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Count Data Models

This analysis compares Poisson and Negative Binomial regression models to assess the frequency of doctor visits among elderly patients aged 65 to 80, factoring in chronic conditions, race, income, and educational background. The results indicate significant relationships with age, chronic conditions, and demographic factors, revealing patterns in healthcare accessibility and utilization. Key findings demonstrate overdispersion in count data, leading to a preference for the negative binomial model based on likelihood-ratio tests. This research provides insights into healthcare practices for aging populations.

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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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