------------------------------------------------------------------------------------------------------------------------------- name: log: c:\acdbookrevision\stata_final_programs_2013\racd06p2.txt log type: text opened on: 25 Jan 2013, 09:42:34 . . ********** OVERVIEW OF racd06p2.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 . . * To run you need file . * racd06data2rectrips.dta . * and user-written Stata addon . * hnblgit . * in your directory . . ********** SETUP ********** . . set more off . version 12 . clear all . * set linesize 82 . set scheme s1mono /* Graphics scheme */ . . ************ . . * This STATA program analyzes doctor visits data for chapter 6.3 . * 6.4 RECREATIONAL TRIPS . . ********** DATA DESCRIPTION . . * A detailed discussion of the variables can be found in . * C. Sellar, J.R. Stoll and J.P. Chavas (1985), . * "Validation of Empirical Measures of Welfare Change: A Comparison of nonmarket . * Techniques," Land Economics, 61, 156-175. . * Data used with permission of Sellar et al. (1985) . * And also T. Ozuna and I. Gomaz (1995) . * "Specification and Testing of Count Data Recreation Demand Functions," . * Empirical Economics, 20, 543-550. . . * See these articles for more detailed discussion . * Also see racd06makedata2rectrips.dta.do for further details . . ********** RESULTS FOR ONE MODEL HERE DIFFER FROM THE BOOK . . * This Stata program reanalyzes the data given in the published paper by . * Gurmu and Trivedi (1996). Their results used quite different code written . * in a program other than Stata. . . * Virtually all the results are reproduced here, except chisquare goodness-of-fit . * tests and predicted probabilities are obtained only for some of the models. . . * Also the results obtained here for the finite mixture Poisson two-component . * model differ from the Gurmu and Trivedi (1996) estimates. . * Their paper found a higher log-likelihood for this model than we find here. . * So the book reports the original Gurmu and Trivedi (1996) estimates . . * The results obtained below for Table 6.12 are . * Finite mixture 2 component Poisson regression . * Variable Low Users High users . * -------------+---------------------------------------------------------------- . * _cons | -1.766 6.19 2.479 6.19 . * SO | .655 14.97 .086 0.63 . * SKI | .438 2.45 .631 3.43 . * I | -.010 0.20 .003 0.02 . * FC3 | 1.543 8.04 -.687 1.90 . * C1 | -.044 2.40 .074 3.36 . * C3 | -.030 2.85 -.073 5.66 . * C4 | .060 5.03 -.014 0.83 . * pi | .909 .092 . * -lnL | 939 . * BIC | 1987 . * . * Variable Low Users High users . * -------------+---------------------------------------------------------------- . * _cons | -1.243 -5.09 4.707 6.46 . * SO | .616 16.84 -.053 -0.63 . * SKI | .476 2.67 .363 1.64 . * I | -.073 -1.60 -.374 -3.24 . * FC3 | 1.316 7.02 -.849 -1.54 . * C1 | -.002 -0.14 .005 0.30 . * C3 | -.058 -7.53 -.012 -1.04 . * C4 | .054 5.22 -.005 -0.58 . * pi | .920 .080 . * lnL | 956 . * BIC | 1947 . . . ********** 6.4.1 RECREATIONAL TRIPS DATA: READ AND SUMMARIZE . . use racd06data2rectrips.dta, clear . . ********* Tables 6.9 and 6.10 Data Description . . *** TABLE 6.9: FREQUENCIES . . tabulate TRIPS Number of | boating | trips to | Lake | Somerville | in 1980 | Freq. Percent Cum. ------------+----------------------------------- 0 | 417 63.28 63.28 1 | 68 10.32 73.60 2 | 38 5.77 79.36 3 | 34 5.16 84.52 4 | 17 2.58 87.10 5 | 13 1.97 89.07 6 | 11 1.67 90.74 7 | 2 0.30 91.05 8 | 8 1.21 92.26 9 | 1 0.15 92.41 10 | 13 1.97 94.39 11 | 2 0.30 94.69 12 | 5 0.76 95.45 15 | 14 2.12 97.57 16 | 1 0.15 97.72 20 | 3 0.46 98.18 25 | 3 0.46 98.63 26 | 1 0.15 98.79 30 | 3 0.46 99.24 40 | 3 0.46 99.70 50 | 1 0.15 99.85 88 | 1 0.15 100.00 ------------+----------------------------------- Total | 659 100.00 . . *** TABLE 6.10: VARIABLE DESCRIPTIONS AND SUMMARY STATISTICS . . describe Contains data from racd06data2rectrips.dta obs: 659 vars: 8 7 Jun 2011 10:46 size: 21,088 ------------------------------------------------------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------------------------------------------------------- TRIPS float %9.0g Number of boating trips to Lake Somerville in 1980 SO float %9.0g Facility's subjective quality ranking on a scale of 1 to 5 SKI float %9.0g Equals 1 if engaged in water-skiing at Lake I float %9.0g Household income of the head of the group Income ($1,000/year) FC3 float %9.0g Equals 1 if user's fee paid at Lake Somerville C1 float %9.0g Dollar expenditure when visiting Lake Conroe C3 float %9.0g Dollar expenditure when visiting Lake Somerville C4 float %9.0g Dollar expenditure when visiting Lake Houston ------------------------------------------------------------------------------------------------------------------------------- Sorted by: . summarize Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- TRIPS | 659 2.24431 6.292475 0 88 SO | 659 1.418816 1.811986 0 5 SKI | 659 .3672231 .4824142 0 1 I | 659 3.852807 1.851937 1 9 FC3 | 659 .0197269 .1391657 0 1 -------------+-------------------------------------------------------- C1 | 659 55.4237 46.68265 4.34 493.77 C3 | 659 59.92805 46.37668 4.767 491.547 C4 | 659 55.9903 46.13321 5.7 491.049 . correlate (obs=659) | TRIPS SO SKI I FC3 C1 C3 C4 -------------+------------------------------------------------------------------------ TRIPS | 1.0000 SO | 0.3864 1.0000 SKI | 0.0790 0.1263 1.0000 I | -0.0600 0.0374 0.2936 1.0000 FC3 | 0.2791 0.1359 0.0278 -0.0241 1.0000 C1 | -0.0422 0.0772 0.1607 0.1379 0.0093 1.0000 C3 | -0.1237 0.0034 0.1547 0.1392 -0.0342 0.9767 1.0000 C4 | -0.0205 0.0898 0.1437 0.1176 0.0165 0.9865 0.9646 1.0000 . . ********* 6.4.2 INITIAL SPECIFICATIONS: POISSON and NB2 MODELS (Table 6.11) . . * Global for the regressors . global XLIST SO SKI I FC3 C1 C3 C4 . . * Poisson . poisson TRIPS $XLIST Iteration 0: log likelihood = -2866.625 Iteration 1: log likelihood = -1811.5015 Iteration 2: log likelihood = -1536.5136 Iteration 3: log likelihood = -1529.4565 Iteration 4: log likelihood = -1529.4313 Iteration 5: log likelihood = -1529.4313 Poisson regression Number of obs = 659 LR chi2(7) = 2543.90 Prob > chi2 = 0.0000 Log likelihood = -1529.4313 Pseudo R2 = 0.4540 ------------------------------------------------------------------------------ TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .4717259 .0170905 27.60 0.000 .4382291 .5052227 SKI | .4182137 .0571905 7.31 0.000 .3061224 .5303051 I | -.1113232 .0195885 -5.68 0.000 -.1497159 -.0729304 FC3 | .8981652 .0789854 11.37 0.000 .7433567 1.052974 C1 | -.0034297 .0031178 -1.10 0.271 -.0095405 .0026811 C3 | -.0425364 .0016703 -25.47 0.000 -.0458102 -.0392626 C4 | .0361336 .0027096 13.34 0.000 .0308229 .0414444 _cons | .2649934 .0937224 2.83 0.005 .0813009 .4486859 ------------------------------------------------------------------------------ . estimates store POISSdef . poisson TRIPS $XLIST, vce(robust) Iteration 0: log pseudolikelihood = -2866.625 Iteration 1: log pseudolikelihood = -1811.5015 Iteration 2: log pseudolikelihood = -1536.5136 Iteration 3: log pseudolikelihood = -1529.4565 Iteration 4: log pseudolikelihood = -1529.4313 Iteration 5: log pseudolikelihood = -1529.4313 Poisson regression Number of obs = 659 Wald chi2(7) = 273.48 Prob > chi2 = 0.0000 Log pseudolikelihood = -1529.4313 Pseudo R2 = 0.4540 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .4717259 .048887 9.65 0.000 .3759092 .5675426 SKI | .4182137 .1940159 2.16 0.031 .0379495 .798478 I | -.1113232 .0503458 -2.21 0.027 -.2099991 -.0126472 FC3 | .8981652 .2470961 3.63 0.000 .4138657 1.382465 C1 | -.0034297 .0147083 -0.23 0.816 -.0322575 .0253981 C3 | -.0425364 .0117435 -3.62 0.000 -.0655533 -.0195195 C4 | .0361336 .0093932 3.85 0.000 .0177232 .054544 _cons | .2649934 .4327988 0.61 0.540 -.5832767 1.113264 ------------------------------------------------------------------------------ . estimates store POISSON . . * Diagnostics . quietly glm TRIPS SO SKI I C1 C3 C4 FC3, vce(robust) family(poisson) . display "Pearson statistic = " e(dispers_p) Pearson statistic = 6.2981465 . display "Deviance statistic = " e(dispers) Deviance statistic = 3.5419133 . . * Now get various Rsquareds . predict yhat, mu . quietly correlate TRIPS yhat . display "Squared correlation of TRIPS and predicted mean = " r(rho)^2 Squared correlation of TRIPS and predicted mean = .16877406 . scalar deviance = e(deviance) . scalar pearson = e(deviance_p) . * Need to compare to intercept only model . quietly glm TRIPS, vce(robust) family(poisson) . display "Pearson in fitted model = " pearson " and in intercept model = " e(deviance_p) Pearson in fitted model = 4100.0934 and in intercept model = 11608.767 . display "Pearson R-squared = " pearson/e(deviance_p) Pearson R-squared = .3531894 . display "Deviance in fitted model = " deviance " and in intercept model = " e(deviance) Deviance in fitted model = 2305.7855 and in intercept model = 4849.6861 . display "Deviance R-squared = " deviance/e(deviance) Deviance R-squared = .47545047 . drop yhat . scalar drop pearson deviance . . * Overdispersion tests . quietly poisson TRIPS $XLIST . predict muhat, n . generate ystar = ((TRIPS-muhat)^2-TRIPS)/muhat . regress ystar muhat, noconstant vce(robust) // NB2 form Linear regression Number of obs = 659 F( 1, 658) = 8.31 Prob > F = 0.0041 R-squared = 0.0129 Root MSE = 59.121 ------------------------------------------------------------------------------ | Robust ystar | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- muhat | 1.316051 .4566598 2.88 0.004 .4193649 2.212737 ------------------------------------------------------------------------------ . regress ystar, vce(robust) // NB1 form Linear regression Number of obs = 659 F( 0, 658) = 0.00 Prob > F = . R-squared = 0.0000 Root MSE = 59.247 ------------------------------------------------------------------------------ | Robust ystar | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | 5.5658 2.307927 2.41 0.016 1.034011 10.09759 ------------------------------------------------------------------------------ . drop muhat ystar . . * Predicted probabilities . quietly poisson TRIPS $XLIST, vce(robust) . foreach y of numlist 0/5 8 11 14 17 62 { 2. predict pp`y', pr(`y') 3. predict cump`y', pr(0,`y') 4. } . replace pp8 = cump8 - cump5 (659 real changes made) . replace pp11 = cump11 - cump8 (659 real changes made) . replace pp14 = cump14 - cump11 (659 real changes made) . replace pp17 = cump17 - cump14 (654 real changes made) . replace pp62 = cump62 - cump17 (134 real changes made) . * sum pp* . * sum cump* . . * Chisquare goodness of fit test . * The cells are 0, 1, 2, ...., $MAXCOUNT or more . global MAXCOUNT 5 . generate ycensored = TRIPS . replace ycensored = $MAXCOUNT + 1 if TRIPS >= $MAXCOUNT + 1 (61 real changes made) . generate one = 1 . quietly poisson TRIPS $XLIST, vce(robust) . capture drop pyhat dy* pf* mf* py* pres* pscore* . predict pyhat, n . generate pres = TRIPS - pyhat . foreach var in $XLIST { 2. generate pscore`var' = pres*`var' 3. } . * The cells are 0, 1, 2, ...., $MAXCOUNT or more . generate pfitsum = 0 . forvalues i = 0/$MAXCOUNT { 2. generate dy`i' = ycensored == `i' 3. predict pfit`i', pr(`i') 4. generate mfit`i' = dy`i' - pfit`i' 5. quietly replace pfitsum = pfitsum + pfit`i' 6. } . local i = $MAXCOUNT+1 . generate dy`i' = ycensored == `i' . generate pfit`i' = 1 - pfitsum . generate mfit`i' = dy`i' - pfit`i' . drop pfitsum . * Generate Pearson . scalar Pearson = 0 . scalar range = $MAXCOUNT+1 . global MAXPLUSONE = range . forvalues i = 0/$MAXPLUSONE { 2. quietly sum mfit`i' 3. scalar diffsquared = r(mean)^2 4. quietly sum pfit`i' 5. * display "count" `i' " " r(N)*diffsquared/r(mean) . scalar Pearson = Pearson + r(N)*diffsquared/r(mean) 6. } . display Pearson 136.62723 . * countfit TRIPS $XLIST, prm nograph maxcount(6) . * Generate Andrews chisquare goodness of fittest . scalar range = $MAXCOUNT+1 . global MAXPLUSONE = range . * NR^2 from the uncentered regression has Chisq distribution . local i = $MAXCOUNT+1 . drop mfit`i' . regress one mfit* pres pscore*, noconstant Source | SS df MS Number of obs = 659 -------------+------------------------------ F( 14, 645) = 28.63 Model | 252.58037 14 18.041455 Prob > F = 0.0000 Residual | 406.41963 645 .630107954 R-squared = 0.3833 -------------+------------------------------ Adj R-squared = 0.3699 Total | 659 659 1 Root MSE = .79379 ------------------------------------------------------------------------------ one | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mfit0 | 2.415836 .2012938 12.00 0.000 2.020566 2.811107 mfit1 | .7793654 .1929628 4.04 0.000 .4004542 1.158277 mfit2 | .6401953 .1956595 3.27 0.001 .2559887 1.024402 mfit3 | .7144358 .1983843 3.60 0.000 .3248787 1.103993 mfit4 | .2145685 .2234262 0.96 0.337 -.224162 .6532991 mfit5 | -.0292655 .2515508 -0.12 0.907 -.5232229 .4646918 pres | -.0128264 .0203336 -0.63 0.528 -.0527545 .0271017 pscoreSO | -.0159804 .0057943 -2.76 0.006 -.0273584 -.0046024 pscoreSKI | -.0480466 .0164136 -2.93 0.004 -.0802772 -.015816 pscoreI | .0374864 .0081548 4.60 0.000 .0214732 .0534995 pscoreFC3 | -.0071467 .0267627 -0.27 0.790 -.0596992 .0454059 pscoreC1 | .0024056 .000729 3.30 0.001 .000974 .0038372 pscoreC3 | .001858 .0003785 4.91 0.000 .0011147 .0026013 pscoreC4 | -.0030179 .0007111 -4.24 0.000 -.0044142 -.0016216 ------------------------------------------------------------------------------ . scalar Andrews = e(N)*e(r2) . display "GoF Test N R^2 = " e(N)*e(r2) " with p-value = " chi2tail($MAXCOUNT,e(N)*e(r2)) GoF Test N R^2 = 252.58037 with p-value = 1.536e-52 . . * Negbin2 . nbreg TRIPS $XLIST, dispersion(mean) Fitting Poisson model: Iteration 0: log likelihood = -2866.625 Iteration 1: log likelihood = -1811.5015 Iteration 2: log likelihood = -1536.5136 Iteration 3: log likelihood = -1529.4565 Iteration 4: log likelihood = -1529.4313 Iteration 5: log likelihood = -1529.4313 Fitting constant-only model: Iteration 0: log likelihood = -1320.5971 Iteration 1: log likelihood = -1065.6673 Iteration 2: log likelihood = -1064.723 Iteration 3: log likelihood = -1064.7225 Iteration 4: log likelihood = -1064.7225 Fitting full model: Iteration 0: log likelihood = -992.69381 (not concave) Iteration 1: log likelihood = -922.08966 Iteration 2: log likelihood = -831.14918 Iteration 3: log likelihood = -825.59425 Iteration 4: log likelihood = -825.55759 Iteration 5: log likelihood = -825.55758 Negative binomial regression Number of obs = 659 LR chi2(7) = 478.33 Dispersion = mean Prob > chi2 = 0.0000 Log likelihood = -825.55758 Pseudo R2 = 0.2246 ------------------------------------------------------------------------------ TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .721999 .0453323 15.93 0.000 .6331493 .8108487 SKI | .6121388 .1504163 4.07 0.000 .3173282 .9069493 I | -.0260589 .0452342 -0.58 0.565 -.1147163 .0625986 FC3 | .6691677 .3614399 1.85 0.064 -.0392415 1.377577 C1 | .0480086 .0159516 3.01 0.003 .016744 .0792732 C3 | -.092691 .0082685 -11.21 0.000 -.1088969 -.0764851 C4 | .0388357 .0117139 3.32 0.001 .0158769 .0617945 _cons | -1.121936 .2208284 -5.08 0.000 -1.554752 -.6891205 -------------+---------------------------------------------------------------- /lnalpha | .3157293 .1060209 .1079321 .5235264 -------------+---------------------------------------------------------------- alpha | 1.371259 .1453821 1.113972 1.68797 ------------------------------------------------------------------------------ Likelihood-ratio test of alpha=0: chibar2(01) = 1407.75 Prob>=chibar2 = 0.000 . estimates store NB2def . nbreg TRIPS $XLIST, vce(robust) dispersion(mean) Fitting Poisson model: Iteration 0: log pseudolikelihood = -2866.625 Iteration 1: log pseudolikelihood = -1811.5015 Iteration 2: log pseudolikelihood = -1536.5136 Iteration 3: log pseudolikelihood = -1529.4565 Iteration 4: log pseudolikelihood = -1529.4313 Iteration 5: log pseudolikelihood = -1529.4313 Fitting constant-only model: Iteration 0: log pseudolikelihood = -1320.5971 Iteration 1: log pseudolikelihood = -1065.6673 Iteration 2: log pseudolikelihood = -1064.723 Iteration 3: log pseudolikelihood = -1064.7225 Iteration 4: log pseudolikelihood = -1064.7225 Fitting full model: Iteration 0: log pseudolikelihood = -992.69381 (not concave) Iteration 1: log pseudolikelihood = -922.08966 Iteration 2: log pseudolikelihood = -831.14918 Iteration 3: log pseudolikelihood = -825.59425 Iteration 4: log pseudolikelihood = -825.55759 Iteration 5: log pseudolikelihood = -825.55758 Negative binomial regression Number of obs = 659 Dispersion = mean Wald chi2(7) = 445.58 Log pseudolikelihood = -825.55758 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .721999 .0583691 12.37 0.000 .6075977 .8364004 SKI | .6121388 .2003177 3.06 0.002 .2195233 1.004754 I | -.0260589 .0548465 -0.48 0.635 -.1335561 .0814384 FC3 | .6691677 .3205802 2.09 0.037 .0408421 1.297493 C1 | .0480086 .0283108 1.70 0.090 -.0074795 .1034968 C3 | -.092691 .014518 -6.38 0.000 -.1211458 -.0642362 C4 | .0388357 .0177502 2.19 0.029 .004046 .0736254 _cons | -1.121936 .2964056 -3.79 0.000 -1.702881 -.5409919 -------------+---------------------------------------------------------------- /lnalpha | .3157293 .1350229 .0510892 .5803693 -------------+---------------------------------------------------------------- alpha | 1.371259 .1851514 1.052417 1.786698 ------------------------------------------------------------------------------ . estimates store NB2 . foreach y of numlist 0/5 8 11 14 17 62 { 2. predict pnb`y', pr(`y') 3. predict cumnb`y', pr(0,`y') 4. } . replace pnb8 = cumnb8 - cumnb5 (659 real changes made) . replace pnb11 = cumnb11 - cumnb8 (659 real changes made) . replace pnb14 = cumnb14 - cumnb11 (658 real changes made) . replace pnb17 = cumnb17 - cumnb14 (658 real changes made) . replace pnb62 = cumnb62 - cumnb17 (326 real changes made) . . * Negbin2 check: fitted mean is unusually large . predict munb2 (option n assumed; predicted number of events) . summarize munb2, detail Predicted number of events ------------------------------------------------------------- Percentiles Smallest 1% .0259999 .0006295 5% .0520313 .0147986 10% .0689261 .0151538 Obs 659 25% .111235 .0203141 Sum of Wgt. 659 50% .2366224 Mean 8.962897 Largest Std. Dev. 152.0876 75% 2.78074 66.65919 90% 8.571424 71.44934 Variance 23130.64 95% 15.47732 83.7941 Skewness 25.51657 99% 40.38062 3902.384 Kurtosis 653.7082 . . * Negbin1 . nbreg TRIPS $XLIST, vce(robust) dispersion(constant) Fitting Poisson model: Iteration 0: log pseudolikelihood = -2866.625 Iteration 1: log pseudolikelihood = -1811.5015 Iteration 2: log pseudolikelihood = -1536.5136 Iteration 3: log pseudolikelihood = -1529.4565 Iteration 4: log pseudolikelihood = -1529.4313 Iteration 5: log pseudolikelihood = -1529.4313 Fitting constant-only model: Iteration 0: log pseudolikelihood = -1604.1198 Iteration 1: log pseudolikelihood = -1446.016 Iteration 2: log pseudolikelihood = -1202.8116 Iteration 3: log pseudolikelihood = -1065.0775 Iteration 4: log pseudolikelihood = -1064.7226 Iteration 5: log pseudolikelihood = -1064.7225 Fitting full model: Iteration 0: log pseudolikelihood = -1064.7225 Iteration 1: log pseudolikelihood = -1054.8431 Iteration 2: log pseudolikelihood = -992.64056 Iteration 3: log pseudolikelihood = -868.3528 Iteration 4: log pseudolikelihood = -848.97958 Iteration 5: log pseudolikelihood = -833.63151 Iteration 6: log pseudolikelihood = -833.54833 Iteration 7: log pseudolikelihood = -833.54831 Negative binomial regression Number of obs = 659 Dispersion = constant Wald chi2(7) = 501.90 Log pseudolikelihood = -833.54831 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .5760759 .0273407 21.07 0.000 .5224891 .6296628 SKI | .181337 .1281728 1.41 0.157 -.0698771 .4325511 I | -.0179127 .0302619 -0.59 0.554 -.0772249 .0413994 FC3 | 1.034979 .2866802 3.61 0.000 .4730959 1.596862 C1 | .0018225 .0116311 0.16 0.875 -.0209741 .024619 C3 | -.0279032 .0090972 -3.07 0.002 -.0457333 -.0100731 C4 | .023511 .008059 2.92 0.004 .0077156 .0393063 _cons | -.6201893 .2049484 -3.03 0.002 -1.021881 -.2184979 -------------+---------------------------------------------------------------- /lndelta | 1.884622 .2013934 1.489898 2.279345 -------------+---------------------------------------------------------------- delta | 6.583863 1.325946 4.436642 9.770282 ------------------------------------------------------------------------------ . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 659 -1064.722 -833.5483 9 1685.097 1725.513 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . estimates store NB1 . predict munb1 (option n assumed; predicted number of events) . summarize munb1, detail Predicted number of events ------------------------------------------------------------- Percentiles Smallest 1% .2067848 .0625774 5% .2729032 .1470124 10% .3019193 .1746988 Obs 659 25% .3620908 .1768115 Sum of Wgt. 659 50% .4815007 Mean 2.244309 Largest Std. Dev. 3.82433 75% 3.122336 24.16492 90% 6.307141 30.96744 Variance 14.6255 95% 8.54717 36.73519 Skewness 5.185864 99% 14.80399 46.72718 Kurtosis 46.48673 . . * Negbin2 with quadratic and interactions in costs . generate C1sq = C1*C1 . generate C3sq = C3*C3 . generate C4sq = C4*C4 . generate C1C3 = C1*C3 . generate C1C4 = C1*C4 . generate C3C4 = C3*C4 . nbreg TRIPS SO I SKI FC3 C*, vce(robust) Fitting Poisson model: Iteration 0: log pseudolikelihood = -3184.358 Iteration 1: log pseudolikelihood = -2129.3162 Iteration 2: log pseudolikelihood = -1308.0042 Iteration 3: log pseudolikelihood = -1244.1194 Iteration 4: log pseudolikelihood = -1236.2064 Iteration 5: log pseudolikelihood = -1235.9239 Iteration 6: log pseudolikelihood = -1235.9221 Iteration 7: log pseudolikelihood = -1235.9221 Fitting constant-only model: Iteration 0: log pseudolikelihood = -1320.5971 Iteration 1: log pseudolikelihood = -1065.6673 Iteration 2: log pseudolikelihood = -1064.723 Iteration 3: log pseudolikelihood = -1064.7225 Iteration 4: log pseudolikelihood = -1064.7225 Fitting full model: Iteration 0: log pseudolikelihood = -992.32956 (not concave) Iteration 1: log pseudolikelihood = -882.58831 Iteration 2: log pseudolikelihood = -806.27482 Iteration 3: log pseudolikelihood = -802.84247 Iteration 4: log pseudolikelihood = -802.49382 Iteration 5: log pseudolikelihood = -802.49002 Iteration 6: log pseudolikelihood = -802.49002 Negative binomial regression Number of obs = 659 Dispersion = mean Wald chi2(13) = 531.29 Log pseudolikelihood = -802.49002 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .6776066 .0587344 11.54 0.000 .5624892 .7927239 I | -.0147004 .0530642 -0.28 0.782 -.1187044 .0893035 SKI | .5782513 .1885648 3.07 0.002 .2086711 .9478315 FC3 | .570499 .3344164 1.71 0.088 -.0849451 1.225943 C1 | .0857148 .0370514 2.31 0.021 .0130953 .1583343 C3 | -.1402702 .0209839 -6.68 0.000 -.181398 -.0991424 C4 | .0507941 .0237569 2.14 0.033 .0042313 .0973568 C1sq | -.0053421 .0018563 -2.88 0.004 -.0089804 -.0017038 C3sq | -.0008515 .0007621 -1.12 0.264 -.0023451 .0006422 C4sq | -.0002016 .0003803 -0.53 0.596 -.000947 .0005438 C1C3 | .0060414 .002118 2.85 0.004 .0018902 .0101926 C1C4 | .0038352 .0018945 2.02 0.043 .0001221 .0075483 C3C4 | -.003484 .0021661 -1.61 0.108 -.0077294 .0007614 _cons | -1.160403 .3250511 -3.57 0.000 -1.797492 -.5233147 -------------+---------------------------------------------------------------- /lnalpha | .0938501 .1339843 -.1687543 .3564544 -------------+---------------------------------------------------------------- alpha | 1.098395 .1471677 .8447164 1.428256 ------------------------------------------------------------------------------ . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 659 -1064.722 -802.49 15 1634.98 1702.341 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . predict munb2interact (option n assumed; predicted number of events) . summarize munb2interact, detail Predicted number of events ------------------------------------------------------------- Percentiles Smallest 1% .014851 1.46e-18 5% .0402354 .0041866 10% .061906 .0057527 Obs 659 25% .0988699 .0064088 Sum of Wgt. 659 50% .2306382 Mean 2.799993 Largest Std. Dev. 6.556366 75% 2.492393 38.06474 90% 8.111975 42.24525 Variance 42.98593 95% 13.57655 53.02405 Skewness 4.707932 99% 35.79942 70.33098 Kurtosis 32.9643 . . *** TABLE 6.11: POISSON and NB2 ESTIMATES . . estimates table POISSdef POISSON NB2def NB2, b(%9.3f) t(%10.2f) /// > stats(ll aic bic N k) equations(1) ------------------------------------------------------------------ Variable | POISSdef POISSON NB2def NB2 -------------+---------------------------------------------------- #1 | SO | 0.472 0.472 0.722 0.722 | 27.60 9.65 15.93 12.37 SKI | 0.418 0.418 0.612 0.612 | 7.31 2.16 4.07 3.06 I | -0.111 -0.111 -0.026 -0.026 | -5.68 -2.21 -0.58 -0.48 FC3 | 0.898 0.898 0.669 0.669 | 11.37 3.63 1.85 2.09 C1 | -0.003 -0.003 0.048 0.048 | -1.10 -0.23 3.01 1.70 C3 | -0.043 -0.043 -0.093 -0.093 | -25.47 -3.62 -11.21 -6.38 C4 | 0.036 0.036 0.039 0.039 | 13.34 3.85 3.32 2.19 _cons | 0.265 0.265 -1.122 -1.122 | 2.83 0.61 -5.08 -3.79 -------------+---------------------------------------------------- lnalpha | _cons | 0.316 0.316 | 2.98 2.34 -------------+---------------------------------------------------- Statistics | ll | -1529.431 -1529.431 -825.558 -825.558 aic | 3074.863 3074.863 1669.115 1669.115 bic | 3110.788 3110.788 1709.532 1709.532 N | 659 659 659 659 k | 8.000 8.000 9.000 9.000 ------------------------------------------------------------------ legend: b/t . . *** TABLE 6.14 (Part 1): PREDICTED PROBABILITIES FROM POISSON AND NB2 . . tabulate TRIPS Number of | boating | trips to | Lake | Somerville | in 1980 | Freq. Percent Cum. ------------+----------------------------------- 0 | 417 63.28 63.28 1 | 68 10.32 73.60 2 | 38 5.77 79.36 3 | 34 5.16 84.52 4 | 17 2.58 87.10 5 | 13 1.97 89.07 6 | 11 1.67 90.74 7 | 2 0.30 91.05 8 | 8 1.21 92.26 9 | 1 0.15 92.41 10 | 13 1.97 94.39 11 | 2 0.30 94.69 12 | 5 0.76 95.45 15 | 14 2.12 97.57 16 | 1 0.15 97.72 20 | 3 0.46 98.18 25 | 3 0.46 98.63 26 | 1 0.15 98.79 30 | 3 0.46 99.24 40 | 3 0.46 99.70 50 | 1 0.15 99.85 88 | 1 0.15 100.00 ------------+----------------------------------- Total | 659 100.00 . sum pp* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- pp0 | 659 .4196377 .2993687 7.85e-37 .982392 pp1 | 659 .2208405 .1181427 6.52e-35 .3678773 pp2 | 659 .1030655 .080823 2.71e-33 .2706588 pp3 | 659 .0616823 .0749082 7.52e-32 .2240418 pp4 | 659 .0448711 .0671734 1.56e-30 .1953618 -------------+-------------------------------------------------------- pp5 | 659 .0344572 .0580832 2.60e-29 .175465 pp8 | 659 .060924 .1206823 0 .4284386 pp11 | 659 .0255609 .0718394 0 .3630392 pp14 | 659 .0117349 .0483664 0 .3211519 pp17 | 659 .0059385 .0321014 0 .2905961 -------------+-------------------------------------------------------- pp62 | 659 .0097842 .0810561 0 .9994811 . sum cump* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- cump0 | 659 .4196377 .2993687 7.85e-37 .982392 cump1 | 659 .6404782 .3694934 6.60e-35 .9998441 cump2 | 659 .7435437 .3554941 2.78e-33 .9999991 cump3 | 659 .8052259 .32044 7.79e-32 1 cump4 | 659 .8500971 .2834526 1.64e-30 1 -------------+-------------------------------------------------------- cump5 | 659 .8845543 .2500909 2.76e-29 1 cump8 | 659 .9454783 .1785921 4.91e-26 1 cump11 | 659 .9710392 .1349753 2.96e-23 1 cump14 | 659 .9827741 .1070785 8.13e-21 1 cump17 | 659 .9887126 .0897666 1.20e-18 1 -------------+-------------------------------------------------------- cump62 | 659 .9984968 .0385877 .0094143 1 . sum pnb* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- pnb0 | 659 .6418745 .3082488 .0019096 .9993709 pnb1 | 659 .1224031 .0561099 .0006286 .224679 pnb2 | 659 .0503028 .0452092 4.69e-07 .1293086 pnb3 | 659 .0303256 .0347147 3.68e-10 .0908396 pnb4 | 659 .0214932 .027299 2.96e-13 .0700097 -------------+-------------------------------------------------------- pnb5 | 659 .0164107 .0221661 2.41e-16 .0569552 pnb8 | 659 .032676 .0475893 0 .1254335 pnb11 | 659 .0196791 .0316183 0 .0887708 pnb14 | 659 .0131008 .0228531 0 .0687326 pnb17 | 659 .0092751 .0174332 0 .0560916 -------------+-------------------------------------------------------- pnb62 | 659 .034165 .0829472 0 .366749 . sum cumnb* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- cumnb0 | 659 .6418745 .3082488 .0019096 .9993709 cumnb1 | 659 .7642776 .296349 .0033019 .9999995 cumnb2 | 659 .8145804 .26861 .0045056 1 cumnb3 | 659 .844906 .244619 .0056004 1 cumnb4 | 659 .8663992 .2249148 .0066209 1 -------------+-------------------------------------------------------- cumnb5 | 659 .8828099 .2085443 .0075859 1 cumnb8 | 659 .9154859 .1724799 .0102482 1 cumnb11 | 659 .935165 .1480781 .0126716 1 cumnb14 | 659 .9482658 .1302771 .0149316 1 cumnb17 | 659 .9575409 .116646 .0170694 1 -------------+-------------------------------------------------------- cumnb62 | 659 .9917059 .0520976 .0425734 1 . . ********* 6.4.3 MODIFIED COUNT MODELS (Tables 6.12 and 6.13) . . *** FINITE MIXTURES MODELS (Table 6.12) . . ** Note: finite Mixtrues here does not reproduce earlier results of Gurmu and Trivedi . * They have lnL = -916.63 . * Here lnL = -938.66 if use difficult option and . * and lnL = -956.84 if do not. . * Gurmu and Trivedi found lower lnL so report that. . . * Finite mixtures Poisson - 2 components unconstrained . * Without difficult option . fmm TRIPS $XLIST, components(2) mixtureof(poisson) vce(robust) Fitting Poisson model: Iteration 0: log likelihood = -2866.625 Iteration 1: log likelihood = -1811.5015 Iteration 2: log likelihood = -1536.5136 Iteration 3: log likelihood = -1529.4565 Iteration 4: log likelihood = -1529.4313 Iteration 5: log likelihood = -1529.4313 Fitting 2 component Poisson model: Iteration 0: log pseudolikelihood = -1524.4609 (not concave) Iteration 1: log pseudolikelihood = -1217.3991 Iteration 2: log pseudolikelihood = -1138.4069 (not concave) Iteration 3: log pseudolikelihood = -1115.5687 (not concave) Iteration 4: log pseudolikelihood = -1080.2392 (not concave) Iteration 5: log pseudolikelihood = -1080.0906 (not concave) Iteration 6: log pseudolikelihood = -1069.6348 (not concave) Iteration 7: log pseudolikelihood = -1048.0558 (not concave) Iteration 8: log pseudolikelihood = -1011.9261 (not concave) Iteration 9: log pseudolikelihood = -996.26291 (not concave) Iteration 10: log pseudolikelihood = -990.61711 Iteration 11: log pseudolikelihood = -960.5608 Iteration 12: log pseudolikelihood = -957.22066 Iteration 13: log pseudolikelihood = -956.8399 Iteration 14: log pseudolikelihood = -956.83968 Iteration 15: log pseudolikelihood = -956.83968 2 component Poisson regression Number of obs = 659 Wald chi2(14) = 1111.14 Log pseudolikelihood = -956.83968 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | SO | .6125998 .0363714 16.84 0.000 .5413132 .6838865 SKI | .4763238 .1781983 2.67 0.008 .1270616 .825586 I | -.073048 .0456672 -1.60 0.110 -.1625541 .0164581 FC3 | 1.315873 .1875421 7.02 0.000 .9482973 1.683449 C1 | -.0017 .01179 -0.14 0.885 -.024808 .0214079 C3 | -.0580426 .0077103 -7.53 0.000 -.0731546 -.0429307 C4 | .0543631 .0104186 5.22 0.000 .0339431 .0747832 _cons | -1.243061 .2442 -5.09 0.000 -1.721684 -.7644376 -------------+---------------------------------------------------------------- component2 | SO | -.0530802 .0836292 -0.63 0.526 -.2169903 .11083 SKI | .3634098 .2212908 1.64 0.101 -.0703122 .7971318 I | -.3740674 .1153315 -3.24 0.001 -.6001129 -.1480218 FC3 | -.8493415 .5523961 -1.54 0.124 -1.932018 .233335 C1 | .0048554 .0161729 0.30 0.764 -.026843 .0365537 C3 | -.0118398 .0113883 -1.04 0.299 -.0341604 .0104808 C4 | -.0051648 .0089645 -0.58 0.565 -.0227349 .0124053 _cons | 4.707441 .7283489 6.46 0.000 3.279904 6.134979 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.441621 .1749126 13.96 0.000 2.098799 2.784443 ------------------------------------------------------------------------------ pi1 | .9199465 .0128814 .8907863 .9418293 pi2 | .0800535 .0128814 .0581707 .1092137 ------------------------------------------------------------------------------ . . * Finite mixtures Poisson - 2 components unconstrained . * With difficult option . fmm TRIPS $XLIST, components(2) mixtureof(poisson) vce(robust) difficult Fitting Poisson model: Iteration 0: log likelihood = -2866.625 Iteration 1: log likelihood = -1811.5015 Iteration 2: log likelihood = -1536.5136 Iteration 3: log likelihood = -1529.4565 Iteration 4: log likelihood = -1529.4313 Iteration 5: log likelihood = -1529.4313 Fitting 2 component Poisson model: Iteration 0: log pseudolikelihood = -1524.4609 (not concave) Iteration 1: log pseudolikelihood = -1280.3416 (not concave) Iteration 2: log pseudolikelihood = -1214.9785 (not concave) Iteration 3: log pseudolikelihood = -1046.3108 (not concave) Iteration 4: log pseudolikelihood = -961.73474 Iteration 5: log pseudolikelihood = -959.10633 Iteration 6: log pseudolikelihood = -954.30525 Iteration 7: log pseudolikelihood = -948.87554 Iteration 8: log pseudolikelihood = -948.81289 Iteration 9: log pseudolikelihood = -942.35939 Iteration 10: log pseudolikelihood = -938.71046 Iteration 11: log pseudolikelihood = -938.66008 Iteration 12: log pseudolikelihood = -938.66004 2 component Poisson regression Number of obs = 659 Wald chi2(14) = 943.65 Log pseudolikelihood = -938.66004 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | SO | .6551551 .0437756 14.97 0.000 .5693564 .7409537 SKI | .4376842 .1787585 2.45 0.014 .0873241 .7880443 I | -.0098197 .049289 -0.20 0.842 -.1064245 .086785 FC3 | 1.542281 .1919338 8.04 0.000 1.166098 1.918465 C1 | -.0442385 .0184437 -2.40 0.016 -.0803875 -.0080894 C3 | -.0292213 .0102599 -2.85 0.004 -.0493303 -.0091123 C4 | .0695349 .0138194 5.03 0.000 .0424494 .0966203 _cons | -1.766423 .2855313 -6.19 0.000 -2.326054 -1.206792 -------------+---------------------------------------------------------------- component2 | SO | .0859619 .1370339 0.63 0.530 -.1826197 .3545435 SKI | .630614 .1841031 3.43 0.001 .2697785 .9914495 I | .002736 .1559299 0.02 0.986 -.302881 .3083531 FC3 | -.6874224 .3623183 -1.90 0.058 -1.397553 .0227084 C1 | .0740427 .0220197 3.36 0.001 .0308848 .1172005 C3 | -.072647 .012837 -5.66 0.000 -.0978071 -.0474869 C4 | -.0137317 .0166229 -0.83 0.409 -.0463119 .0188485 _cons | 2.479197 1.10946 2.23 0.025 .3046957 4.653698 -------------+---------------------------------------------------------------- /imlogitpi1 | 2.298382 .213278 10.78 0.000 1.880365 2.716399 ------------------------------------------------------------------------------ pi1 | .9087429 .017687 .867653 .9379874 pi2 | .0912571 .017687 .0620126 .132347 ------------------------------------------------------------------------------ . estimates store FMP2 . predict fmmpmu1, eq(component1) . predict fmmpmu2, eq(component2) . summarize fmmpmu1 fmmpmu2, detail predicted mean: component1 ------------------------------------------------------------- Percentiles Smallest 1% .0417949 .0021269 5% .0655968 .0089509 10% .0787248 .0232972 Obs 659 25% .1112899 .0296951 Sum of Wgt. 659 50% .2107916 Mean 1.586541 Largest Std. Dev. 8.625211 75% 1.390841 23.42982 90% 3.381974 31.72486 Variance 74.39427 95% 5.191111 45.49994 Skewness 21.10818 99% 18.00034 207.6996 Kurtosis 497.778 predicted mean: component2 ------------------------------------------------------------- Percentiles Smallest 1% .4786181 .0779567 5% 1.571355 .0811914 10% 2.324083 .0968075 Obs 659 25% 3.564886 .1239639 Sum of Wgt. 659 50% 5.936271 Mean 18.12704 Largest Std. Dev. 196.6486 75% 10.94436 54.97381 90% 16.15627 77.84518 Variance 38670.67 95% 24.3079 1534.837 Skewness 22.81481 99% 50.37337 4818.031 Kurtosis 545.6433 . . * Finite mixtures NB2 - 2 components unconstrained . fmm TRIPS $XLIST, components(2) mixtureof(negbin2) vce(robust) Fitting Negative Binomial-2 model: Iteration 0: log likelihood = -2866.625 Iteration 1: log likelihood = -1811.5015 Iteration 2: log likelihood = -1536.5136 Iteration 3: log likelihood = -1529.4565 Iteration 4: log likelihood = -1529.4313 Iteration 5: log likelihood = -1529.4313 Iteration 0: log likelihood = -1320.5971 Iteration 1: log likelihood = -1065.6673 Iteration 2: log likelihood = -1064.723 Iteration 3: log likelihood = -1064.7225 Iteration 4: log likelihood = -1064.7225 Iteration 0: log likelihood = -992.69381 (not concave) Iteration 1: log likelihood = -922.08966 Iteration 2: log likelihood = -831.14918 Iteration 3: log likelihood = -825.59425 Iteration 4: log likelihood = -825.55759 Iteration 5: log likelihood = -825.55758 Fitting 2 component Negative Binomial-2 model: Iteration 0: log pseudolikelihood = -825.5329 (not concave) Iteration 1: log pseudolikelihood = -825.45949 (not concave) Iteration 2: log pseudolikelihood = -823.21264 (not concave) Iteration 3: log pseudolikelihood = -811.45138 (not concave) Iteration 4: log pseudolikelihood = -806.56567 (not concave) Iteration 5: log pseudolikelihood = -805.06456 (not concave) Iteration 6: log pseudolikelihood = -803.84485 (not concave) Iteration 7: log pseudolikelihood = -803.26165 (not concave) Iteration 8: log pseudolikelihood = -802.79504 (not concave) Iteration 9: log pseudolikelihood = -802.37502 (not concave) Iteration 10: log pseudolikelihood = -801.93829 (not concave) Iteration 11: log pseudolikelihood = -801.50465 (not concave) Iteration 12: log pseudolikelihood = -801.07984 (not concave) Iteration 13: log pseudolikelihood = -800.67995 (not concave) Iteration 14: log pseudolikelihood = -800.32312 (not concave) Iteration 15: log pseudolikelihood = -799.99895 Iteration 16: log pseudolikelihood = -796.70987 (not concave) Iteration 17: log pseudolikelihood = -796.11797 (not concave) Iteration 18: log pseudolikelihood = -795.85818 Iteration 19: log pseudolikelihood = -794.76895 Iteration 20: log pseudolikelihood = -791.38168 Iteration 21: log pseudolikelihood = -791.09041 (not concave) Iteration 22: log pseudolikelihood = -791.0208 (not concave) Iteration 23: log pseudolikelihood = -790.89092 (not concave) Iteration 24: log pseudolikelihood = -790.74051 (not concave) Iteration 25: log pseudolikelihood = -790.5897 (not concave) Iteration 26: log pseudolikelihood = -790.21083 (not concave) Iteration 27: log pseudolikelihood = -790.14548 Iteration 28: log pseudolikelihood = -789.83716 (not concave) Iteration 29: log pseudolikelihood = -788.71971 Iteration 30: log pseudolikelihood = -787.77451 Iteration 31: log pseudolikelihood = -786.69223 Iteration 32: log pseudolikelihood = -786.07348 Iteration 33: log pseudolikelihood = -786.03456 Iteration 34: log pseudolikelihood = -786.01032 Iteration 35: log pseudolikelihood = -786.01004 Iteration 36: log pseudolikelihood = -786.01004 2 component Negative Binomial-2 regression Number of obs = 659 Wald chi2(14) = 971.59 Log pseudolikelihood = -786.01004 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | SO | .8897931 .0447052 19.90 0.000 .8021725 .9774138 SKI | .4493153 .1794648 2.50 0.012 .0975707 .8010598 I | -.0487088 .0476779 -1.02 0.307 -.1421558 .0447381 FC3 | 1.069746 .3599138 2.97 0.003 .3643283 1.775165 C1 | -.0001105 .0178368 -0.01 0.995 -.0350701 .034849 C3 | -.0500733 .0095576 -5.24 0.000 -.0688059 -.0313407 C4 | .0469594 .0151094 3.11 0.002 .0173455 .0765732 _cons | -1.876866 .2056477 -9.13 0.000 -2.279928 -1.473804 -------------+---------------------------------------------------------------- component2 | SO | -.0949407 .2232259 -0.43 0.671 -.5324554 .3425739 SKI | 1.369172 .3856075 3.55 0.000 .613395 2.124949 I | -.0327249 .1394548 -0.23 0.814 -.3060514 .2406015 FC3 | -.1294348 .3026502 -0.43 0.669 -.7226183 .4637488 C1 | .1858894 .0247869 7.50 0.000 .1373079 .2344708 C3 | -.2527872 .0265495 -9.52 0.000 -.3048233 -.2007512 C4 | .0486012 .0142185 3.42 0.001 .0207335 .0764689 _cons | 1.006089 .9680322 1.04 0.299 -.8912195 2.903397 -------------+---------------------------------------------------------------- /imlogitpi1 | 1.952194 .5181711 3.77 0.000 .9365978 2.967791 /lnalpha1 | -.1916578 .1318739 -1.45 0.146 -.4501258 .0668102 /lnalpha2 | -1.646558 .5327954 -3.09 0.002 -2.690818 -.6022984 ------------------------------------------------------------------------------ alpha1 | .8255893 .1088737 .6375479 1.069093 alpha2 | .192712 .1026761 .0678254 .5475517 pi1 | .8756857 .0564082 .7184119 .9510976 pi2 | .1243143 .0564082 .0489024 .2815881 ------------------------------------------------------------------------------ . estimates store FMNB2 . predict fmmnb2mu1, eq(component1) . predict fmmnb2mu2, eq(component2) . summarize fmmnb2mu1 fmmnb2mu2, detail predicted mean: component1 ------------------------------------------------------------- Percentiles Smallest 1% .0282895 .0033164 5% .0485094 .0224942 10% .0559414 .0236705 Obs 659 25% .0765332 .0250522 Sum of Wgt. 659 50% .1354479 Mean 2.767834 Largest Std. Dev. 11.62284 75% 2.365206 56.20646 90% 6.883991 64.61595 Variance 135.0904 95% 12.02669 73.07887 Skewness 16.80953 99% 30.49224 257.0614 Kurtosis 353.0671 predicted mean: component2 ------------------------------------------------------------- Percentiles Smallest 1% .001958 2.06e-07 5% .0111711 .0003645 10% .0248065 .0004218 Obs 659 25% .0938323 .0009144 Sum of Wgt. 659 50% .2847602 Mean 29313.54 Largest Std. Dev. 539008.6 75% 1.623237 845.1647 90% 10.30647 62751.63 Variance 2.91e+11 95% 31.85419 7829068 Skewness 18.96553 99% 251.8368 1.14e+07 Kurtosis 370.3982 . . * Finite mixtures NB1 - 2 components unconstrained . fmm TRIPS $XLIST, components(2) mixtureof(negbin1) vce(robust) Fitting Negative Binomial-1 model: Iteration 0: log likelihood = -2866.625 Iteration 1: log likelihood = -1811.5015 Iteration 2: log likelihood = -1536.5136 Iteration 3: log likelihood = -1529.4565 Iteration 4: log likelihood = -1529.4313 Iteration 5: log likelihood = -1529.4313 Iteration 0: log likelihood = -1604.1198 Iteration 1: log likelihood = -1446.016 Iteration 2: log likelihood = -1202.8116 Iteration 3: log likelihood = -1065.0775 Iteration 4: log likelihood = -1064.7226 Iteration 5: log likelihood = -1064.7225 Iteration 0: log likelihood = -1064.7225 Iteration 1: log likelihood = -1054.8431 Iteration 2: log likelihood = -992.64056 Iteration 3: log likelihood = -868.3528 Iteration 4: log likelihood = -848.97958 Iteration 5: log likelihood = -833.63151 Iteration 6: log likelihood = -833.54833 Iteration 7: log likelihood = -833.54831 Fitting 2 component Negative Binomial-1 model: Iteration 0: log pseudolikelihood = -833.54883 (not concave) Iteration 1: log pseudolikelihood = -832.9275 (not concave) Iteration 2: log pseudolikelihood = -831.58497 (not concave) Iteration 3: log pseudolikelihood = -823.67474 (not concave) Iteration 4: log pseudolikelihood = -820.6545 (not concave) Iteration 5: log pseudolikelihood = -818.97364 (not concave) Iteration 6: log pseudolikelihood = -817.04827 (not concave) Iteration 7: log pseudolikelihood = -815.57719 (not concave) Iteration 8: log pseudolikelihood = -814.56683 (not concave) Iteration 9: log pseudolikelihood = -813.57901 (not concave) Iteration 10: log pseudolikelihood = -810.51864 (not concave) Iteration 11: log pseudolikelihood = -807.62792 (not concave) Iteration 12: log pseudolikelihood = -806.16542 (not concave) Iteration 13: log pseudolikelihood = -805.36078 (not concave) Iteration 14: log pseudolikelihood = -804.54236 (not concave) Iteration 15: log pseudolikelihood = -802.40439 (not concave) Iteration 16: log pseudolikelihood = -801.25777 (not concave) Iteration 17: log pseudolikelihood = -800.8177 (not concave) Iteration 18: log pseudolikelihood = -800.58694 (not concave) Iteration 19: log pseudolikelihood = -800.3811 (not concave) Iteration 20: log pseudolikelihood = -800.22547 (not concave) Iteration 21: log pseudolikelihood = -800.09644 (not concave) Iteration 22: log pseudolikelihood = -799.98204 (not concave) Iteration 23: log pseudolikelihood = -799.85523 (not concave) Iteration 24: log pseudolikelihood = -799.65886 (not concave) Iteration 25: log pseudolikelihood = -799.51985 (not concave) Iteration 26: log pseudolikelihood = -799.37826 (not concave) Iteration 27: log pseudolikelihood = -799.2473 (not concave) Iteration 28: log pseudolikelihood = -799.15169 (not concave) Iteration 29: log pseudolikelihood = -799.08573 (not concave) Iteration 30: log pseudolikelihood = -799.01712 (not concave) Iteration 31: log pseudolikelihood = -797.43501 (not concave) Iteration 32: log pseudolikelihood = -796.76575 (not concave) Iteration 33: log pseudolikelihood = -796.59355 (not concave) Iteration 34: log pseudolikelihood = -796.53124 (not concave) Iteration 35: log pseudolikelihood = -796.48198 (not concave) Iteration 36: log pseudolikelihood = -796.44097 (not concave) Iteration 37: log pseudolikelihood = -796.40559 (not concave) Iteration 38: log pseudolikelihood = -796.36935 (not concave) Iteration 39: log pseudolikelihood = -796.34033 (not concave) Iteration 40: log pseudolikelihood = -796.31301 (not concave) Iteration 41: log pseudolikelihood = -796.28411 (not concave) Iteration 42: log pseudolikelihood = -796.25644 (not concave) Iteration 43: log pseudolikelihood = -796.22963 (not concave) Iteration 44: log pseudolikelihood = -796.20184 (not concave) Iteration 45: log pseudolikelihood = -796.17326 (not concave) Iteration 46: log pseudolikelihood = -796.14422 (not concave) Iteration 47: log pseudolikelihood = -796.11461 (not concave) Iteration 48: log pseudolikelihood = -796.08421 (not concave) Iteration 49: log pseudolikelihood = -796.05324 (not concave) Iteration 50: log pseudolikelihood = -796.02187 (not concave) Iteration 51: log pseudolikelihood = -795.99023 (not concave) Iteration 52: log pseudolikelihood = -795.95831 (not concave) Iteration 53: log pseudolikelihood = -795.92621 (not concave) Iteration 54: log pseudolikelihood = -795.8939 (not concave) Iteration 55: log pseudolikelihood = -795.8614 (not concave) Iteration 56: log pseudolikelihood = -795.8286 (not concave) Iteration 57: log pseudolikelihood = -795.79549 (not concave) Iteration 58: log pseudolikelihood = -795.762 (not concave) Iteration 59: log pseudolikelihood = -795.72809 (not concave) Iteration 60: log pseudolikelihood = -795.69373 (not concave) Iteration 61: log pseudolikelihood = -795.6589 (not concave) Iteration 62: log pseudolikelihood = -795.62358 (not concave) Iteration 63: log pseudolikelihood = -795.58783 (not concave) Iteration 64: log pseudolikelihood = -795.55167 (not concave) Iteration 65: log pseudolikelihood = -795.51522 Iteration 66: log pseudolikelihood = -794.99016 Iteration 67: log pseudolikelihood = -794.58803 Iteration 68: log pseudolikelihood = -794.58224 Iteration 69: log pseudolikelihood = -794.58222 2 component Negative Binomial-1 regression Number of obs = 659 Wald chi2(14) = 965.62 Log pseudolikelihood = -794.58222 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | SO | .92547 .0626901 14.76 0.000 .8025996 1.04834 SKI | -.4255404 .2365718 -1.80 0.072 -.8892126 .0381318 I | .0731551 .1204633 0.61 0.544 -.1629485 .3092588 FC3 | -.6314727 .2284892 -2.76 0.006 -1.079303 -.1836421 C1 | -.0270125 .017598 -1.53 0.125 -.0615039 .0074789 C3 | .0025677 .0060045 0.43 0.669 -.0092009 .0143362 C4 | .0253309 .0160878 1.57 0.115 -.0062006 .0568623 _cons | -2.63441 .4901937 -5.37 0.000 -3.595172 -1.673648 -------------+---------------------------------------------------------------- component2 | SO | .5105455 .0418441 12.20 0.000 .4285325 .5925585 SKI | .7456464 .1503196 4.96 0.000 .4510255 1.040267 I | -.0543847 .0438442 -1.24 0.215 -.1403177 .0315484 FC3 | .3046122 .2396505 1.27 0.204 -.1650941 .7743185 C1 | .0596445 .0110443 5.40 0.000 .0379981 .0812909 C3 | -.0963347 .0102403 -9.41 0.000 -.1164053 -.076264 C4 | .0298933 .0074505 4.01 0.000 .0152906 .044496 _cons | -.2869701 .2608747 -1.10 0.271 -.7982752 .2243349 -------------+---------------------------------------------------------------- /imlogitpi1 | -.7479719 .2559513 -2.92 0.003 -1.249627 -.2463166 /lndelta1 | -13.69168 1.777844 -7.70 0.000 -17.17619 -10.20717 /lndelta2 | 1.742019 .2504394 6.96 0.000 1.251167 2.232871 ------------------------------------------------------------------------------ delta1 | 1.13e-06 2.01e-06 3.47e-08 .0000369 delta2 | 5.708858 1.429723 3.494418 9.326606 pi1 | .3212634 .055811 .2227647 .4387303 pi2 | .6787366 .055811 .5612697 .7772353 ------------------------------------------------------------------------------ . estimates store FMNB1 . predict fmmnb1mu1, eq(component1) . predict fmmnb1mu2, eq(component2) . summarize fmmnb1mu1 fmmnb1mu2, detail predicted mean: component1 ------------------------------------------------------------- Percentiles Smallest 1% .0527696 .004925 5% .0619004 .0476774 10% .0706775 .0503531 Obs 659 25% .0859038 .0505571 Sum of Wgt. 659 50% .1169077 Mean 1.417252 Largest Std. Dev. 2.784524 75% 1.378191 12.67304 90% 4.676682 14.10757 Variance 7.753572 95% 7.774936 14.69514 Skewness 3.591086 99% 11.82099 29.77579 Kurtosis 23.17944 predicted mean: component2 ------------------------------------------------------------- Percentiles Smallest 1% .0465634 .0011169 5% .093645 .0234085 10% .1364622 .0250417 Obs 659 25% .2231292 .0328587 Sum of Wgt. 659 50% .470687 Mean 8.843421 Largest Std. Dev. 152.461 75% 2.893963 42.72643 90% 7.871804 66.10026 Variance 23244.35 95% 12.31917 83.66249 Skewness 25.53441 99% 38.01073 3912.738 Kurtosis 654.3214 . . * TO DO - get predicted probabilities . . * Finite mixtures NB2 with quadratic and interactions in costs . fmm TRIPS SO I SKI FC3 C*, components(2) mixtureof(negbin2) vce(robust) iter(120) Fitting Negative Binomial-2 model: Iteration 0: log likelihood = -3184.358 Iteration 1: log likelihood = -2129.3162 Iteration 2: log likelihood = -1308.0042 Iteration 3: log likelihood = -1244.1194 Iteration 4: log likelihood = -1236.2064 Iteration 5: log likelihood = -1235.9239 Iteration 6: log likelihood = -1235.9221 Iteration 7: log likelihood = -1235.9221 Iteration 0: log likelihood = -1320.5971 Iteration 1: log likelihood = -1065.6673 Iteration 2: log likelihood = -1064.723 Iteration 3: log likelihood = -1064.7225 Iteration 4: log likelihood = -1064.7225 Iteration 0: log likelihood = -992.32956 (not concave) Iteration 1: log likelihood = -882.58831 Iteration 2: log likelihood = -806.27482 Iteration 3: log likelihood = -802.84247 Iteration 4: log likelihood = -802.49382 Iteration 5: log likelihood = -802.49002 Iteration 6: log likelihood = -802.49002 Fitting 2 component Negative Binomial-2 model: Iteration 0: log pseudolikelihood = -802.46926 (not concave) Iteration 1: log pseudolikelihood = -799.71423 (not concave) Iteration 2: log pseudolikelihood = -787.25268 (not concave) Iteration 3: log pseudolikelihood = -784.25839 (not concave) Iteration 4: log pseudolikelihood = -782.98413 (not concave) Iteration 5: log pseudolikelihood = -782.3245 (not concave) Iteration 6: log pseudolikelihood = -780.72215 (not concave) Iteration 7: log pseudolikelihood = -779.98831 (not concave) Iteration 8: log pseudolikelihood = -779.55662 (not concave) Iteration 9: log pseudolikelihood = -779.27651 (not concave) Iteration 10: log pseudolikelihood = -779.14581 (not concave) Iteration 11: log pseudolikelihood = -778.81098 (not concave) Iteration 12: log pseudolikelihood = -778.19088 (not concave) Iteration 13: log pseudolikelihood = -778.17448 (not concave) Iteration 14: log pseudolikelihood = -777.96353 (not concave) Iteration 15: log pseudolikelihood = -777.8582 (not concave) Iteration 16: log pseudolikelihood = -777.7557 (not concave) Iteration 17: log pseudolikelihood = -777.65543 (not concave) Iteration 18: log pseudolikelihood = -777.55607 (not concave) Iteration 19: log pseudolikelihood = -777.45859 (not concave) Iteration 20: log pseudolikelihood = -777.36319 (not concave) Iteration 21: log pseudolikelihood = -777.26963 (not concave) Iteration 22: log pseudolikelihood = -777.17756 (not concave) Iteration 23: log pseudolikelihood = -777.08729 (not concave) Iteration 24: log pseudolikelihood = -776.99846 (not concave) Iteration 25: log pseudolikelihood = -776.91091 (not concave) Iteration 26: log pseudolikelihood = -776.82416 (not concave) Iteration 27: log pseudolikelihood = -776.7382 (not concave) Iteration 28: log pseudolikelihood = -776.65248 (not concave) Iteration 29: log pseudolikelihood = -776.56688 (not concave) Iteration 30: log pseudolikelihood = -776.48072 (not concave) Iteration 31: log pseudolikelihood = -776.39391 (not concave) Iteration 32: log pseudolikelihood = -776.30563 (not concave) Iteration 33: log pseudolikelihood = -776.21579 (not concave) Iteration 34: log pseudolikelihood = -776.12334 (not concave) Iteration 35: log pseudolikelihood = -776.02824 (not concave) Iteration 36: log pseudolikelihood = -775.9293 (not concave) Iteration 37: log pseudolikelihood = -775.82655 (not concave) Iteration 38: log pseudolikelihood = -775.71879 (not concave) Iteration 39: log pseudolikelihood = -775.60636 (not concave) Iteration 40: log pseudolikelihood = -775.48835 (not concave) Iteration 41: log pseudolikelihood = -775.36572 (not concave) Iteration 42: log pseudolikelihood = -775.23807 (not concave) Iteration 43: log pseudolikelihood = -775.10727 (not concave) Iteration 44: log pseudolikelihood = -774.97349 (not concave) Iteration 45: log pseudolikelihood = -774.83921 (not concave) Iteration 46: log pseudolikelihood = -774.70503 (not concave) Iteration 47: log pseudolikelihood = -774.57291 (not concave) Iteration 48: log pseudolikelihood = -774.44406 (not concave) Iteration 49: log pseudolikelihood = -774.31873 (not concave) Iteration 50: log pseudolikelihood = -774.19896 (not concave) Iteration 51: log pseudolikelihood = -774.08346 (not concave) Iteration 52: log pseudolikelihood = -773.97423 (not concave) Iteration 53: log pseudolikelihood = -773.86934 (not concave) Iteration 54: log pseudolikelihood = -773.7701 (not concave) Iteration 55: log pseudolikelihood = -773.67451 (not concave) Iteration 56: log pseudolikelihood = -773.58315 (not concave) Iteration 57: log pseudolikelihood = -773.49413 (not concave) Iteration 58: log pseudolikelihood = -773.40758 (not concave) Iteration 59: log pseudolikelihood = -773.32194 (not concave) Iteration 60: log pseudolikelihood = -773.23766 (not concave) Iteration 61: log pseudolikelihood = -773.15403 (not concave) Iteration 62: log pseudolikelihood = -773.07258 (not concave) Iteration 63: log pseudolikelihood = -772.99332 (not concave) Iteration 64: log pseudolikelihood = -772.91798 (not concave) Iteration 65: log pseudolikelihood = -772.84623 (not concave) Iteration 66: log pseudolikelihood = -772.7791 (not concave) Iteration 67: log pseudolikelihood = -772.71591 (not concave) Iteration 68: log pseudolikelihood = -772.65715 (not concave) Iteration 69: log pseudolikelihood = -772.60207 (not concave) Iteration 70: log pseudolikelihood = -772.55094 (not concave) Iteration 71: log pseudolikelihood = -772.50305 (not concave) Iteration 72: log pseudolikelihood = -772.45856 (not concave) Iteration 73: log pseudolikelihood = -772.41683 (not concave) Iteration 74: log pseudolikelihood = -772.37797 (not concave) Iteration 75: log pseudolikelihood = -772.34138 (not concave) Iteration 76: log pseudolikelihood = -772.30714 (not concave) Iteration 77: log pseudolikelihood = -772.27473 (not concave) Iteration 78: log pseudolikelihood = -772.24417 (not concave) Iteration 79: log pseudolikelihood = -772.21503 (not concave) Iteration 80: log pseudolikelihood = -772.18733 (not concave) Iteration 81: log pseudolikelihood = -772.1607 (not concave) Iteration 82: log pseudolikelihood = -772.13514 (not concave) Iteration 83: log pseudolikelihood = -772.11036 (not concave) Iteration 84: log pseudolikelihood = -772.08637 (not concave) Iteration 85: log pseudolikelihood = -772.06293 (not concave) Iteration 86: log pseudolikelihood = -772.04006 (not concave) Iteration 87: log pseudolikelihood = -772.01756 (not concave) Iteration 88: log pseudolikelihood = -771.99548 (not concave) Iteration 89: log pseudolikelihood = -771.97363 (not concave) Iteration 90: log pseudolikelihood = -771.9521 (not concave) Iteration 91: log pseudolikelihood = -771.9307 (not concave) Iteration 92: log pseudolikelihood = -771.90956 (not concave) Iteration 93: log pseudolikelihood = -771.88855 (not concave) Iteration 94: log pseudolikelihood = -771.86785 (not concave) Iteration 95: log pseudolikelihood = -771.84749 (not concave) Iteration 96: log pseudolikelihood = -771.82776 (not concave) Iteration 97: log pseudolikelihood = -771.8085 (not concave) Iteration 98: log pseudolikelihood = -771.78968 (not concave) Iteration 99: log pseudolikelihood = -771.77111 (not concave) Iteration 100: log pseudolikelihood = -771.75282 (not concave) Iteration 101: log pseudolikelihood = -771.73472 (not concave) Iteration 102: log pseudolikelihood = -771.71687 (not concave) Iteration 103: log pseudolikelihood = -771.71512 (not concave) Iteration 104: log pseudolikelihood = -771.69537 (not concave) Iteration 105: log pseudolikelihood = -771.68393 (not concave) Iteration 106: log pseudolikelihood = -771.66476 (not concave) Iteration 107: log pseudolikelihood = -771.64722 (not concave) Iteration 108: log pseudolikelihood = -771.64368 (not concave) Iteration 109: log pseudolikelihood = -771.64184 (not concave) Iteration 110: log pseudolikelihood = -771.64078 (not concave) Iteration 111: log pseudolikelihood = -771.6401 (not concave) Iteration 112: log pseudolikelihood = -771.63976 (not concave) Iteration 113: log pseudolikelihood = -771.63641 (not concave) Iteration 114: log pseudolikelihood = -771.63641 (not concave) Iteration 115: log pseudolikelihood = -771.63641 (not concave) Iteration 116: log pseudolikelihood = -771.63641 (not concave) Iteration 117: log pseudolikelihood = -771.63641 (not concave) Iteration 118: log pseudolikelihood = -771.63641 (not concave) Iteration 119: log pseudolikelihood = -771.63641 (not concave) Iteration 120: log pseudolikelihood = -771.63641 (not concave) convergence not achieved 2 component Negative Binomial-2 regression Number of obs = 659 Wald chi2(23) = . Log pseudolikelihood = -771.63641 Prob > chi2 = . ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- component1 | SO | .786909 .1580699 4.98 0.000 .4770976 1.09672 I | -.0063495 .0526086 -0.12 0.904 -.1094604 .0967614 SKI | .3895712 .255352 1.53 0.127 -.1109095 .8900519 FC3 | .7828721 .4721001 1.66 0.097 -.1424272 1.708171 C1 | .0735316 .1604521 0.46 0.647 -.2409488 .3880119 C3 | -.1232798 .0583072 -2.11 0.034 -.2375598 -.0089997 C4 | .0485691 .1988938 0.24 0.807 -.3412556 .4383938 C1sq | -.00537 .0166719 -0.32 0.747 -.0380463 .0273064 C3sq | -.000856 .0008718 -0.98 0.326 -.0025647 .0008527 C4sq | -.0001763 .0038796 -0.05 0.964 -.0077803 .0074276 C1C3 | .0060281 .0189599 0.32 0.751 -.0311327 .0431889 C1C4 | .0038351 .0143795 0.27 0.790 -.0243482 .0320185 C3C4 | -.0034684 .0212139 -0.16 0.870 -.0450469 .0381102 _cons | -1.846232 .3894935 -4.74 0.000 -2.609626 -1.082839 -------------+---------------------------------------------------------------- component2 | SO | .1448624 1.021254 0.14 0.887 -1.856758 2.146483 I | -.309624 . . . . . SKI | .6939544 . . . . . FC3 | -.1964491 .9614425 -0.20 0.838 -2.080842 1.687944 C1 | .1055798 . . . . . C3 | -.1564606 .0462175 -3.39 0.001 -.2470453 -.065876 C4 | .0578239 .0722821 0.80 0.424 -.0838463 .1994942 C1sq | -.0053296 .1462352 -0.04 0.971 -.2919453 .2812861 C3sq | -.0008106 .0204489 -0.04 0.968 -.0408897 .0392685 C4sq | -.0002298 .0054603 -0.04 0.966 -.0109319 .0104723 C1C3 | .0060468 .1731465 0.03 0.972 -.3333141 .3454077 C1C4 | .0038264 .1175322 0.03 0.974 -.2265324 .2341852 C3C4 | -.0035058 .1295272 -0.03 0.978 -.2573745 .2503628 _cons | 2.228115 . . . . . -------------+---------------------------------------------------------------- /imlogitpi1 | 3.218809 .8579006 3.75 0.000 1.537355 4.900263 /lnalpha1 | -.3614631 .3058778 -1.18 0.237 -.9609726 .2380463 /lnalpha2 | -25.82672 6.244484 -4.14 0.000 -38.06568 -13.58776 ------------------------------------------------------------------------------ Warning: convergence not achieved alpha1 | .6966563 .2130917 .3825207 1.268768 alpha2 | 6.08e-12 3.79e-11 2.94e-17 1.26e-06 pi1 | .961536 .0317291 .8230798 .9926104 pi2 | .038464 .0317291 .0073896 .1769202 ------------------------------------------------------------------------------ . estimates store FMNB2interact . . *** TABLE 6.12: FINITE MIXTURES MODELS . . estimates table FMP2 FMNB2 FMNB1, b(%10.3f) t(%10.2f) eq(1) stats(ll aic bic N k) ----------------------------------------------------- Variable | FMP2 FMNB2 FMNB1 -------------+--------------------------------------- #1 | SO | 0.655 0.890 0.925 | 14.97 19.90 14.76 SKI | 0.438 0.449 -0.426 | 2.45 2.50 -1.80 I | -0.010 -0.049 0.073 | -0.20 -1.02 0.61 FC3 | 1.542 1.070 -0.631 | 8.04 2.97 -2.76 C1 | -0.044 -0.000 -0.027 | -2.40 -0.01 -1.53 C3 | -0.029 -0.050 0.003 | -2.85 -5.24 0.43 C4 | 0.070 0.047 0.025 | 5.03 3.11 1.57 _cons | -1.766 -1.877 -2.634 | -6.19 -9.13 -5.37 -------------+--------------------------------------- component2 | SO | 0.086 -0.095 0.511 | 0.63 -0.43 12.20 SKI | 0.631 1.369 0.746 | 3.43 3.55 4.96 I | 0.003 -0.033 -0.054 | 0.02 -0.23 -1.24 FC3 | -0.687 -0.129 0.305 | -1.90 -0.43 1.27 C1 | 0.074 0.186 0.060 | 3.36 7.50 5.40 C3 | -0.073 -0.253 -0.096 | -5.66 -9.52 -9.41 C4 | -0.014 0.049 0.030 | -0.83 3.42 4.01 _cons | 2.479 1.006 -0.287 | 2.23 1.04 -1.10 -------------+--------------------------------------- imlogitpi1 | _cons | 2.298 1.952 -0.748 | 10.78 3.77 -2.92 -------------+--------------------------------------- lnalpha1 | _cons | -0.192 | -1.45 -------------+--------------------------------------- lnalpha2 | _cons | -1.647 | -3.09 -------------+--------------------------------------- lndelta1 | _cons | -13.692 | -7.70 -------------+--------------------------------------- lndelta2 | _cons | 1.742 | 6.96 -------------+--------------------------------------- Statistics | ll | -938.660 -786.010 -794.582 aic | 1911.320 1610.020 1627.164 bic | 1987.662 1695.344 1712.488 N | 659 659 659 k | 17.000 19.000 19.000 ----------------------------------------------------- legend: b/t . . *** HURDLE AND ZERO-INFLATED MODELS (Table 6.13) . . generate DTRIPS = TRIPS > 0 . . * Problem: TRIPS are necessarily > 0 if FC3 = 1 . tabulate FC3 DTRIPS Equals 1 | if user's | fee paid | at Lake | DTRIPS Somerville | 0 1 | Total -----------+----------------------+---------- 0 | 417 229 | 646 1 | 0 13 | 13 -----------+----------------------+---------- Total | 417 242 | 659 . . global XLIST SO SKI I FC3 C1 C3 C4 . global XLISTSHORT SO SKI I C1 C3 C4 . . * Hurdle first component: NB2 - recode a to exp(a) . * Has problems after about 20 iterations . . program lfNB2binary 1. version 10.1 2. args lnf theta1 a 3. tempvar mu p expa 4. local y "$ML_y1" 5. generate double `mu' = exp(`theta1') 6. generate double `expa' = exp(`a') 7. generate double `p' = 1 - (1/(1+`expa'*`mu'))^(1/`expa') 8. quietly replace `lnf' = `y'*ln(`p') + ln(1-`p') - `y'*ln(1-`p') 9. end . . * This includes SKI which is not identified . ml model lf lfNB2binary (DTRIPS = $XLIST) (), vce(robust) . ml maximize, iter(20) initial: log pseudolikelihood = -456.78399 alternative: log pseudolikelihood = -435.07645 rescale: log pseudolikelihood = -435.07645 rescale eq: log pseudolikelihood = -433.27603 Iteration 0: log pseudolikelihood = -433.27603 (not concave) Iteration 1: log pseudolikelihood = -224.31498 Iteration 2: log pseudolikelihood = -185.89869 Iteration 3: log pseudolikelihood = -173.65472 (not concave) Iteration 4: log pseudolikelihood = -173.17159 Iteration 5: log pseudolikelihood = -171.79856 Iteration 6: log pseudolikelihood = -152.84317 (not concave) Iteration 7: log pseudolikelihood = -150.74778 Iteration 8: log pseudolikelihood = -146.87911 Iteration 9: log pseudolikelihood = -140.21812 (not concave) Iteration 10: log pseudolikelihood = -138.75854 Iteration 11: log pseudolikelihood = -138.17864 Iteration 12: log pseudolikelihood = -131.91503 Iteration 13: log pseudolikelihood = -130.147 Iteration 14: log pseudolikelihood = -128.72613 Iteration 15: log pseudolikelihood = -127.96385 (not concave) Iteration 16: log pseudolikelihood = -127.88657 Iteration 17: log pseudolikelihood = -127.59187 Iteration 18: log pseudolikelihood = -127.33461 Iteration 19: log pseudolikelihood = -127.32984 (backed up) Iteration 20: log pseudolikelihood = -127.32976 (backed up) convergence not achieved Number of obs = 659 Wald chi2(7) = 193.24 Log pseudolikelihood = -127.32976 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust DTRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- eq1 | SO | 20.626 2.305418 8.95 0.000 16.10746 25.14453 SKI | 4.422545 2.308856 1.92 0.055 -.1027287 8.947819 I | -.0816789 .3973798 -0.21 0.837 -.8605291 .6971712 FC3 | 244.905 41.10006 5.96 0.000 164.3503 325.4596 C1 | .2726978 .294918 0.92 0.355 -.3053308 .8507265 C3 | -.5110286 .2299707 -2.22 0.026 -.9617628 -.0602944 C4 | .2259611 .184293 1.23 0.220 -.1352465 .5871687 _cons | -5.025266 2.820849 -1.78 0.075 -10.55403 .5034959 -------------+---------------------------------------------------------------- eq2 | _cons | 3.51824 .1317104 26.71 0.000 3.260092 3.776387 ------------------------------------------------------------------------------ Warning: convergence not achieved . . * This drops SKI which is not identified . ml model lf lfNB2binary (DTRIPS = $XLISTSHORT) (), vce(robust) . ml maximize, iter(12) initial: log pseudolikelihood = -456.78399 alternative: log pseudolikelihood = -435.07645 rescale: log pseudolikelihood = -435.07645 rescale eq: log pseudolikelihood = -433.27603 Iteration 0: log pseudolikelihood = -433.27603 (not concave) Iteration 1: log pseudolikelihood = -225.67756 (not concave) Iteration 2: log pseudolikelihood = -212.45596 Iteration 3: log pseudolikelihood = -170.00965 (not concave) Iteration 4: log pseudolikelihood = -168.55899 Iteration 5: log pseudolikelihood = -162.21633 Iteration 6: log pseudolikelihood = -148.75943 Iteration 7: log pseudolikelihood = -141.98322 Iteration 8: log pseudolikelihood = -137.10163 Iteration 9: log pseudolikelihood = -131.10183 (not concave) Iteration 10: log pseudolikelihood = -130.74531 Iteration 11: log pseudolikelihood = -130.70568 Iteration 12: log pseudolikelihood = -129.80954 convergence not achieved Number of obs = 659 Wald chi2(6) = 6.16 Log pseudolikelihood = -129.80954 Prob > chi2 = 0.4051 ------------------------------------------------------------------------------ | Robust DTRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- eq1 | SO | 18.13441 15.56548 1.17 0.244 -12.37337 48.6422 SKI | 3.832226 4.18135 0.92 0.359 -4.363069 12.02752 I | -.0677034 .4117861 -0.16 0.869 -.8747894 .7393825 C1 | .2626725 .3704435 0.71 0.478 -.4633833 .9887283 C3 | -.4913213 .3819919 -1.29 0.198 -1.240012 .257369 C4 | .2159826 .1904966 1.13 0.257 -.1573838 .5893491 _cons | -4.613904 2.926218 -1.58 0.115 -10.34919 1.121379 -------------+---------------------------------------------------------------- eq2 | _cons | 3.339855 .8754861 3.81 0.000 1.623934 5.055776 ------------------------------------------------------------------------------ Warning: convergence not achieved . estimates store H1NB2 . scalar llH1NB2 = e(ll) . scalar kH1NB2 = e(k) . . * Get the predicted probability of a zero . * This code only works for this example . matrix bhurd = e(b) . scalar bSO = bhurd[1,1] . scalar bSKI = bhurd[1,2] . scalar bI = bhurd[1,3] . scalar bC1 = bhurd[1,4] . scalar bC3 = bhurd[1,5] . scalar bC4 = bhurd[1,6] . scalar bcons = bhurd[1,7] . * Recall that reparameterized as exp(alpha) not alpha . scalar alpha1 = ln(bhurd[1,e(k)]) . di "alpha for first part of hurdle NB2 = " alpha1 alpha for first part of hurdle NB2 = 1.2059274 . generate xbhurd = bSO*SO + bSKI*SKI + bI*I + bC1*C1 + bC3*C3 + bC4*C4 + bcons . generate f10 = (1 + alpha1*exp(xbhurd))^(-1/alpha1) . . * Check by compare to logit predicted probability . quietly logit DTRIPS $XLISTSHORT . predict plogit (option pr assumed; Pr(DTRIPS)) . generate f10logit = 1 - plogit . correlate f10 f10logit (obs=659) | f10 f10logit -------------+------------------ f10 | 1.0000 f10logit | 0.8945 1.0000 . * scatter f10 f10logit . . * Hurdle second component: NB2 . ztnb TRIPS $XLIST if TRIPS>0, dispersion(mean) vce(robust) Fitting Zero-truncated poisson model: Iteration 0: log pseudolikelihood = -1017.652 Iteration 1: log pseudolikelihood = -1014.8441 Iteration 2: log pseudolikelihood = -1014.8355 Iteration 3: log pseudolikelihood = -1014.8355 Fitting constant-only model: Iteration 0: log pseudolikelihood = -662.19114 Iteration 1: log pseudolikelihood = -635.45582 Iteration 2: log pseudolikelihood = -631.90906 Iteration 3: log pseudolikelihood = -631.01142 Iteration 4: log pseudolikelihood = -630.91687 Iteration 5: log pseudolikelihood = -630.91359 Iteration 6: log pseudolikelihood = -630.91357 Fitting full model: Iteration 0: log pseudolikelihood = -610.44577 Iteration 1: log pseudolikelihood = -602.75223 Iteration 2: log pseudolikelihood = -599.46049 Iteration 3: log pseudolikelihood = -591.63316 Iteration 4: log pseudolikelihood = -591.56343 Iteration 5: log pseudolikelihood = -591.56316 Iteration 6: log pseudolikelihood = -591.56316 Zero-truncated negative binomial regression Number of obs = 242 Dispersion = mean Wald chi2(7) = 103.55 Log likelihood = -591.56316 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- SO | .1716984 .0718771 2.39 0.017 .0308219 .3125749 SKI | .6223606 .1851015 3.36 0.001 .2595684 .9851529 I | -.0570864 .0588069 -0.97 0.332 -.1723457 .0581729 FC3 | .5763336 .2464433 2.34 0.019 .0933135 1.059354 C1 | .0570692 .0249603 2.29 0.022 .0081479 .1059905 C3 | -.0775205 .0131743 -5.88 0.000 -.1033417 -.0516994 C4 | .0123727 .0157709 0.78 0.433 -.0185377 .0432832 _cons | .8419364 .3668235 2.30 0.022 .1229757 1.560897 -------------+---------------------------------------------------------------- /lnalpha | .530299 .2768831 -.0123819 1.07298 -------------+---------------------------------------------------------------- alpha | 1.69944 .4705463 .9876945 2.92408 ------------------------------------------------------------------------------ . estimates store H2NB2 . scalar llH2NB2 = e(ll) . scalar kH2NB2 = e(k) . . * Get the predicted probability of a zero in the second part of model . predict mu2, n . scalar alpha2 = e(alpha) . generate f20 = (1 + alpha2*mu2)^(-1/alpha2) . . * Combine to get fitted mean . generate muhurdle = mu2*(1-f10)/(1-f20) . * or using binary logit . generate muhurdlelogit = mu2*(1-f10logit)/(1-f20) . . * Combine to get fitted probabilities . * Not done. Need to code predictions from ztnb as predict after ztnb . * does not have option pr( ). THen multiply these by (1-f10)/(1-f20) . . * ZIP with only an interept for the zeros . zip TRIPS $XLIST, inflate($XLIST) vce(robust) Fitting constant-only model: Iteration 0: log pseudolikelihood = -2280.2755 Iteration 1: log pseudolikelihood = -1631.497 Iteration 2: log pseudolikelihood = -1474.0656 Iteration 3: log pseudolikelihood = -1468.9929 Iteration 4: log pseudolikelihood = -1468.7085 Iteration 5: log pseudolikelihood = -1468.6493 Iteration 6: log pseudolikelihood = -1468.6359 Iteration 7: log pseudolikelihood = -1468.6331 Iteration 8: log pseudolikelihood = -1468.6326 Iteration 9: log pseudolikelihood = -1468.6326 Iteration 10: log pseudolikelihood = -1468.6326 Fitting full model: Iteration 0: log pseudolikelihood = -1468.6326 Iteration 1: log pseudolikelihood = -1273.7416 Iteration 2: log pseudolikelihood = -1164.1206 Iteration 3: log pseudolikelihood = -1163.4193 Iteration 4: log pseudolikelihood = -1163.4191 Iteration 5: log pseudolikelihood = -1163.4191 Zero-inflated Poisson regression Number of obs = 659 Nonzero obs = 242 Zero obs = 417 Inflation model = logit Wald chi2(7) = 75.75 Log pseudolikelihood = -1163.419 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- TRIPS | SO | .0396788 .0834161 0.48 0.634 -.1238138 .2031715 SKI | .4691185 .1763189 2.66 0.008 .1235398 .8146972 I | -.0943536 .0477011 -1.98 0.048 -.1878461 -.0008612 FC3 | .6050712 .2358399 2.57 0.010 .1428335 1.067309 C1 | .0023539 .0144217 0.16 0.870 -.0259121 .0306199 C3 | -.0364429 .0108506 -3.36 0.001 -.0577096 -.0151762 C4 | .0235891 .0081585 2.89 0.004 .0075987 .0395795 _cons | 2.113707 .5032877 4.20 0.000 1.127281 3.100133 -------------+---------------------------------------------------------------- inflate | SO | -1.651993 .2076671 -7.96 0.000 -2.059013 -1.244973 SKI | .0588168 .4614636 0.13 0.899 -.8456352 .9632688 I | -.0719113 .1110972 -0.65 0.517 -.2896579 .1458352 FC3 | -20.59898 .6327039 -32.56 0.000 -21.83905 -19.3589 C1 | -.0058103 .0244693 -0.24 0.812 -.0537693 .0421486 C3 | .0723226 .0208863 3.46 0.001 .0313861 .113259 C4 | -.0753998 .0251974 -2.99 0.003 -.1247858 -.0260137 _cons | 3.558284 .532032 6.69 0.000 2.51552 4.601047 ------------------------------------------------------------------------------ . estimates store ZIPint . . * ZIP . zip TRIPS $XLIST, inflate($XLIST) vce(robust) Fitting constant-only model: Iteration 0: log pseudolikelihood = -2280.2755 Iteration 1: log pseudolikelihood = -1631.497 Iteration 2: log pseudolikelihood = -1474.0656 Iteration 3: log pseudolikelihood = -1468.9929 Iteration 4: log pseudolikelihood = -1468.7085 Iteration 5: log pseudolikelihood = -1468.6493 Iteration 6: log pseudolikelihood = -1468.6359 Iteration 7: log pseudolikelihood = -1468.6331 Iteration 8: log pseudolikelihood = -1468.6326 Iteration 9: log pseudolikelihood = -1468.6326 Iteration 10: log pseudolikelihood = -1468.6326 Fitting full model: Iteration 0: log pseudolikelihood = -1468.6326 Iteration 1: log pseudolikelihood = -1273.7416 Iteration 2: log pseudolikelihood = -1164.1206 Iteration 3: log pseudolikelihood = -1163.4193 Iteration 4: log pseudolikelihood = -1163.4191 Iteration 5: log pseudolikelihood = -1163.4191 Zero-inflated Poisson regression Number of obs = 659 Nonzero obs = 242 Zero obs = 417 Inflation model = logit Wald chi2(7) = 75.75 Log pseudolikelihood = -1163.419 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- TRIPS | SO | .0396788 .0834161 0.48 0.634 -.1238138 .2031715 SKI | .4691185 .1763189 2.66 0.008 .1235398 .8146972 I | -.0943536 .0477011 -1.98 0.048 -.1878461 -.0008612 FC3 | .6050712 .2358399 2.57 0.010 .1428335 1.067309 C1 | .0023539 .0144217 0.16 0.870 -.0259121 .0306199 C3 | -.0364429 .0108506 -3.36 0.001 -.0577096 -.0151762 C4 | .0235891 .0081585 2.89 0.004 .0075987 .0395795 _cons | 2.113707 .5032877 4.20 0.000 1.127281 3.100133 -------------+---------------------------------------------------------------- inflate | SO | -1.651993 .2076671 -7.96 0.000 -2.059013 -1.244973 SKI | .0588168 .4614636 0.13 0.899 -.8456352 .9632688 I | -.0719113 .1110972 -0.65 0.517 -.2896579 .1458352 FC3 | -20.59898 .6327039 -32.56 0.000 -21.83905 -19.3589 C1 | -.0058103 .0244693 -0.24 0.812 -.0537693 .0421486 C3 | .0723226 .0208863 3.46 0.001 .0313861 .113259 C4 | -.0753998 .0251974 -2.99 0.003 -.1247858 -.0260137 _cons | 3.558284 .532032 6.69 0.000 2.51552 4.601047 ------------------------------------------------------------------------------ . estimates store ZIP . . * ZINB with only an interept for the zeros . zinb TRIPS $XLIST, inflate(_cons) vce(robust) Fitting constant-only model: Iteration 0: log pseudolikelihood = -1174.5746 Iteration 1: log pseudolikelihood = -1160.9705 Iteration 2: log pseudolikelihood = -1077.3398 (not concave) Iteration 3: log pseudolikelihood = -1068.049 Iteration 4: log pseudolikelihood = -1066.7146 Iteration 5: log pseudolikelihood = -1065.335 Iteration 6: log pseudolikelihood = -1065.1735 Iteration 7: log pseudolikelihood = -1064.9077 Iteration 8: log pseudolikelihood = -1064.8298 Iteration 9: log pseudolikelihood = -1064.7656 Iteration 10: log pseudolikelihood = -1064.7235 Iteration 11: log pseudolikelihood = -1064.7226 Iteration 12: log pseudolikelihood = -1064.7225 Iteration 13: log pseudolikelihood = -1064.7225 Fitting full model: Iteration 0: log pseudolikelihood = -1064.7225 (not concave) Iteration 1: log pseudolikelihood = -966.48963 Iteration 2: log pseudolikelihood = -837.49649 Iteration 3: log pseudolikelihood = -825.85671 Iteration 4: log pseudolikelihood = -825.55776 Iteration 5: log pseudolikelihood = -825.55758 Iteration 6: log pseudolikelihood = -825.55758 Zero-inflated negative binomial regression Number of obs = 659 Nonzero obs = 242 Zero obs = 417 Inflation model = logit Wald chi2(7) = 445.58 Log pseudolikelihood = -825.5576 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- TRIPS | SO | .721999 .0583691 12.37 0.000 .6075977 .8364004 SKI | .6121388 .2003177 3.06 0.002 .2195233 1.004754 I | -.0260588 .0548466 -0.48 0.635 -.1335561 .0814384 FC3 | .6691677 .3205802 2.09 0.037 .040842 1.297493 C1 | .0480086 .0283108 1.70 0.090 -.0074795 .1034968 C3 | -.092691 .014518 -6.38 0.000 -.1211458 -.0642362 C4 | .0388357 .0177502 2.19 0.029 .004046 .0736254 _cons | -1.121936 .2964056 -3.79 0.000 -1.702881 -.5409919 -------------+---------------------------------------------------------------- inflate | _cons | -39.01491 .2093301 -186.38 0.000 -39.42519 -38.60463 -------------+---------------------------------------------------------------- /lnalpha | .3157293 .1350229 2.34 0.019 .0510893 .5803693 -------------+---------------------------------------------------------------- alpha | 1.371259 .1851514 1.052417 1.786698 ------------------------------------------------------------------------------ . estimates store ZINBint . . * ZINB . zinb TRIPS $XLIST, inflate($XLIST) vce(robust) Fitting constant-only model: Iteration 0: log pseudolikelihood = -1174.5746 (not concave) Iteration 1: log pseudolikelihood = -896.55816 Iteration 2: log pseudolikelihood = -821.43104 Iteration 3: log pseudolikelihood = -801.058 Iteration 4: log pseudolikelihood = -787.22109 Iteration 5: log pseudolikelihood = -785.05939 Iteration 6: log pseudolikelihood = -784.778 Iteration 7: log pseudolikelihood = -784.76497 Iteration 8: log pseudolikelihood = -784.76482 Iteration 9: log pseudolikelihood = -784.76478 Iteration 10: log pseudolikelihood = -784.76478 Fitting full model: Iteration 0: log pseudolikelihood = -784.76478 Iteration 1: log pseudolikelihood = -730.80649 Iteration 2: log pseudolikelihood = -722.75848 (not concave) Iteration 3: log pseudolikelihood = -722.57622 Iteration 4: log pseudolikelihood = -722.41048 Iteration 5: log pseudolikelihood = -719.92151 Iteration 6: log pseudolikelihood = -719.48716 Iteration 7: log pseudolikelihood = -719.39618 Iteration 8: log pseudolikelihood = -719.37474 Iteration 9: log pseudolikelihood = -719.37052 Iteration 10: log pseudolikelihood = -719.36961 Iteration 11: log pseudolikelihood = -719.3694 Iteration 12: log pseudolikelihood = -719.36935 Iteration 13: log pseudolikelihood = -719.36934 Zero-inflated negative binomial regression Number of obs = 659 Nonzero obs = 242 Zero obs = 417 Inflation model = logit Wald chi2(7) = 140.80 Log pseudolikelihood = -719.3693 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Robust TRIPS | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- TRIPS | SO | .170791 .0566653 3.01 0.003 .059729 .281853 SKI | .492453 .1459854 3.37 0.001 .2063268 .7785792 I | -.0688226 .0414572 -1.66 0.097 -.1500773 .0124321 FC3 | .547295 .2205721 2.48 0.013 .1149817 .9796083 C1 | .0399582 .0184614 2.16 0.030 .0037745 .0761418 C3 | -.0658707 .0104456 -6.31 0.000 -.0863437 -.0453977 C4 | .0207245 .0113653 1.82 0.068 -.0015512 .0430001 _cons | 1.091936 .2919291 3.74 0.000 .5197651 1.664106 -------------+---------------------------------------------------------------- inflate | SO | -38.63617 2.002578 -19.29 0.000 -42.56115 -34.71119 SKI | -16.06663 1.083902 -14.82 0.000 -18.19104 -13.94222 I | -.2029069 .3395567 -0.60 0.550 -.8684258 .462612 FC3 | -11.42997 2.420961 -4.72 0.000 -16.17496 -6.684971 C1 | -.023586 .0152638 -1.55 0.122 -.0535026 .0063305 C3 | .0775286 .0214598 3.61 0.000 .0354681 .1195891 C4 | -.0628993 .0214707 -2.93 0.003 -.1049811 -.0208175 _cons | 20.97537 2.850511 7.36 0.000 15.38847 26.56227 -------------+---------------------------------------------------------------- /lnalpha | -.1832683 .1150975 -1.59 0.111 -.4088553 .0423186 -------------+---------------------------------------------------------------- alpha | .8325447 .0958238 .6644104 1.043227 ------------------------------------------------------------------------------ . estat ic ----------------------------------------------------------------------------- Model | Obs ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 659 -784.7648 -719.3693 17 1472.739 1549.081 ----------------------------------------------------------------------------- Note: N=Obs used in calculating BIC; see [R] BIC note . estimates store ZINB . quietly zinb TRIPS $XLIST, inflate($XLIST) vuong . display "Vuong statistic: " e(vuong) Vuong statistic: 8.6194315 . foreach y of numlist 0/5 8 11 14 17 62 { 2. predict pzinb`y', pr(`y') 3. predict cumzinb`y', pr(0,`y') 4. } . replace pzinb8 = cumzinb8 - cumzinb5 (659 real changes made) . replace pzinb11 = cumzinb11 - cumzinb8 (659 real changes made) . replace pzinb14 = cumzinb14 - cumzinb11 (659 real changes made) . replace pzinb17 = cumzinb17 - cumzinb14 (659 real changes made) . replace pzinb62 = cumzinb62 - cumzinb17 (634 real changes made) . predict muZINB (option n assumed; predicted number of events) . summarize muZINB, detail Predicted number of events ------------------------------------------------------------- Percentiles Smallest 1% 2.86e-10 6.69e-13 5% 5.44e-10 1.13e-10 10% 7.40e-10 2.08e-10 Obs 659 25% 1.54e-09 2.32e-10 Sum of Wgt. 659 50% .0333058 Mean 2.724989 Largest Std. Dev. 14.22079 75% 3.165464 20.7974 90% 6.526104 28.08683 Variance 202.2309 95% 10.06582 28.60975 Skewness 22.94258 99% 18.91398 353.8577 Kurtosis 565.8138 . . *** TABLE 6.13: HURDLE and ZINB . . estimates table H1NB2 H2NB2 ZINB , b(%10.3f) t(%10.2f) eq(1) stats(ll aic bic N k) ----------------------------------------------------- Variable | H1NB2 H2NB2 ZINB -------------+--------------------------------------- #1 | SO | 18.134 0.172 0.171 | 1.17 2.39 3.01 SKI | 3.832 0.622 0.492 | 0.92 3.36 3.37 I | -0.068 -0.057 -0.069 | -0.16 -0.97 -1.66 C1 | 0.263 0.057 0.040 | 0.71 2.29 2.16 C3 | -0.491 -0.078 -0.066 | -1.29 -5.88 -6.31 C4 | 0.216 0.012 0.021 | 1.13 0.78 1.82 FC3 | 0.576 0.547 | 2.34 2.48 _cons | -4.614 0.842 1.092 | -1.58 2.30 3.74 -------------+--------------------------------------- eq2 | _cons | 3.340 | 3.81 -------------+--------------------------------------- lnalpha | _cons | 0.530 -0.183 | 1.92 -1.59 -------------+--------------------------------------- inflate | SO | -38.636 | -19.29 SKI | -16.067 | -14.82 I | -0.203 | -0.60 FC3 | -11.430 | -4.72 C1 | -0.024 | -1.55 C3 | 0.078 | 3.61 C4 | -0.063 | -2.93 _cons | 20.975 | 7.36 -------------+--------------------------------------- Statistics | ll | -129.810 -591.563 -719.369 aic | 275.619 1201.126 1472.739 bic | 311.545 1232.527 1549.081 N | 659 242 659 k | 8.000 9.000 17.000 ----------------------------------------------------- legend: b/t . . summarize muhurdle muhurdlelogit muZINB Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- muhurdle | 659 3.769482 24.7447 0 594.8442 muhurdlelo~t | 659 3.145244 23.44168 .0001906 594.8148 muZINB | 659 2.724989 14.22079 6.69e-13 353.8577 . . *** TABLE 6.14 (Part 2): PREDICTED PROBABILITIES FROM ZERO-INFLATED NB2 . . * This program does not compute predicted probabilities for hurdle NB2 . sum pzinb* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- pzinb0 | 659 .6564488 .3977694 .0010773 1 pzinb1 | 659 .0719351 .0917837 6.33e-13 .2636209 pzinb2 | 659 .0535687 .0644303 1.69e-14 .1589722 pzinb3 | 659 .040301 .047849 4.36e-16 .1141585 pzinb4 | 659 .0308389 .0371937 1.11e-17 .0891283 -------------+-------------------------------------------------------- pzinb5 | 659 .024008 .0298886 2.79e-19 .0731233 pzinb8 | 659 .0465845 .0624331 0 .162215 pzinb11 | 659 .0256087 .0393284 0 .1159534 pzinb14 | 659 .0152644 .0267292 0 .0902659 pzinb17 | 659 .0096573 .0191613 0 .0739125 -------------+-------------------------------------------------------- pzinb62 | 659 .023506 .0676858 0 .4622448 . sum cumzinb* Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- cumzinb0 | 659 .6564488 .3977694 .0010773 1 cumzinb1 | 659 .7283839 .3334541 .0023669 1 cumzinb2 | 659 .7819526 .2871336 .0037815 1 cumzinb3 | 659 .8222536 .2516807 .0052857 1 cumzinb4 | 659 .8530925 .2233906 .0068602 1 -------------+-------------------------------------------------------- cumzinb5 | 659 .8771005 .2001971 .0084926 1 cumzinb8 | 659 .923685 .1504095 .0136589 1 cumzinb11 | 659 .9492936 .1185557 .0191292 1 cumzinb14 | 659 .964558 .0968503 .0248233 1 cumzinb17 | 659 .9742154 .0814114 .030691 1 -------------+-------------------------------------------------------- cumzinb62 | 659 .9977213 .0346661 .1267748 1 . . ********** CLOSE OUTPUT . . * log close . * clear . * exit . end of do-file . exit, clear