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Count Data Models

Count Data Models. * run poisson regression; poisson drvisits age65 age70 age75 age80 chronic excel good fair female black hispanic hs_drop hs_grad mcaid incomel ; * run neg binomial regression; nbreg drvisits age65 age70 age75 age80 chronic excel good fair female

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Count Data Models

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  1. Count Data Models

  2. * run poisson regression; poissondrvisits age65 age70 age75 age80 chronic excel good fair female black hispanichs_drophs_gradmcaidincomel; * run neg binomial regression; nbregdrvisits age65 age70 age75 age80 chronic excel good fair female black hispanichs_drophs_gradmcaidincomel, dispersion(constant); Fix the overdispersion parameter to be a constant for all obs. Default is to allow the overdispersion parameter to vary based on the same X’s as the mean

  3. Poisson regression Number of obs = 5299 LR chi2(15) = 3334.46 Prob > chi2 = 0.0000 Log likelihood = -22275.351 Pseudo R2 = 0.0696 ------------------------------------------------------------------------------ drvisits | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age65 | .2144282 .026267 8.16 0.000 .1629458 .2659106 age70 | .286831 .0263077 10.90 0.000 .2352689 .3383931 age75 | .2801504 .0269802 10.38 0.000 .2272702 .3330307 age80 | .24314 .0292045 8.33 0.000 .1859001 .3003798 chronic | .4997173 .0137789 36.27 0.000 .4727111 .5267235 excel | -.7836622 .0305392 -25.66 0.000 -.8435178 -.7238065 good | -.4774853 .0159987 -29.85 0.000 -.5088422 -.4461284 fair | -.2578352 .0155473 -16.58 0.000 -.2883073 -.2273631 female | .0960976 .0123182 7.80 0.000 .0719543 .1202409 black | -.2838081 .0202163 -14.04 0.000 -.3234314 -.2441849 hispanic | -.2051023 .0368764 -5.56 0.000 -.2773788 -.1328258 hs_drop | -.2323802 .016066 -14.46 0.000 -.263869 -.2008914 hs_grad | -.1200559 .016517 -7.27 0.000 -.1524287 -.0876831 mcaid | .1535708 .0203414 7.55 0.000 .1137025 .1934392 incomel | .0211453 .0072946 2.90 0.004 .0068481 .0354425 _cons | 1.348084 .0804659 16.75 0.000 1.190374 1.505795 ------------------------------------------------------------------------------

  4. Negative binomial regression Number of obs = 5299 LR chi2(15) = 642.43 Dispersion = constant Prob > chi2 = 0.0000 Log likelihood = -14519.721 Pseudo R2 = 0.0216 ------------------------------------------------------------------------------ drvisits | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- age65 | .1034281 .054664 1.89 0.058 -.0037113 .2105675 age70 | .2039634 .0546788 3.73 0.000 .0967949 .3111319 age75 | .2094928 .0560412 3.74 0.000 .0996541 .3193314 age80 | .2227169 .0605925 3.68 0.000 .1039579 .341476 chronic | .5091666 .0292189 17.43 0.000 .4518986 .5664347 excel | -.5272908 .0594584 -8.87 0.000 -.6438271 -.4107545 good | -.3422506 .0353507 -9.68 0.000 -.4115368 -.2729645 fair | -.1526385 .0351632 -4.34 0.000 -.2215571 -.0837198 female | .1321966 .0263028 5.03 0.000 .0806441 .183749 black | -.3300031 .0438969 -7.52 0.000 -.4160395 -.2439668 hispanic | -.1527763 .0763018 -2.00 0.045 -.3023251 -.0032275 hs_drop | -.1912903 .0344335 -5.56 0.000 -.2587787 -.1238018 hs_grad | -.0869843 .0354543 -2.45 0.014 -.1564733 -.0174952 mcaid | .1341325 .0442797 3.03 0.002 .0473459 .2209191 incomel | .0379834 .0155687 2.44 0.015 .0074693 .0684975 _cons | 1.11029 .17092 6.50 0.000 .7752924 1.445287 -------------+---------------------------------------------------------------- /lndelta | 1.65017 .0286445 1.594027 1.706312 -------------+---------------------------------------------------------------- delta | 5.207863 .1491766 4.923538 5.508607 ------------------------------------------------------------------------------ Likelihood-ratio test of delta=0: chibar2(01) = 1.6e+04 Prob>=chibar2 = 0.000

  5. -2 log likelihood test • LL for Poisson = -22275.351 • LL for NB = 14519.721 • -2 LL difference = -15511

  6. Some Results

  7. Cond. count data models • State level data on deaths of motor cycle drivers/riders, 1991-2004 for people aged 16-30 • Over this period, tremendous changes in motor cycle helmet laws • Do laws reduce mortality?

  8. Covariates • Poisson/NB models • Ln(pop), ln(pci), helmet law, state & year effects • Conditional Poisson/NB models • The same except we condition on the state and drop the state effects • Ln(pop), ln(pci), helmet law, & year effects

  9. Asking for fixed or random effects xtpoisson mc_deaths1630 `xlist2', i(fips) fe; xtnbreg mc_deaths1630 `xlist2', i(fips) fe; Dimension over which you condition

  10. Summarize • Coefficients (std errors) on helmet law • Cond. Poisson -0.387 (0.032) • Cond. NB -0.348 (0.045) • Log likelihood • Cond. Poisson -1838.3 • Cond. NB -1813.7 • -2 log likelihood = 49.2 =χ2(1) • Reject Poisson is the correct model

  11. Results similar to cond. model but w/ smaller std errors Easily reject delta=0

  12. Notice that stand errors increase by a factor of 2.5

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