029 5.04 0.000 .1371855 .3116338 NUMCHRON | .1873671 .0102801 18.23 0.000 .1672185 .2075157 ADLDIFF | .020037 .0376594 0.53 0.595 -.0537741 .0938481 NOREAST | .0826042 .0392089 2.11 0.035 .0057561 .1594523 MIDWEST | .0108504 .0352983 0.31 0.759 -.0583331 .0800338 WEST | .1035372 .0397691 2.60 0.009 .0255912 .1814832 AGE | .001084 .0235608 0.05 0.963 -.0450943 .0472623 BLACK | -.1307365 .0502246 -2.60 0.009 -.2291749 -.032298 MALE | -.1271959 .030551 -4.16 0.000 -.1870747 -.0673171 MARRIED | .0192235 .0319836 0.60 0.548 -.0434633 .0819103 SCHOOL | .0222097 .0043064 5.16 0.000 .0137693 .0306501 FAMINC | -.0000323 .0048077 -0.01 0.995 -.0094552 .0093907 EMPLOYED | -.0292248 .0482797 -0.61 0.545 -.1238513 .0654016 PRIVINS | .3366376 .0431284 7.81 0.000 .2521076 .4211677 MEDICAID | .3541806 .0565374 6.26 0.000 .2433694 .4649918 _cons | -.6062152 1.018715 -0.60 0.552 -2.602861 1.39043 -------------+---------------------------------------------------------------- component3 | EXCLHLTH | -.2859587 .0584868 -4.89 0.000 -.4005907 -.1713268 POORHLTH | .2244097 .0445029 5.04 0.000 .1371855 .3116338 NUMCHRON | .1873671 .0102801 18.23 0.000 .1672185 .2075157 ADLDIFF | .020037 .0376594 0.53 0.595 -.0537741 .0938481 NOREAST | .0826042 .0392089 2.11 0.035 .0057561 .1594523 MIDWEST | .0108504 .0352983 0.31 0.759 -.0583331 .0800338 WEST | .1035372 .0397691 2.60 0.009 .0255912 .1814832 AGE | .001084 .0235608 0.05 0.963 -.0450943 .0472623 BLACK | -.1307365 .0502246 -2.60 0.009 -.2291749 -.032298 MALE | -.1271959 .030551 -4.16 0.000 -.1870747 -.0673171 MARRIED | .0192235 .0319836 0.60 0.548 -.0434633 .0819103 SCHOOL | .0222097 .0043064 5.16 0.000 .0137693 .0306501 FAMINC | -.0000323 .0048077 -0.01 0.995 -.0094552 .0093907 EMPLOYED | -.0292248 .0482797 -0.61 0.545 -.1238513 .0654016 PRIVINS | .3366376 .0431284 7.81 0.000 .2521076 .4211677 MEDICAID | .3541806 .0565374 6.26 0.000 .2433694 .4649918 _cons | 1.972971 .5695372 3.46 0.001 .8566988 3.089244 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.870311 .9256407 3.10 0.002 1.056088 4.684533 /imlogitpi2 | .3373018 1.114322 0.30 0.762 -1.84673 2.521333 /lndelta1 | 1.138816 .0959347 11.87 0.000 .950787 1.326844 /lndelta2 | 1.675134 .9262184 1.81 0.071 -.1402202 3.490489 /lndelta3 | 2.618106 .3613286 7.25 0.000 1.909915 3.326297 ------------------------------------------------------------------------------ delta1 | 3.123067 .2996107 2.587745 3.76913 delta2 | 5.339513 4.945555 .8691668 32.80199 delta3 | 13.70973 4.953718 6.752513 27.83507 pi1 | .8802034 .0704887 .6646643 .9645851 pi2 | .0699055 .0527626 .015088 .2694067 pi3 | .0498911 .0434282 -.0352265 .1350087 ------------------------------------------------------------------------------ . estimates store CFM3NB1 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- CFM3NB1 | 4406 . -12095.48 24 24238.97 24392.34 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llCFM3NB1 = e(ll) . * e(rank) gives number of parameters (e(k)) minus number of constraints . scalar kCFM3NB1 = e(rank) . . **** NB2 Finite Mixtures Models . . * Finite mixtures NB2 - 2 components unconstrained . fmm OFP $XLIST, components(2) mixtureof(negbin2) vce(robust) Fitting Negative Binomial-2 model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Iteration 0: log likelihood = -12492.848 Iteration 1: log likelihood = -12492.829 Iteration 2: log likelihood = -12492.829 Iteration 0: log likelihood = -12234.27 Iteration 1: log likelihood = -12202.779 Iteration 2: log likelihood = -12202.168 Iteration 3: log likelihood = -12202.168 Fitting 2 component Negative Binomial-2 model: Iteration 0: log pseudolikelihood = -12202.32 (not concave) Iteration 1: log pseudolikelihood = -12198.906 (not concave) Iteration 2: log pseudolikelihood = -12159.509 (not concave) Iteration 3: log pseudolikelihood = -12150.843 (not concave) Iteration 4: log pseudolikelihood = -12146.777 (not concave) Iteration 5: log pseudolikelihood = -12145.177 (not concave) Iteration 6: log pseudolikelihood = -12144.146 Iteration 7: log pseudolikelihood = -12141.278 Iteration 8: log pseudolikelihood = -12140.438 Iteration 9: log pseudolikelihood = -12139.364 Iteration 10: log pseudolikelihood = -12139.312 Iteration 11: log pseudolikelihood = -12139.311 2 component Negative Binomial-2 regression Number of obs = 4406 Wald chi2(32) = 648.98 Log pseudolikelihood = -12139.311 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.3426896 .1047837 -3.27 0.001 -.548062 -.1373173 POORHLTH | .3005766 .0673126 4.47 0.000 .1686463 .4325069 NUMCHRON | .1959699 .0282356 6.94 0.000 .1406292 .2513106 ADLDIFF | .0244121 .0599872 0.41 0.684 -.0931606 .1419848 NOREAST | .0883721 .0646314 1.37 0.172 -.0383031 .2150472 MIDWEST | -.0161452 .0549346 -0.29 0.769 -.1238149 .0915246 WEST | .1293117 .0633766 2.04 0.041 .005096 .2535275 AGE | .0226357 .0451345 0.50 0.616 -.0658264 .1110978 BLACK | -.1354242 .1185305 -1.14 0.253 -.3677398 .0968914 MALE | -.1414463 .0656796 -2.15 0.031 -.270176 -.0127166 MARRIED | .0199709 .0590666 0.34 0.735 -.0957976 .1357394 SCHOOL | .0173049 .0113197 1.53 0.126 -.0048813 .0394911 FAMINC | .0037294 .0075404 0.49 0.621 -.0110495 .0185082 EMPLOYED | -.0954093 .086701 -1.10 0.271 -.2653401 .0745215 PRIVINS | .3976839 .1137834 3.50 0.000 .1746726 .6206952 MEDICAID | .4758504 .1411235 3.37 0.001 .1992535 .7524474 _cons | .6283805 .4994702 1.26 0.208 -.3505631 1.607324 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.4649237 .2834436 -1.64 0.101 -1.020463 .0906155 POORHLTH | .3486711 .1597575 2.18 0.029 .0355522 .66179 NUMCHRON | .1962416 .0696944 2.82 0.005 .059643 .3328402 ADLDIFF | .2066445 .1537203 1.34 0.179 -.0946418 .5079308 NOREAST | .19344 .1886035 1.03 0.305 -.1762161 .5630961 MIDWEST | .0576896 .1404966 0.41 0.681 -.2176786 .3330578 WEST | .1708078 .1433771 1.19 0.234 -.1102061 .4518218 AGE | -.169431 .1244261 -1.36 0.173 -.4133016 .0744397 BLACK | .0838284 .2329012 0.36 0.719 -.3726496 .5403063 MALE | .0744306 .1538221 0.48 0.628 -.2270552 .3759164 MARRIED | -.1727413 .1552317 -1.11 0.266 -.4769898 .1315071 SCHOOL | .0471951 .0265373 1.78 0.075 -.004817 .0992072 FAMINC | -.0120272 .0151732 -0.79 0.428 -.041766 .0177117 EMPLOYED | .240546 .1721045 1.40 0.162 -.0967726 .5778646 PRIVINS | .2476738 .2061784 1.20 0.230 -.1564283 .651776 MEDICAID | -.2692255 .2715047 -0.99 0.321 -.8013649 .2629139 _cons | 2.022578 1.131613 1.79 0.074 -.1953437 4.240499 -------------+---------------------------------------------------------------- /imlogitpi1 | .9963767 .5049348 1.97 0.048 .0067227 1.986031 /lnalpha1 | -.7459393 .1657751 -4.50 0.000 -1.070853 -.421026 /lnalpha2 | .6905924 .3298288 2.09 0.036 .0441398 1.337045 ------------------------------------------------------------------------------ alpha1 | .4742886 .0786253 .3427162 .656373 alpha2 | 1.994897 .6579744 1.045128 3.807775 pi1 | .7303456 .0994423 .5016807 .8793226 pi2 | .2696544 .0994423 .1206774 .4983193 ------------------------------------------------------------------------------ . estimates store FM2NB2 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- FM2NB2 | 4406 . -12139.31 37 24352.62 24589.08 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llFM2NB2 = e(ll) . scalar kFM2NB2 = e(k) . . * Finite mixtures NB2 - 3 components unconstrained . * This convergence after about 35 iterations . fmm OFP $XLIST, components(3) mixtureof(negbin2) vce(robust) iter(30) Fitting 3 component Negative Binomial-2 model: Iteration 0: log pseudolikelihood = -12139.314 (not concave) Iteration 1: log pseudolikelihood = -12139.208 (not concave) Iteration 2: log pseudolikelihood = -12139.17 (not concave) Iteration 3: log pseudolikelihood = -12132.621 (not concave) Iteration 4: log pseudolikelihood = -12127.701 (not concave) Iteration 5: log pseudolikelihood = -12123.302 (not concave) Iteration 6: log pseudolikelihood = -12121.701 (not concave) Iteration 7: log pseudolikelihood = -12117.97 (not concave) Iteration 8: log pseudolikelihood = -12113.651 (not concave) Iteration 9: log pseudolikelihood = -12112.276 (not concave) Iteration 10: log pseudolikelihood = -12112.082 (not concave) Iteration 11: log pseudolikelihood = -12110.774 (not concave) Iteration 12: log pseudolikelihood = -12110.488 (not concave) Iteration 13: log pseudolikelihood = -12110.295 (not concave) Iteration 14: log pseudolikelihood = -12110.099 (not concave) Iteration 15: log pseudolikelihood = -12109.161 (not concave) Iteration 16: log pseudolikelihood = -12108.691 (not concave) Iteration 17: log pseudolikelihood = -12107.687 (not concave) Iteration 18: log pseudolikelihood = -12106.202 (not concave) Iteration 19: log pseudolikelihood = -12105.49 (not concave) Iteration 20: log pseudolikelihood = -12104.647 (not concave) Iteration 21: log pseudolikelihood = -12103.392 (not concave) Iteration 22: log pseudolikelihood = -12102.167 (not concave) Iteration 23: log pseudolikelihood = -12101.143 Iteration 24: log pseudolikelihood = -12100.186 Iteration 25: log pseudolikelihood = -12092.703 (not concave) Iteration 26: log pseudolikelihood = -12086.945 (not concave) Iteration 27: log pseudolikelihood = -12086.223 (not concave) Iteration 28: log pseudolikelihood = -12085.366 (not concave) Iteration 29: log pseudolikelihood = -12084.429 Iteration 30: log pseudolikelihood = -12080.305 convergence not achieved 3 component Negative Binomial-2 regression Number of obs = 4406 Wald chi2(48) = 631.10 Log pseudolikelihood = -12080.305 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.3069728 .1201853 -2.55 0.011 -.5425316 -.0714139 POORHLTH | .2112318 .1337996 1.58 0.114 -.0510107 .4734743 NUMCHRON | .3152104 .0632571 4.98 0.000 .1912287 .4391921 ADLDIFF | -.0273817 .1061207 -0.26 0.796 -.2353745 .1806111 NOREAST | .0785365 .0956965 0.82 0.412 -.1090252 .2660982 MIDWEST | .0238574 .0867542 0.28 0.783 -.1461777 .1938925 WEST | .0403989 .0947387 0.43 0.670 -.1452856 .2260834 AGE | .0703012 .0662799 1.06 0.289 -.0596051 .2002074 BLACK | .0710501 .1477301 0.48 0.631 -.2184956 .3605958 MALE | -.2198397 .0862113 -2.55 0.011 -.3888107 -.0508688 MARRIED | .12712 .0990002 1.28 0.199 -.0669169 .321157 SCHOOL | .0328169 .0144766 2.27 0.023 .0044433 .0611905 FAMINC | -.001271 .0132979 -0.10 0.924 -.0273344 .0247924 EMPLOYED | -.0439764 .1123906 -0.39 0.696 -.2642579 .1763051 PRIVINS | .5692395 .1735835 3.28 0.001 .2290222 .9094569 MEDICAID | .7139406 .1979373 3.61 0.000 .3259906 1.101891 _cons | -.5777845 .8499702 -0.68 0.497 -2.243695 1.088126 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.4420629 .4146846 -1.07 0.286 -1.25483 .370704 POORHLTH | .1122814 .2588186 0.43 0.664 -.3949938 .6195565 NUMCHRON | .3232806 .1058804 3.05 0.002 .1157587 .5308024 ADLDIFF | .3661313 .1842962 1.99 0.047 .0049174 .7273453 NOREAST | .2096477 .2177568 0.96 0.336 -.2171479 .6364432 MIDWEST | -.1872171 .1960387 -0.96 0.340 -.5714458 .1970116 WEST | .1783576 .200998 0.89 0.375 -.2155913 .5723065 AGE | -.4451608 .1650422 -2.70 0.007 -.7686377 -.121684 BLACK | -2.834763 .8827678 -3.21 0.001 -4.564956 -1.104569 MALE | -.0783003 .2084911 -0.38 0.707 -.4869354 .3303347 MARRIED | -.240057 .210552 -1.14 0.254 -.6527313 .1726173 SCHOOL | .0665267 .0301083 2.21 0.027 .0075155 .1255378 FAMINC | -.003118 .0190446 -0.16 0.870 -.0404446 .0342087 EMPLOYED | .3395326 .2187126 1.55 0.121 -.0891362 .7682014 PRIVINS | .3006408 .3756528 0.80 0.424 -.4356252 1.036907 MEDICAID | -.802673 .4801247 -1.67 0.095 -1.7437 .138354 _cons | 3.728895 1.692473 2.20 0.028 .4117091 7.046082 -------------+---------------------------------------------------------------- component3 | EXCLHLTH | -.3890602 .1174845 -3.31 0.001 -.6193256 -.1587949 POORHLTH | .3818311 .0954857 4.00 0.000 .1946825 .5689797 NUMCHRON | .0091595 .0426411 0.21 0.830 -.0744156 .0927347 ADLDIFF | .0399851 .080342 0.50 0.619 -.1174822 .1974525 NOREAST | .1008982 .0872597 1.16 0.248 -.0701277 .271924 MIDWEST | .060597 .0865619 0.70 0.484 -.1090612 .2302552 WEST | .2029805 .0866995 2.34 0.019 .0330526 .3729083 AGE | .0229968 .0558171 0.41 0.680 -.0864027 .1323963 BLACK | .1982031 .1597422 1.24 0.215 -.1148857 .511292 MALE | .049132 .083003 0.59 0.554 -.1135508 .2118148 MARRIED | -.1204505 .0699406 -1.72 0.085 -.2575315 .0166305 SCHOOL | .005898 .0112979 0.52 0.602 -.0162455 .0280415 FAMINC | .001406 .0194766 0.07 0.942 -.0367675 .0395795 EMPLOYED | -.110756 .1173202 -0.94 0.345 -.3406994 .1191874 PRIVINS | .1458273 .0846204 1.72 0.085 -.0200256 .3116802 MEDICAID | .1005101 .0912081 1.10 0.270 -.0782544 .2792747 _cons | 1.719513 .3856617 4.46 0.000 .9636298 2.475396 -------------+---------------------------------------------------------------- /imlogitpi1 | .7364091 .4181539 1.76 0.078 -.0831575 1.555976 /imlogitpi2 | -.4576738 .5716087 -0.80 0.423 -1.578006 .6626586 /lnalpha1 | -.8616757 .3185856 -2.70 0.007 -1.486092 -.2372594 /lnalpha2 | .7232871 .2710878 2.67 0.008 .1919648 1.254609 /lnalpha3 | -1.402518 .1821059 -7.70 0.000 -1.759439 -1.045597 ------------------------------------------------------------------------------ Warning: convergence not achieved alpha1 | .4224536 .1345876 .2262552 .7887866 alpha2 | 2.061197 .5587655 1.211628 3.506468 alpha3 | .2459768 .0447938 .1721414 .3514819 pi1 | .5612264 .0718498 .4192809 .6938133 pi2 | .1700413 .0572417 .0846872 .3120899 pi3 | .2687322 .084426 .1032602 .4342042 ------------------------------------------------------------------------------ . estimates store FM3NB2 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- FM3NB2 | 4406 . -12080.31 56 24272.61 24630.49 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llFM3NB2 = e(ll) . scalar kFM3NB2 = e(k) . . * Constrained Finite mixtures NB2 - 2 components only intercept varies . local i 1 . foreach var of varlist $XLIST { 2. constraint `i' [component1]`var' = [component2]`var' 3. local i = `i' + 1 4. } . fmm OFP $XLIST, components(2) mixtureof(negbin2) constraints(1/`i') Fitting Negative Binomial-2 model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Iteration 0: log likelihood = -12492.848 Iteration 1: log likelihood = -12492.829 Iteration 2: log likelihood = -12492.829 Iteration 0: log likelihood = -12234.27 Iteration 1: log likelihood = -12202.779 Iteration 2: log likelihood = -12202.168 Iteration 3: log likelihood = -12202.168 Fitting 2 component Negative Binomial-2 model: (note: constraint number 17 caused error r(303)) Iteration 0: log likelihood = -12202.32 (not concave) Iteration 1: log likelihood = -12200.226 (not concave) Iteration 2: log likelihood = -12161.598 (not concave) Iteration 3: log likelihood = -12152.604 Iteration 4: log likelihood = -12149.699 Iteration 5: log likelihood = -12148.819 Iteration 6: log likelihood = -12148.789 Iteration 7: log likelihood = -12148.789 2 component Negative Binomial-2 regression Number of obs = 4406 Wald chi2(16) = 575.44 Log likelihood = -12148.789 Prob > chi2 = 0.0000 ( 1) [component1]EXCLHLTH - [component2]EXCLHLTH = 0 ( 2) [component1]POORHLTH - [component2]POORHLTH = 0 ( 3) [component1]NUMCHRON - [component2]NUMCHRON = 0 ( 4) [component1]ADLDIFF - [component2]ADLDIFF = 0 ( 5) [component1]NOREAST - [component2]NOREAST = 0 ( 6) [component1]MIDWEST - [component2]MIDWEST = 0 ( 7) [component1]WEST - [component2]WEST = 0 ( 8) [component1]AGE - [component2]AGE = 0 ( 9) [component1]BLACK - [component2]BLACK = 0 (10) [component1]MALE - [component2]MALE = 0 (11) [component1]MARRIED - [component2]MARRIED = 0 (12) [component1]SCHOOL - [component2]SCHOOL = 0 (13) [component1]FAMINC - [component2]FAMINC = 0 (14) [component1]EMPLOYED - [component2]EMPLOYED = 0 (15) [component1]PRIVINS - [component2]PRIVINS = 0 (16) [component1]MEDICAID - [component2]MEDICAID = 0 ------------------------------------------------------------------------------ OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.3743761 .0623097 -6.01 0.000 -.496501 -.2522513 POORHLTH | .3126258 .0496397 6.30 0.000 .2153338 .4099179 NUMCHRON | .1935047 .0126581 15.29 0.000 .1686953 .218314 ADLDIFF | .0690818 .0428187 1.61 0.107 -.0148413 .1530049 NOREAST | .0924278 .0438674 2.11 0.035 .0064493 .1784064 MIDWEST | -.0077268 .0402346 -0.19 0.848 -.0865851 .0711314 WEST | .133032 .0451132 2.95 0.003 .0446117 .2214522 AGE | -.0137971 .0271393 -0.51 0.611 -.0669891 .0393949 BLACK | -.0828304 .055285 -1.50 0.134 -.191187 .0255261 MALE | -.1033339 .0353879 -2.92 0.003 -.172693 -.0339749 MARRIED | -.0156072 .0364331 -0.43 0.668 -.0870147 .0558003 SCHOOL | .0243634 .0048534 5.02 0.000 .0148509 .0338759 FAMINC | .0002944 .0055077 0.05 0.957 -.0105006 .0110893 EMPLOYED | -.0214448 .0546587 -0.39 0.695 -.1285739 .0856842 PRIVINS | .352906 .0477607 7.39 0.000 .2592967 .4465153 MEDICAID | .3371142 .0643838 5.24 0.000 .2109244 .4633041 _cons | .8786717 .22084 3.98 0.000 .4458332 1.31151 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.3743761 .0623097 -6.01 0.000 -.496501 -.2522513 POORHLTH | .3126258 .0496397 6.30 0.000 .2153338 .4099179 NUMCHRON | .1935047 .0126581 15.29 0.000 .1686953 .218314 ADLDIFF | .0690818 .0428187 1.61 0.107 -.0148413 .1530049 NOREAST | .0924278 .0438674 2.11 0.035 .0064493 .1784064 MIDWEST | -.0077268 .0402346 -0.19 0.848 -.0865851 .0711314 WEST | .133032 .0451132 2.95 0.003 .0446117 .2214522 AGE | -.0137971 .0271393 -0.51 0.611 -.0669891 .0393949 BLACK | -.0828304 .055285 -1.50 0.134 -.191187 .0255261 MALE | -.1033339 .0353879 -2.92 0.003 -.172693 -.0339749 MARRIED | -.0156072 .0364331 -0.43 0.668 -.0870147 .0558003 SCHOOL | .0243634 .0048534 5.02 0.000 .0148509 .0338759 FAMINC | .0002944 .0055077 0.05 0.957 -.0105006 .0110893 EMPLOYED | -.0214448 .0546587 -0.39 0.695 -.1285739 .0856842 PRIVINS | .352906 .0477607 7.39 0.000 .2592967 .4465153 MEDICAID | .3371142 .0643838 5.24 0.000 .2109244 .4633041 _cons | 1.073366 .2241211 4.79 0.000 .6340971 1.512636 -------------+---------------------------------------------------------------- /imlogitpi1 | 1.19749 .3900064 3.07 0.002 .4330913 1.961888 /lnalpha1 | -.7059758 .1243765 -5.68 0.000 -.9497492 -.4622024 /lnalpha2 | .869542 .2064089 4.21 0.000 .4649879 1.274096 ------------------------------------------------------------------------------ alpha1 | .4936267 .0613955 .386838 .6298948 alpha2 | 2.385818 .4924541 1.591995 3.575468 pi1 | .7680779 .0694735 .6066116 .8767371 pi2 | .2319221 .0694735 .1232629 .3933884 ------------------------------------------------------------------------------ . estimates store CFM2NB2 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- CFM2NB2 | 4406 . -12148.79 21 24339.58 24473.78 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llCFM2NB2 = e(ll) . * e(rank) gives number of parameters (e(k)) minus number of constraints . scalar kCFM2NB2 = e(rank) . . * Constrained Finite mixtures NB2 - 3 components only intercept varies . * This needs to directly follow the constrained 2 components case . * Note the constraints 1=2 are remembered so only need to add constraints that 2=3 . foreach var of varlist $XLIST { 2. constraint `i' [component2]`var' = [component3]`var' 3. local i = `i' + 1 4. } . fmm OFP $XLIST, components(3) mixtureof(negbin2) constraints(1/`i') Fitting 3 component Negative Binomial-2 model: Iteration 0: log likelihood = -12148.794 (not concave) Iteration 1: log likelihood = -12148.785 (not concave) Iteration 2: log likelihood = -12148.77 (not concave) Iteration 3: log likelihood = -12148.59 (not concave) Iteration 4: log likelihood = -12148.443 (not concave) Iteration 5: log likelihood = -12148.345 (not concave) Iteration 6: log likelihood = -12148.262 (not concave) Iteration 7: log likelihood = -12148.176 (not concave) Iteration 8: log likelihood = -12148.081 (not concave) Iteration 9: log likelihood = -12147.901 (not concave) Iteration 10: log likelihood = -12147.264 (not concave) Iteration 11: log likelihood = -12146.729 (not concave) Iteration 12: log likelihood = -12146.184 (not concave) Iteration 13: log likelihood = -12145.584 (not concave) Iteration 14: log likelihood = -12145.31 Iteration 15: log likelihood = -12144.985 Iteration 16: log likelihood = -12144.439 Iteration 17: log likelihood = -12144.342 Iteration 18: log likelihood = -12144.335 Iteration 19: log likelihood = -12144.333 Iteration 20: log likelihood = -12144.333 Iteration 21: log likelihood = -12144.333 Iteration 22: log likelihood = -12144.333 3 component Negative Binomial-2 regression Number of obs = 4406 Wald chi2(16) = 619.00 Log likelihood = -12144.333 Prob > chi2 = 0.0000 ( 1) [component1]EXCLHLTH - [component2]EXCLHLTH = 0 ( 2) [component1]POORHLTH - [component2]POORHLTH = 0 ( 3) [component1]NUMCHRON - [component2]NUMCHRON = 0 ( 4) [component1]ADLDIFF - [component2]ADLDIFF = 0 ( 5) [component1]NOREAST - [component2]NOREAST = 0 ( 6) [component1]MIDWEST - [component2]MIDWEST = 0 ( 7) [component1]WEST - [component2]WEST = 0 ( 8) [component1]AGE - [component2]AGE = 0 ( 9) [component1]BLACK - [component2]BLACK = 0 (10) [component1]MALE - [component2]MALE = 0 (11) [component1]MARRIED - [component2]MARRIED = 0 (12) [component1]SCHOOL - [component2]SCHOOL = 0 (13) [component1]FAMINC - [component2]FAMINC = 0 (14) [component1]EMPLOYED - [component2]EMPLOYED = 0 (15) [component1]PRIVINS - [component2]PRIVINS = 0 (16) [component1]MEDICAID - [component2]MEDICAID = 0 (17) [component2]EXCLHLTH - [component3]EXCLHLTH = 0 (18) [component2]POORHLTH - [component3]POORHLTH = 0 (19) [component2]NUMCHRON - [component3]NUMCHRON = 0 (20) [component2]ADLDIFF - [component3]ADLDIFF = 0 (21) [component2]NOREAST - [component3]NOREAST = 0 (22) [component2]MIDWEST - [component3]MIDWEST = 0 (23) [component2]WEST - [component3]WEST = 0 (24) [component2]AGE - [component3]AGE = 0 (25) [component2]BLACK - [component3]BLACK = 0 (26) [component2]MALE - [component3]MALE = 0 (27) [component2]MARRIED - [component3]MARRIED = 0 (28) [component2]SCHOOL - [component3]SCHOOL = 0 (29) [component2]FAMINC - [component3]FAMINC = 0 (30) [component2]EMPLOYED - [component3]EMPLOYED = 0 (31) [component2]PRIVINS - [component3]PRIVINS = 0 (32) [component2]MEDICAID - [component3]MEDICAID = 0 ------------------------------------------------------------------------------ OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.3738447 .0613775 -6.09 0.000 -.4941425 -.2535469 POORHLTH | .3110358 .0505049 6.16 0.000 .2120481 .4100236 NUMCHRON | .1998143 .0125221 15.96 0.000 .1752714 .2243571 ADLDIFF | .0668725 .0430328 1.55 0.120 -.0174702 .1512153 NOREAST | .0950157 .0445374 2.13 0.033 .007724 .1823074 MIDWEST | -.0024811 .0395222 -0.06 0.950 -.0799432 .0749809 WEST | .1262491 .0446504 2.83 0.005 .038736 .2137623 AGE | -.0173924 .0268963 -0.65 0.518 -.0701082 .0353233 BLACK | -.0728597 .054605 -1.33 0.182 -.1798835 .0341641 MALE | -.1020928 .0352657 -2.89 0.004 -.1712124 -.0329732 MARRIED | -.0073032 .036324 -0.20 0.841 -.078497 .0638906 SCHOOL | .0258393 .0048672 5.31 0.000 .0162997 .0353788 FAMINC | -.0007272 .0055991 -0.13 0.897 -.0117012 .0102469 EMPLOYED | -.0145815 .0547655 -0.27 0.790 -.12192 .092757 PRIVINS | .3577015 .047715 7.50 0.000 .2641818 .4512212 MEDICAID | .346743 .0630647 5.50 0.000 .2231385 .4703475 _cons | .8173341 .2178241 3.75 0.000 .3904067 1.244262 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.3738447 .0613775 -6.09 0.000 -.4941425 -.2535469 POORHLTH | .3110358 .0505049 6.16 0.000 .2120481 .4100236 NUMCHRON | .1998143 .0125221 15.96 0.000 .1752714 .2243571 ADLDIFF | .0668725 .0430328 1.55 0.120 -.0174702 .1512153 NOREAST | .0950157 .0445374 2.13 0.033 .007724 .1823074 MIDWEST | -.0024811 .0395222 -0.06 0.950 -.0799432 .0749809 WEST | .1262491 .0446504 2.83 0.005 .038736 .2137623 AGE | -.0173924 .0268963 -0.65 0.518 -.0701082 .0353233 BLACK | -.0728597 .054605 -1.33 0.182 -.1798835 .0341641 MALE | -.1020928 .0352657 -2.89 0.004 -.1712124 -.0329732 MARRIED | -.0073032 .036324 -0.20 0.841 -.078497 .0638906 SCHOOL | .0258393 .0048672 5.31 0.000 .0162997 .0353788 FAMINC | -.0007272 .0055991 -0.13 0.897 -.0117012 .0102469 EMPLOYED | -.0145815 .0547655 -0.27 0.790 -.12192 .092757 PRIVINS | .3577015 .047715 7.50 0.000 .2641818 .4512212 MEDICAID | .346743 .0630647 5.50 0.000 .2231385 .4703475 _cons | 1.002316 .2223712 4.51 0.000 .5664765 1.438156 -------------+---------------------------------------------------------------- component3 | EXCLHLTH | -.3738447 .0613775 -6.09 0.000 -.4941425 -.2535469 POORHLTH | .3110358 .0505049 6.16 0.000 .2120481 .4100236 NUMCHRON | .1998143 .0125221 15.96 0.000 .1752714 .2243571 ADLDIFF | .0668725 .0430328 1.55 0.120 -.0174702 .1512153 NOREAST | .0950157 .0445374 2.13 0.033 .007724 .1823074 MIDWEST | -.0024811 .0395222 -0.06 0.950 -.0799432 .0749809 WEST | .1262491 .0446504 2.83 0.005 .038736 .2137623 AGE | -.0173924 .0268963 -0.65 0.518 -.0701082 .0353233 BLACK | -.0728597 .054605 -1.33 0.182 -.1798835 .0341641 MALE | -.1020928 .0352657 -2.89 0.004 -.1712124 -.0329732 MARRIED | -.0073032 .036324 -0.20 0.841 -.078497 .0638906 SCHOOL | .0258393 .0048672 5.31 0.000 .0162997 .0353788 FAMINC | -.0007272 .0055991 -0.13 0.897 -.0117012 .0102469 EMPLOYED | -.0145815 .0547655 -0.27 0.790 -.12192 .092757 PRIVINS | .3577015 .047715 7.50 0.000 .2641818 .4512212 MEDICAID | .346743 .0630647 5.50 0.000 .2231385 .4703475 _cons | 2.03998 .2200978 9.27 0.000 1.608596 2.471363 -------------+---------------------------------------------------------------- /imlogitpi1 | 3.349516 .3831715 8.74 0.000 2.598514 4.100518 /imlogitpi2 | 2.121435 .4248021 4.99 0.000 1.288838 2.954031 /lnalpha1 | -.875997 .1291408 -6.78 0.000 -1.129108 -.6228857 /lnalpha2 | 1.028545 .2012039 5.11 0.000 .6341922 1.422897 /lnalpha3 | -15.77926 597.1939 -0.03 0.979 -1186.258 1154.699 ------------------------------------------------------------------------------ alpha1 | .4164466 .0537802 .3233215 .5363943 alpha2 | 2.796992 .5627656 1.885498 4.149122 alpha3 | 1.40e-07 .0000838 0 . pi1 | .7530374 .05288 .6358911 .8418665 pi2 | .22053 .0516948 .1356377 .3377904 pi3 | .0264326 .0095693 .0076772 .045188 ------------------------------------------------------------------------------ . estimates store CFM3NB2 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- CFM3NB2 | 4406 . -12144.33 24 24336.67 24490.04 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . scalar llCFM3NB2 = e(ll) . * e(rank) gives number of parameters (e(k)) minus number of constraints . scalar kCFM3NB2 = e(rank) . . *** TABLE 6.3: OFP VISITS LIKELIHOOD RATIO TESTS . . *** This differs from book as Trivedi and Deb (1977) used different program . . * NB1 likelihood ratio tests . dis "NB1 vs NB1H : " 2*(llHNB1-llNB1) " DofF = " kHNB1log-kNB1 NB1 vs NB1H : 59.899948 DofF = 17 . dis "NB1 vs CFM2 NB1 : " 2*(llCFM2NB1-llNB1) " DofF = " kCFM2NB1-kNB1 NB1 vs CFM2 NB1 : 116.70417 DofF = 3 . dis "NB1 vs FM2 NB1 : " 2*(llFM2NB1-llNB1) " DofF = " kFM2NB1-kNB1 NB1 vs FM2 NB1 : 127.54677 DofF = 19 . dis "CFM2 NB1 vs FM2 NB1 : " 2*(llFM2NB1-llCFM2NB1) " DofF = " kFM2NB1-kCFM2NB1 CFM2 NB1 vs FM2 NB1 : 10.842605 DofF = 16 . dis "CFM2 NB1 vs CFM3 NB1 : " 2*(llCFM3NB1-llCFM2NB1) " DofF = " kCFM3NB1-kCFM2NB1 CFM2 NB1 vs CFM3 NB1 : 4.7349458 DofF = 3 . dis "FM3 NB1 vs FM2 NB1 : " 2*(llFM3NB1-llFM2NB1) " DofF = " kFM3NB1-kFM2NB1 FM3 NB1 vs FM2 NB1 : 84.650649 DofF = 18 . . * NB2 likelihood ratio tests . dis "NB2 vs NB2H : " 2*(llHNB2-llNB2) " DofF = " kHNB2log-kNB2 NB2 vs NB2H : 187.31303 DofF = 17 . dis "NB2 vs CFM2 NB2 : " 2*(llCFM2NB2-llNB2) " DofF = " kCFM2NB2-kNB2 NB2 vs CFM2 NB2 : 106.75709 DofF = 3 . dis "NB2 vs FM2 NB2 : " 2*(llFM2NB2-llNB2) " DofF = " kFM2NB2-kNB2 NB2 vs FM2 NB2 : 125.71262 DofF = 19 . dis "CFM2 NB2 vs FM2 NB2 : " 2*(llFM2NB2-llCFM2NB2) " DofF = " kFM2NB2-kCFM2NB2 CFM2 NB2 vs FM2 NB2 : 18.955532 DofF = 16 . dis "CFM2 NB2 vs CFM3 NB2 : " 2*(llCFM3NB2-llCFM2NB2) " DofF = " kCFM3NB2-kCFM2NB2 CFM2 NB2 vs CFM3 NB2 : 8.9127166 DofF = 3 . dis "FM3 NB2 vs FM2 NB2 : " 2*(llFM3NB2-llFM2NB2) " DofF = " kFM3NB2-kFM2NB2 FM3 NB2 vs FM2 NB2 : 118.01239 DofF = 19 . . *** TABLE 6.4: OFP VISITS LL and AIC for various models . . *** This differs from book as Trivedi and Deb (1977) used different program . *** Also we do not calculate GoF tests here . . ** TABLE 6.4: NB1 and NB2 Hurdle models - second row of table . . display "Hurdle: NB1 / NB1 : k = " kHNB1 " and ll = " llHNB1 " and AIC = " AICHNB1 " and BIC = " BICHNB1 Hurdle: NB1 / NB1 : k = 36 and ll = -12126.253 and AIC = 24324.505 and BIC = 24554.571 . display "Hurdle: NB2 / NB2 : k = " kHNB2 " and ll = " llHNB2 " and AIC = " AICHNB2 " and BIC = " BICHNB2 Hurdle: NB2 / NB2 : k = 36 and ll = -12108.511 and AIC = 24289.022 and BIC = 24519.088 . . * ASIDE: Instead use logit at first stage . display "Hurdle: Logit / NB1 : k = " kHNB1log " and ll = " llHNB1log " and AIC = " AICHNB1log " and BIC = " BICHNB1log Hurdle: Logit / NB1 : k = 35 and ll = -12113.027 and AIC = 24296.053 and BIC = 24519.728 . display "Hurdle: Logit / NB2 : k = " kHNB2log " and ll = " llHNB2log " and AIC = " AICHNB2log " and BIC = " BICHNB2log Hurdle: Logit / NB2 : k = 35 and ll = -12110.492 and AIC = 24290.983 and BIC = 24514.658 . . ** TABLE 6.4: Remaining NB1 models . . estimates table POISSON NB1 CFM2NB1 FM2NB1 CFM3NB1 FM3NB1, keep(EXCLHLTH) /// > b(%10.3f) t(%10.2f) stats(l ll aic bic N) equations(1) -------------------------------------------------------------------------------------------- Variable | POISSON NB1 CFM2NB1 FM2NB1 CFM3NB1 FM3NB1 -------------+------------------------------------------------------------------------------ EXCLHLTH | -0.386 -0.268 -0.281 -0.229 -0.286 -0.285 | -4.91 -5.29 -4.93 -3.85 -4.89 -4.33 -------------+------------------------------------------------------------------------------ l | ll | -18134.567 -12156.202 -12097.850 -12092.429 -12095.483 -12050.104 aic | 36303.133 24348.405 24237.701 24258.858 24238.966 24210.208 bic | 36411.775 24463.438 24371.906 24495.315 24392.343 24561.697 N | 4406 4406 4406 4406 4406 4406 -------------------------------------------------------------------------------------------- legend: b/t . . ** TABLE 6.4: Remaining NB2 models . . estimates table POISSON NB2 CFM2NB2 FM2NB2 CFM3NB2 FM3NB2, keep(EXCLHLTH) /// > b(%10.3f) t(%10.2f) stats(l ll aic bic N) equations(1) -------------------------------------------------------------------------------------------- Variable | POISSON NB2 CFM2NB2 FM2NB2 CFM3NB2 FM3NB2 -------------+------------------------------------------------------------------------------ EXCLHLTH | -0.386 -0.385 -0.374 -0.343 -0.374 -0.307 | -4.91 -4.92 -6.01 -3.27 -6.09 -2.55 -------------+------------------------------------------------------------------------------ l | ll | -18134.567 -12202.168 -12148.789 -12139.311 -12144.333 -12080.305 aic | 36303.133 24440.335 24339.578 24352.623 24336.665 24272.610 bic | 36411.775 24555.368 24473.783 24589.079 24490.043 24630.491 N | 4406 4406 4406 4406 4406 4406 -------------------------------------------------------------------------------------------- legend: b/t . . ** Focus on probabilities and overdispersion parameters in FM . estimates table CFM3NB1 FM3NB1 CFM3NB2 FM3NB2, keep (imlogitpi1:_cons imlogitpi2:_cons lnalpha1:_cons lnalpha2:_cons lnalpha1 > :_cons) ------------------------------------------------------------------ Variable | CFM3NB1 FM3NB1 CFM3NB2 FM3NB2 -------------+---------------------------------------------------- imlogitpi1 | _cons | 2.8703108 2.2169451 3.3495159 .7364091 -------------+---------------------------------------------------- imlogitpi2 | _cons | .33730178 -.29406864 2.1214345 -.45767375 -------------+---------------------------------------------------- lnalpha1 | _cons | -.87599699 -.86167567 -------------+---------------------------------------------------- lnalpha2 | _cons | 1.0285445 .72328708 -------------+---------------------------------------------------- lnalpha1 | _cons | -.87599699 -.86167567 ------------------------------------------------------------------ . . *********** 6.3.8 HURDLE MODEL (Table 6.8) . . *** TABLE 6.8: NB2 HURDLE ESTIMATES WITH LOGIT FIRST STAGE . . * Could use earlier results . * Simpler to use user-written addon command hnblogit . hnblogit OFP $XLIST, vce(robust) initial: log pseudolikelihood = -20689.057 alternative: log pseudolikelihood = -14973.253 rescale: log pseudolikelihood = -12983.223 rescale eq: log pseudolikelihood = -12845.236 Iteration 0: log pseudolikelihood = -12845.236 (not concave) Iteration 1: log pseudolikelihood = -12402.134 Iteration 2: log pseudolikelihood = -12362.641 Iteration 3: log pseudolikelihood = -12114.183 Iteration 4: log pseudolikelihood = -12110.5 Iteration 5: log pseudolikelihood = -12110.492 Iteration 6: log pseudolikelihood = -12110.492 Negative Binomial-Logit Hurdle Regression Number of obs = 4406 Wald chi2(16) = 279.07 Log pseudolikelihood = -12110.492 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- logit | EXCLHLTH | -.328511 .1422489 -2.31 0.021 -.6073137 -.0497083 POORHLTH | .0708379 .1687321 0.42 0.675 -.2598709 .4015468 NUMCHRON | .556512 .0527686 10.55 0.000 .4530874 .6599367 ADLDIFF | -.1881658 .1299432 -1.45 0.148 -.4428498 .0665183 NOREAST | .1292212 .1250505 1.03 0.301 -.1158732 .3743157 MIDWEST | .1008883 .1146354 0.88 0.379 -.1237929 .3255696 WEST | .2016634 .1336443 1.51 0.131 -.0602747 .4636014 AGE | .1904976 .0811478 2.35 0.019 .0314509 .3495443 BLACK | -.3269721 .1334663 -2.45 0.014 -.5885612 -.0653829 MALE | -.4644473 .09852 -4.71 0.000 -.6575429 -.2713517 MARRIED | .2472641 .1039523 2.38 0.017 .0435213 .4510069 SCHOOL | .0542073 .0131949 4.11 0.000 .0283458 .0800688 FAMINC | .0067446 .0184979 0.36 0.715 -.0295106 .0429998 EMPLOYED | -.0123197 .145099 -0.08 0.932 -.2967086 .2720692 PRIVINS | .7624605 .1173052 6.50 0.000 .5325465 .9923745 MEDICAID | .553514 .1812261 3.05 0.002 .1983173 .9087106 _cons | -1.475312 .6464113 -2.28 0.022 -2.742255 -.2083689 -------------+---------------------------------------------------------------- negbinomial | EXCLHLTH | -.3775071 .0872882 -4.32 0.000 -.5485887 -.2064254 POORHLTH | .3325089 .0567568 5.86 0.000 .2212676 .4437502 NUMCHRON | .1429372 .0134916 10.59 0.000 .1164941 .1693804 ADLDIFF | .1290355 .051603 2.50 0.012 .0278954 .2301756 NOREAST | .1040669 .0527805 1.97 0.049 .000619 .2075148 MIDWEST | -.0163184 .0475067 -0.34 0.731 -.1094298 .076793 WEST | .123247 .0504022 2.45 0.014 .0244605 .2220335 AGE | -.0753009 .032266 -2.33 0.020 -.1385412 -.0120606 BLACK | .0016163 .070014 0.02 0.982 -.1356086 .1388412 MALE | .0041276 .0421937 0.10 0.922 -.0785705 .0868257 MARRIED | -.0920324 .0437353 -2.10 0.035 -.1777521 -.0063127 SCHOOL | .0216107 .0056616 3.82 0.000 .0105142 .0327072 FAMINC | -.0022357 .0058903 -0.38 0.704 -.0137805 .0093091 EMPLOYED | .0296559 .0739406 0.40 0.688 -.1152651 .1745769 PRIVINS | .2271509 .0566732 4.01 0.000 .1160735 .3382283 MEDICAID | .1847927 .066457 2.78 0.005 .0545393 .3150461 _cons | 1.630983 .2692104 6.06 0.000 1.10334 2.158626 -------------+---------------------------------------------------------------- /lnalpha | -.2959882 .0542073 -5.46 0.000 -.4022325 -.1897438 ------------------------------------------------------------------------------ AIC Statistic = 5.505 . scalar llhnblogit = e(ll) . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 4406 . -12110.49 35 24290.98 24514.66 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . . *********** 6.3.5-6.3.7 DETAILED ANALYSIS OF UNCONSTRAINED FNM NB1 model with 2 components . . preserve . . * TABLES 6.5, 6.6 and 6.7 recode the largest value of OFP from 89 to 70 . . replace OFP = 70 if OFP > 70 (1 real change made) . . * See how NB1 loglikelihood changes as mentioned in text . quietly nbreg OFP $XLIST, vce(robust) dispersion(constant) . display "Fitted log-likelihood for NB1 = " e(ll) Fitted log-likelihood for NB1 = -12152.738 . . * Estimate FMM model model and save results . fmm OFP $XLIST, components(2) mixtureof(negbin1) vce(robust) Fitting Negative Binomial-1 model: Iteration 0: log likelihood = -18090.998 Iteration 1: log likelihood = -18090.913 Iteration 2: log likelihood = -18090.913 Iteration 0: log likelihood = -14539.129 Iteration 1: log likelihood = -12648.799 Iteration 2: log likelihood = -12490.01 Iteration 3: log likelihood = -12489.804 Iteration 4: log likelihood = -12489.804 Iteration 0: log likelihood = -12489.804 Iteration 1: log likelihood = -12298.424 Iteration 2: log likelihood = -12153.535 Iteration 3: log likelihood = -12152.738 Iteration 4: log likelihood = -12152.738 Fitting 2 component Negative Binomial-1 model: Iteration 0: log pseudolikelihood = -12153.274 (not concave) Iteration 1: log pseudolikelihood = -12152.052 (not concave) Iteration 2: log pseudolikelihood = -12119.599 (not concave) Iteration 3: log pseudolikelihood = -12101.578 Iteration 4: log pseudolikelihood = -12084.198 (not concave) Iteration 5: log pseudolikelihood = -12080.404 Iteration 6: log pseudolikelihood = -12079.653 Iteration 7: log pseudolikelihood = -12078.334 Iteration 8: log pseudolikelihood = -12077.21 Iteration 9: log pseudolikelihood = -12076.934 Iteration 10: log pseudolikelihood = -12076.91 Iteration 11: log pseudolikelihood = -12076.909 2 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(32) = 795.46 Log pseudolikelihood = -12076.909 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.2497655 .057929 -4.31 0.000 -.3633043 -.1362268 POORHLTH | .2338421 .065056 3.59 0.000 .1063347 .3613496 NUMCHRON | .1858892 .0127116 14.62 0.000 .160975 .2108034 ADLDIFF | -.0158776 .0431165 -0.37 0.713 -.1003844 .0686291 NOREAST | .0829703 .0483592 1.72 0.086 -.0118119 .1777526 MIDWEST | .0180267 .0395598 0.46 0.649 -.0595091 .0955626 WEST | .0892005 .0488985 1.82 0.068 -.0066388 .1850397 AGE | .0284182 .0266794 1.07 0.287 -.0238726 .0807089 BLACK | -.0792232 .0705989 -1.12 0.262 -.2175945 .059148 MALE | -.1360233 .0347308 -3.92 0.000 -.2040944 -.0679521 MARRIED | .0474489 .0354877 1.34 0.181 -.0221058 .1170036 SCHOOL | .0142692 .0052279 2.73 0.006 .0040226 .0245157 FAMINC | -.0003394 .0052844 -0.06 0.949 -.0106967 .0100179 EMPLOYED | -.0585768 .0561586 -1.04 0.297 -.1686457 .0514921 PRIVINS | .2542815 .05307 4.79 0.000 .1502663 .3582967 MEDICAID | .3528854 .0620136 5.69 0.000 .231341 .4744298 _cons | .7780131 .2235745 3.48 0.001 .3398151 1.216211 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.7513363 .7367241 -1.02 0.308 -2.195289 .6926165 POORHLTH | .039149 .65878 0.06 0.953 -1.252036 1.330334 NUMCHRON | .1388443 .104259 1.33 0.183 -.0654995 .3431882 ADLDIFF | .5458759 .2679258 2.04 0.042 .0207511 1.071001 NOREAST | .178225 .485191 0.37 0.713 -.772732 1.129182 MIDWEST | .0419492 .3572626 0.12 0.907 -.6582726 .742171 WEST | .2363191 .4852752 0.49 0.626 -.7148029 1.187441 AGE | -.6110602 .2475692 -2.47 0.014 -1.096287 -.1258335 BLACK | -1.064927 1.090272 -0.98 0.329 -3.201821 1.071967 MALE | .1204642 .2603865 0.46 0.644 -.3898839 .6308124 MARRIED | -.5129287 .331818 -1.55 0.122 -1.16328 .1374226 SCHOOL | .1517549 .0822947 1.84 0.065 -.0095398 .3130496 FAMINC | -.005429 .0200526 -0.27 0.787 -.0447314 .0338735 EMPLOYED | .3717573 .6895927 0.54 0.590 -.9798197 1.723334 PRIVINS | 3.020036 2.69528 1.12 0.263 -2.262616 8.302688 MEDICAID | -3.147283 3.233294 -0.97 0.330 -9.484422 3.189856 _cons | 1.86179 2.627607 0.71 0.479 -3.288225 7.011806 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.334341 .3467302 6.73 0.000 1.654762 3.01392 /lndelta1 | 1.250592 .0810018 15.44 0.000 1.091831 1.409352 /lndelta2 | 2.796696 .4079347 6.86 0.000 1.997159 3.596233 ------------------------------------------------------------------------------ delta1 | 3.492409 .2828914 2.979725 4.093303 delta2 | 16.3904 6.686215 7.368091 36.46064 pi1 | .9116815 .0279181 .8395336 .953199 pi2 | .0883185 .0279181 .046801 .1604664 ------------------------------------------------------------------------------ . estimates store FMMalt70 . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- FMMalt70 | 4406 . -12076.91 37 24227.82 24464.27 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . . * Create fitted means and variances in the two components . matrix theta = e(b) . scalar delta1 = exp(theta[1,e(k)-1]) . scalar delta2 = exp(theta[1,e(k)]) . predict mu1, mean equation(component1) . predict mu2, mean equation(component2) . generate mu1alt = mu1 . generate mu2alt = mu2 . generate var1 = mu1*(1+delta1) . generate var2 = mu2*(1+delta2) . predict p1, prior equation(component1) . predict posterior1, posterior equation(component1) . generate mufm = p1*mu1 + (1-p1)*mu2 . * The following differs from Table 6.5 - need to check . generate varfm = p1*(mu1^2 + var1) + (1-p1)*(mu2^2 + var2) - mufm^2 . . * Create predicted probabilities for preferred 2-component NB1 finite mixture model . * For 2-component NB2 estimate 2 component NB2 model and then . * change generate ainvmu = mu1/delta1 to ainvmu = 1/delta1 . * change replace ainvmu = mu2/delta2 to ainvmu = 1/delta2 . . global MAXCOUNT 20 . * First component . generate mu = mu1 . generate ainvmu = mu1/delta1 // For NB1: (1/a)*mu For NB2: use (1/a) . generate pfit1sum = 0 . forvalues i = 0/$MAXCOUNT { 2. generate pfit1`i' = lngamma(`i'+ainvmu) - lngamma(ainvmu) - lnfactorial(`i') + ainvmu*ln(ainvmu/(ainvmu+mu)) + `i'*ln(m > u/(ainvmu+mu)) 3. quietly replace pfit1`i' = exp(pfit1`i') 4. quietly replace pfit1sum = pfit1sum + pfit1`i' 5. } . * Second component . replace mu = mu2 (4406 real changes made) . replace ainvmu = mu2/delta2 (4406 real changes made) . generate pfit2sum = 0 . forvalues i = 0/$MAXCOUNT { 2. generate pfit2`i' = lngamma(`i'+ainvmu) - lngamma(ainvmu) - lnfactorial(`i') + ainvmu*ln(ainvmu/(ainvmu+mu)) + `i'*ln(m > u/(ainvmu+mu)) 3. quietly replace pfit2`i' = exp(pfit2`i') 4. quietly replace pfit2sum = pfit2sum + pfit2`i' 5. } . * Combined . generate pfitsum = 0 . forvalues i = 0/$MAXCOUNT { 2. generate pfitfm`i' = p1*pfit1`i' + (1-p1)*pfit2`i' 3. } . generate pfitfmsum = p1*pfit1sum + (1-p1)*pfit2sum . generate pfitfmge10 = 1 . forvalues i = 0/9 { 2. replace pfitfmge10 = pfitfmge10 - pfitfm`i' 3. } (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) (4406 real changes made) . . *** TABLE 6.5: FITTED PROBABILITIES FROM THE TWO COMPONENT MODEL . . display "Fitted probabilities from 2 component NB1 finite mixture model" Fitted probabilities from 2 component NB1 finite mixture model . summarize pfitfm* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- pfitfm0 | 4406 .1503509 .0847528 .0010897 .5103663 pfitfm1 | 4406 .1159523 .0409432 .0030036 .1832897 pfitfm2 | 4406 .1053953 .0253215 .0033814 .1297264 pfitfm3 | 4406 .0935062 .0159368 .0040264 .1054766 pfitfm4 | 4406 .0815833 .0112362 .0056819 .0910873 -------------+-------------------------------------------------------- pfitfm5 | 4406 .0703565 .010061 .0081193 .0813111 pfitfm6 | 4406 .0601635 .0104913 .0111791 .0741069 pfitfm7 | 4406 .0511216 .0111262 .0146903 .068548 pfitfm8 | 4406 .0432274 .0114868 .0116213 .0640454 pfitfm9 | 4406 .036414 .0115049 .0085459 .0603456 -------------+-------------------------------------------------------- pfitfm10 | 4406 .0305839 .011233 .0063207 .0572259 pfitfm11 | 4406 .0256282 .0107473 .0046969 .0544785 pfitfm12 | 4406 .0214378 .0101183 .0035039 .0521853 pfitfm13 | 4406 .0179095 .0094038 .0026226 .050112 pfitfm14 | 4406 .0149486 .0086483 .0019686 .0480914 -------------+-------------------------------------------------------- pfitfm15 | 4406 .0124709 .0078847 .0014814 .0463336 pfitfm16 | 4406 .0104022 .0071366 .0011172 .0445443 pfitfm17 | 4406 .0086781 .00642 .0008442 .0432813 pfitfm18 | 4406 .0072433 .0057452 .0006391 .0422218 pfitfm19 | 4406 .0060507 .0051185 .0004846 .040765 -------------+-------------------------------------------------------- pfitfm20 | 4406 .0050603 .0045425 .000368 .0389894 pfitfmsum | 4406 .9684846 .0340814 .5646738 .998804 pfitfmge10 | 4406 .191929 .115718 .0252433 .847298 . . *** TABLE 6.6: FMM MODEL MEANS and VARIANCE in the TWO COMPONENTS . . * Summary statistics . summarize mu1 mu2 var1 var2 mufm varfm p1 posterior1 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- mu1 | 4406 5.539224 2.145586 1.787157 21.25769 mu2 | 4406 8.178798 8.572553 .000796 79.82777 var1 | 4406 24.88446 9.638848 8.02864 95.49821 var2 | 4406 142.2326 149.0801 .013842 1388.237 mufm | 4406 5.772347 2.266985 1.632626 19.51864 -------------+-------------------------------------------------------- varfm | 4406 41.35636 33.16822 7.623593 595.8615 p1 | 4406 .9116815 0 .9116815 .9116815 posterior1 | 4406 .9116827 .1324927 .0002258 .9999993 . . *** FIGURE 6.3: PREDICTED MEANS IN THE TWO COMPONENTS . . * Histogram of means . quietly histogram mu1, width(2) name(_comp_1, replace) scale(1.5) . quietly histogram mu2, width(2) name(_comp_2, replace) scale(1.5) . graph combine _comp_1 _comp_2, iscale(0.7) ysize(3) xsize(6) xcommon . quietly graph export racd06fig3.wmf, replace . quietly graph export racd06fig3.eps, replace . . *** TABLE 6.7: FMM MODEL ESTIMATES . . * Tabulate results for earlier estimated model and save results . estimates table FMMalt70, b(%10.3f) t(%10.2f) stats(l ll aic bic N) equations(1) --------------------------- Variable | FMMalt70 -------------+------------- #1 | EXCLHLTH | -0.250 | -4.31 POORHLTH | 0.234 | 3.59 NUMCHRON | 0.186 | 14.62 ADLDIFF | -0.016 | -0.37 NOREAST | 0.083 | 1.72 MIDWEST | 0.018 | 0.46 WEST | 0.089 | 1.82 AGE | 0.028 | 1.07 BLACK | -0.079 | -1.12 MALE | -0.136 | -3.92 MARRIED | 0.047 | 1.34 SCHOOL | 0.014 | 2.73 FAMINC | -0.000 | -0.06 EMPLOYED | -0.059 | -1.04 PRIVINS | 0.254 | 4.79 MEDICAID | 0.353 | 5.69 _cons | 0.778 | 3.48 -------------+------------- component2 | EXCLHLTH | -0.751 | -1.02 POORHLTH | 0.039 | 0.06 NUMCHRON | 0.139 | 1.33 ADLDIFF | 0.546 | 2.04 NOREAST | 0.178 | 0.37 MIDWEST | 0.042 | 0.12 WEST | 0.236 | 0.49 AGE | -0.611 | -2.47 BLACK | -1.065 | -0.98 MALE | 0.120 | 0.46 MARRIED | -0.513 | -1.55 SCHOOL | 0.152 | 1.84 FAMINC | -0.005 | -0.27 EMPLOYED | 0.372 | 0.54 PRIVINS | 3.020 | 1.12 MEDICAID | -3.147 | -0.97 _cons | 1.862 | 0.71 -------------+------------- imlogitpi1 | _cons | 2.334 | 6.73 -------------+------------- lndelta1 | _cons | 1.251 | 15.44 -------------+------------- lndelta2 | _cons | 2.797 | 6.86 -------------+------------- Statistics | l | ll | -12076.909 aic | 24227.818 bic | 24464.275 N | 4406 --------------------------- legend: b/t . . ****** DIRECTIONAL GRADIENTS . . restore . . * NB1 model . nbreg OFP $XLIST, dispersion(constant) Fitting Poisson model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Fitting constant-only model: Iteration 0: log likelihood = -14552.718 Iteration 1: log likelihood = -12647.886 Iteration 2: log likelihood = -12493.025 Iteration 3: log likelihood = -12492.829 Iteration 4: log likelihood = -12492.829 Fitting full model: Iteration 0: log likelihood = -12492.829 Iteration 1: log likelihood = -12301.184 Iteration 2: log likelihood = -12157 Iteration 3: log likelihood = -12156.203 Iteration 4: log likelihood = -12156.202 Negative binomial regression Number of obs = 4406 LR chi2(16) = 673.25 Dispersion = constant Prob > chi2 = 0.0000 Log likelihood = -12156.202 Pseudo R2 = 0.0269 ------------------------------------------------------------------------------ OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- EXCLHLTH | -.2679127 .0576981 -4.64 0.000 -.3809989 -.1548265 POORHLTH | .1890825 .0411083 4.60 0.000 .1085117 .2696533 NUMCHRON | .1774737 .0095852 18.52 0.000 .1586871 .1962604 ADLDIFF | .0054215 .0367353 0.15 0.883 -.0665783 .0774213 NOREAST | .0715408 .0377765 1.89 0.058 -.0024998 .1455814 MIDWEST | .0138372 .0346677 0.40 0.690 -.0541102 .0817846 WEST | .1049489 .0382474 2.74 0.006 .0299853 .1799125 AGE | -.0032939 .022647 -0.15 0.884 -.0476813 .0410935 BLACK | -.1275746 .0481892 -2.65 0.008 -.2220236 -.0331255 MALE | -.1231018 .0297265 -4.14 0.000 -.1813646 -.064839 MARRIED | .0221482 .0308539 0.72 0.473 -.0383244 .0826208 SCHOOL | .0212676 .0041187 5.16 0.000 .0131952 .0293401 FAMINC | -.000249 .0047198 -0.05 0.958 -.0094996 .0090016 EMPLOYED | -.0180486 .0472 -0.38 0.702 -.1105589 .0744617 PRIVINS | .3364587 .0407839 8.25 0.000 .2565237 .4163938 MEDICAID | .3180563 .0529574 6.01 0.000 .2142618 .4218509 _cons | .949961 .1819063 5.22 0.000 .5934312 1.306491 -------------+---------------------------------------------------------------- /lndelta | 1.576208 .0311676 1.515121 1.637295 -------------+---------------------------------------------------------------- delta | 4.836581 .1507445 4.549971 5.141246 ------------------------------------------------------------------------------ Likelihood-ratio test of delta=0: chibar2(01) = 1.2e+04 Prob>=chibar2 = 0.000 . predict exb (option n assumed; predicted number of events) . scalar delta = exp(_b[/lndelta]) . generate psi = exb / delta . scalar phi = ln(1+delta) . . forvalues y=0/12 { 2. generate f`y'_nb1 = exp(lngamma(`y'+psi) - lngamma(`y'+1) /// > - lngamma(psi) + _b[/lndelta]*`y' - (`y'+psi)*phi) 3. } . drop exb psi . . * FM model . fmm OFP $XLIST, mix(negbin1) components(2) Fitting Negative Binomial-1 model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Iteration 0: log likelihood = -14552.718 Iteration 1: log likelihood = -12647.886 Iteration 2: log likelihood = -12493.025 Iteration 3: log likelihood = -12492.829 Iteration 4: log likelihood = -12492.829 Iteration 0: log likelihood = -12492.829 Iteration 1: log likelihood = -12301.184 Iteration 2: log likelihood = -12157 Iteration 3: log likelihood = -12156.203 Iteration 4: log likelihood = -12156.202 Fitting 2 component Negative Binomial-1 model: Iteration 0: log likelihood = -12156.74 (not concave) Iteration 1: log likelihood = -12155.694 (not concave) Iteration 2: log likelihood = -12134.293 (not concave) Iteration 3: log likelihood = -12108.437 (not concave) Iteration 4: log likelihood = -12100.205 Iteration 5: log likelihood = -12095.077 Iteration 6: log likelihood = -12093.661 Iteration 7: log likelihood = -12092.693 Iteration 8: log likelihood = -12092.43 Iteration 9: log likelihood = -12092.429 Iteration 10: log likelihood = -12092.429 2 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(32) = 813.60 Log likelihood = -12092.429 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.2290118 .0657969 -3.48 0.001 -.3579714 -.1000522 POORHLTH | .1499097 .0482609 3.11 0.002 .05532 .2444994 NUMCHRON | .1836232 .0115675 15.87 0.000 .1609514 .2062951 ADLDIFF | -.0520085 .0437403 -1.19 0.234 -.1377379 .033721 NOREAST | .0546492 .045218 1.21 0.227 -.0339765 .1432748 MIDWEST | .0191861 .0410324 0.47 0.640 -.0612359 .0996081 WEST | .0944858 .0442702 2.13 0.033 .0077179 .1812538 AGE | .0148273 .0272407 0.54 0.586 -.0385634 .068218 BLACK | -.1799111 .0630175 -2.85 0.004 -.3034232 -.0563991 MALE | -.1377495 .035128 -3.92 0.000 -.2065991 -.0688998 MARRIED | .0513625 .036238 1.42 0.156 -.0196628 .1223877 SCHOOL | .0133302 .0054999 2.42 0.015 .0025507 .0241097 FAMINC | .0007834 .0051657 0.15 0.879 -.0093412 .0109079 EMPLOYED | -.0807253 .0538157 -1.50 0.134 -.1862022 .0247516 PRIVINS | .3593702 .0538514 6.67 0.000 .2538233 .464917 MEDICAID | .4204549 .0826951 5.08 0.000 .2583755 .5825343 _cons | .7733975 .2262585 3.42 0.001 .329939 1.216856 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.8178674 .4061745 -2.01 0.044 -1.613955 -.02178 POORHLTH | .718358 .2390433 3.01 0.003 .2498417 1.186874 NUMCHRON | .1908478 .0762596 2.50 0.012 .0413818 .3403138 ADLDIFF | .549827 .1972346 2.79 0.005 .1632543 .9363997 NOREAST | .2279207 .2653733 0.86 0.390 -.2922015 .7480429 MIDWEST | -.0123035 .2647277 -0.05 0.963 -.5311603 .5065532 WEST | .2660744 .2394914 1.11 0.267 -.2033202 .735469 AGE | -.1334189 .1863378 -0.72 0.474 -.4986342 .2317964 BLACK | .2680242 .3900981 0.69 0.492 -.4965539 1.032602 MALE | -.0228589 .2018914 -0.11 0.910 -.4185587 .3728409 MARRIED | -.242328 .2003793 -1.21 0.227 -.6350642 .1504082 SCHOOL | .1023137 .0321577 3.18 0.001 .0392858 .1653416 FAMINC | -.0011579 .0223861 -0.05 0.959 -.0450338 .042718 EMPLOYED | .5400458 .257839 2.09 0.036 .0346906 1.045401 PRIVINS | .227208 .3724258 0.61 0.542 -.5027332 .9571493 MEDICAID | -.6163631 .5590777 -1.10 0.270 -1.712135 .479409 _cons | 1.554799 1.597789 0.97 0.331 -1.57681 4.686408 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.290933 .3138519 7.30 0.000 1.675794 2.906071 /lndelta1 | 1.259071 .0537703 23.42 0.000 1.153683 1.364459 /lndelta2 | 2.441911 .2382819 10.25 0.000 1.974887 2.908935 ------------------------------------------------------------------------------ delta1 | 3.522148 .189387 3.169847 3.913605 delta2 | 11.49499 2.739047 7.205806 18.33726 pi1 | .9081233 .0261864 .8423468 .9481457 pi2 | .0918767 .0261864 .0518543 .1576532 ------------------------------------------------------------------------------ . predict exb1, eq(component1) . predict exb2, eq(component2) . sum exb1 exb2 Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- exb1 | 4406 5.205164 1.934959 1.483609 19.76001 exb2 | 4406 11.79034 10.14905 .64758 107.9005 . scalar delta1 = exp(_b[/lndelta1]) . scalar delta2 = exp(_b[/lndelta2]) . generate psi1 = exb1 / delta1 . generate psi2 = exb2 / delta2 . scalar phi1 = ln(1+delta1) . scalar phi2 = ln(1+delta2) . forvalues y=0/12 { 2. generate f`y'_fmnb1 = e(pi1_est) * (exp(lngamma(`y'+psi1) - lngamma(`y'+1) /// > - lngamma(psi1) + _b[/lndelta1]*`y' - (`y'+psi1)*phi1)) /// > + e(pi2_est) * (exp(lngamma(`y'+psi2) - lngamma(`y'+1) /// > - lngamma(psi2) + _b[/lndelta2]*`y' - (`y'+psi2)*phi2)) 3. } . drop exb1 exb2 psi1 psi2 . . * Compute directional gradients . forvalues y = 0/12 { 2. gen d`y' = f`y'_nb1 / f`y'_fmnb1 - 1 3. } . preserve . collapse (mean) d0-d12 . gen i = _n . reshape long d, i(i) j(y) (note: j = 0 1 2 3 4 5 6 7 8 9 10 11 12) Data wide -> long ----------------------------------------------------------------------------- Number of obs. 1 -> 13 Number of variables 14 -> 3 j variable (13 values) -> y xij variables: d0 d1 ... d12 -> d ----------------------------------------------------------------------------- . . display "Directional gradients from 2 component NB1 finite mixture model" Directional gradients from 2 component NB1 finite mixture model . list d y +----------------+ | d y | |----------------| 1. | .0937744 0 | 2. | .0042625 1 | 3. | -.0400999 2 | 4. | -.0575196 3 | 5. | -.0600343 4 | |----------------| 6. | -.0531821 5 | 7. | -.0399194 6 | 8. | -.0220267 7 | 9. | -.000694 8 | 10. | .0232024 9 | |----------------| 11. | .0489557 10 | 12. | .0759485 11 | 13. | .1036068 12 | +----------------+ . . *** FIGURE 6.2: OFP VISITS: DIRECTIONAL GRADIENTS . twoway line d y, xlabel(0(1)12) yline(0) . . restore . . ******* SENSITIVITY TO OUTLIERS (end 6.3.6) . . * Same model with original sample . fmm OFP $XLIST, components(2) mixtureof(negbin1) vce(robust) Fitting Negative Binomial-1 model: Iteration 0: log likelihood = -18134.655 Iteration 1: log likelihood = -18134.567 Iteration 2: log likelihood = -18134.567 Iteration 0: log likelihood = -14552.718 Iteration 1: log likelihood = -12647.886 Iteration 2: log likelihood = -12493.025 Iteration 3: log likelihood = -12492.829 Iteration 4: log likelihood = -12492.829 Iteration 0: log likelihood = -12492.829 Iteration 1: log likelihood = -12301.184 Iteration 2: log likelihood = -12157 Iteration 3: log likelihood = -12156.203 Iteration 4: log likelihood = -12156.202 Fitting 2 component Negative Binomial-1 model: Iteration 0: log pseudolikelihood = -12156.74 (not concave) Iteration 1: log pseudolikelihood = -12155.694 (not concave) Iteration 2: log pseudolikelihood = -12134.293 (not concave) Iteration 3: log pseudolikelihood = -12108.437 (not concave) Iteration 4: log pseudolikelihood = -12100.205 Iteration 5: log pseudolikelihood = -12095.077 Iteration 6: log pseudolikelihood = -12093.661 Iteration 7: log pseudolikelihood = -12092.693 Iteration 8: log pseudolikelihood = -12092.43 Iteration 9: log pseudolikelihood = -12092.429 Iteration 10: log pseudolikelihood = -12092.429 2 component Negative Binomial-1 regression Number of obs = 4406 Wald chi2(32) = 805.15 Log pseudolikelihood = -12092.429 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust OFP | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | EXCLHLTH | -.2290118 .0595272 -3.85 0.000 -.3456829 -.1123407 POORHLTH | .1499097 .058625 2.56 0.011 .0350068 .2648126 NUMCHRON | .1836232 .0145712 12.60 0.000 .1550641 .2121823 ADLDIFF | -.0520085 .0510709 -1.02 0.309 -.1521055 .0480886 NOREAST | .0546492 .0542024 1.01 0.313 -.0515856 .1608839 MIDWEST | .0191861 .045583 0.42 0.674 -.0701549 .1085271 WEST | .0944858 .047379 1.99 0.046 .0016248 .1873469 AGE | .0148273 .0308493 0.48 0.631 -.0456361 .0752908 BLACK | -.1799111 .0898293 -2.00 0.045 -.3559734 -.0038489 MALE | -.1377495 .0363032 -3.79 0.000 -.2089023 -.0665966 MARRIED | .0513625 .037287 1.38 0.168 -.0217187 .1244436 SCHOOL | .0133302 .0067885 1.96 0.050 .0000249 .0266354 FAMINC | .0007834 .0052861 0.15 0.882 -.0095773 .011144 EMPLOYED | -.0807253 .0543835 -1.48 0.138 -.1873149 .0258643 PRIVINS | .3593702 .0802377 4.48 0.000 .2021073 .5166331 MEDICAID | .4204549 .1516158 2.77 0.006 .1232933 .7176165 _cons | .7733975 .2661744 2.91 0.004 .2517052 1.29509 -------------+---------------------------------------------------------------- component2 | EXCLHLTH | -.8178674 .3848952 -2.12 0.034 -1.572248 -.0634866 POORHLTH | .718358 .3416314 2.10 0.035 .0487726 1.387943 NUMCHRON | .1908478 .0934393 2.04 0.041 .0077101 .3739855 ADLDIFF | .549827 .2893593 1.90 0.057 -.0173069 1.116961 NOREAST | .2279207 .4032265 0.57 0.572 -.5623887 1.01823 MIDWEST | -.0123035 .4114692 -0.03 0.976 -.8187683 .7941612 WEST | .2660744 .2891064 0.92 0.357 -.3005636 .8327125 AGE | -.1334189 .237275 -0.56 0.574 -.5984694 .3316316 BLACK | .2680242 .7090175 0.38 0.705 -1.121625 1.657673 MALE | -.0228589 .1936876 -0.12 0.906 -.4024796 .3567618 MARRIED | -.242328 .1950364 -1.24 0.214 -.6245924 .1399364 SCHOOL | .1023137 .0435288 2.35 0.019 .0169988 .1876287 FAMINC | -.0011579 .0128741 -0.09 0.928 -.0263908 .0240749 EMPLOYED | .5400458 .441916 1.22 0.222 -.3260937 1.406185 PRIVINS | .227208 .6916896 0.33 0.743 -1.128479 1.582895 MEDICAID | -.6163631 1.171503 -0.53 0.599 -2.912467 1.679741 _cons | 1.554799 2.130245 0.73 0.465 -2.620405 5.730003 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.290933 .3660583 6.26 0.000 1.573471 3.008394 /lndelta1 | 1.259071 .059816 21.05 0.000 1.141834 1.376308 /lndelta2 | 2.441911 .4394107 5.56 0.000 1.580682 3.30314 ------------------------------------------------------------------------------ delta1 | 3.522148 .210681 3.132507 3.960255 delta2 | 11.49499 5.05102 4.858268 27.19791 pi1 | .9081233 .0305422 .8282779 .9529519 pi2 | .0918767 .0305422 .0470481 .1717221 ------------------------------------------------------------------------------ . estimates store FMMorig . predict mu1, eq(component1) . predict mu2, eq(component2) . . * Altered and then original . * sum mu1alt mu2alt mu1 mu2 . estimates table FMMalt70 FMMorig, b(%10.3f) t(%10.2f) stats(ll aic bic N k) ---------------------------------------- Variable | FMMalt70 FMMorig -------------+-------------------------- component1 | EXCLHLTH | -0.250 -0.229 | -4.31 -3.85 POORHLTH | 0.234 0.150 | 3.59 2.56 NUMCHRON | 0.186 0.184 | 14.62 12.60 ADLDIFF | -0.016 -0.052 | -0.37 -1.02 NOREAST | 0.083 0.055 | 1.72 1.01 MIDWEST | 0.018 0.019 | 0.46 0.42 WEST | 0.089 0.094 | 1.82 1.99 AGE | 0.028 0.015 | 1.07 0.48 BLACK | -0.079 -0.180 | -1.12 -2.00 MALE | -0.136 -0.138 | -3.92 -3.79 MARRIED | 0.047 0.051 | 1.34 1.38 SCHOOL | 0.014 0.013 | 2.73 1.96 FAMINC | -0.000 0.001 | -0.06 0.15 EMPLOYED | -0.059 -0.081 | -1.04 -1.48 PRIVINS | 0.254 0.359 | 4.79 4.48 MEDICAID | 0.353 0.420 | 5.69 2.77 _cons | 0.778 0.773 | 3.48 2.91 -------------+-------------------------- component2 | EXCLHLTH | -0.751 -0.818 | -1.02 -2.12 POORHLTH | 0.039 0.718 | 0.06 2.10 NUMCHRON | 0.139 0.191 | 1.33 2.04 ADLDIFF | 0.546 0.550 | 2.04 1.90 NOREAST | 0.178 0.228 | 0.37 0.57 MIDWEST | 0.042 -0.012 | 0.12 -0.03 WEST | 0.236 0.266 | 0.49 0.92 AGE | -0.611 -0.133 | -2.47 -0.56 BLACK | -1.065 0.268 | -0.98 0.38 MALE | 0.120 -0.023 | 0.46 -0.12 MARRIED | -0.513 -0.242 | -1.55 -1.24 SCHOOL | 0.152 0.102 | 1.84 2.35 FAMINC | -0.005 -0.001 | -0.27 -0.09 EMPLOYED | 0.372 0.540 | 0.54 1.22 PRIVINS | 3.020 0.227 | 1.12 0.33 MEDICAID | -3.147 -0.616 | -0.97 -0.53 _cons | 1.862 1.555 | 0.71 0.73 -------------+-------------------------- imlogitpi1 | _cons | 2.334 2.291 | 6.73 6.26 -------------+-------------------------- lndelta1 | _cons | 1.251 1.259 | 15.44 21.05 -------------+-------------------------- lndelta2 | _cons | 2.797 2.442 | 6.86 5.56 -------------+-------------------------- Statistics | ll | -12076.909 -12092.429 aic | 24227.818 24258.858 bic | 24464.275 24495.315 N | 4406 4406 k | 37.000 37.000 ---------------------------------------- legend: b/t . . *** Also compare regular NB1 across the two samples (mentioned in text) and FMN-NB2 . . * Original sample - FMM-NB2 and regular NB1 . quietly fmm OFP $XLIST, components(2) mixtureof(negbin2) vce(robust) . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 4406 . -12139.31 37 24352.62 24589.08 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . quietly nbreg OFP $XLIST, dispersion(constant) vce(robust) . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 4406 -12492.83 -12156.2 18 24348.4 24463.44 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . . * Altered sample - FMM-NB2 and regular NB1 dispersion(constant) . preserve . replace OFP = 70 if OFP > 70 (1 real change made) . quietly fmm OFP $XLIST, components(2) mixtureof(negbin2) vce(robust) . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 4406 . -12138.46 37 24350.93 24587.38 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . quietly nbreg OFP $XLIST, dispersion(constant) vce(robust) . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 4406 -12489.8 -12152.74 18 24341.48 24456.51 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . restore . . ********** CLOSE OUTPUT . . * log close . * clear . * exit . . end of do-file . exit, clear