1. Count Data Models 1

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3. 3 * 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 black hispanic hs_drop hs_grad mcaid incomel, 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

4. 4 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 ------------------------------------------------------------------------------

5. 5 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

6. -2 log likelihood test – LL for Poisson = -22275.351 – LL for NB = 14519.721 – -2 LL difference = -15511 6

7. PoissonNegative Binomial VariableParameterStd. error.ParameterStd. error. age650.2140.0260.1030.055 Chronic0.5000.1380.5090.029 excel-0.7840.031-0.5270.059 female0.0960.0120.1320.026 mcaid0.1540.0200.1340.044 incomel0.0210.0070.0380.156 Some Results 7

8. 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

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11. 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 11

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13. xtpoisson mc_deaths1630 `xlist2', i(fips) fe; xtnbreg mc_deaths1630 `xlist2', i(fips) fe; Dimension over which you condition Asking for fixed or random effects 13

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16. 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 =χ 2 (1) – Reject Poisson is the correct model 16

17. Easily reject delta=0 Results similar to cond. model but w/ smaller std errors 17

18. Notice that stand errors increase by a factor of 2.5 18