Count Data Models 1

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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 Poisson regression Number of obs = 5299 LR chi2(15) = Prob > chi2 = Log likelihood = Pseudo R2 = drvisits | Coef. Std. Err. z P>|z| [95% Conf. Interval] age65 | age70 | age75 | age80 | chronic | excel | good | fair | female | black | hispanic | hs_drop | hs_grad | mcaid | incomel | _cons |

5 Negative binomial regression Number of obs = 5299 LR chi2(15) = Dispersion = constant Prob > chi2 = Log likelihood = Pseudo R2 = drvisits | Coef. Std. Err. z P>|z| [95% Conf. Interval] age65 | age70 | age75 | age80 | chronic | excel | good | fair | female | black | hispanic | hs_drop | hs_grad | mcaid | incomel | _cons | /lndelta | delta | Likelihood-ratio test of delta=0: chibar2(01) = 1.6e+04 Prob>=chibar2 = 0.000

-2 log likelihood test – LL for Poisson = – LL for NB = – -2 LL difference =

PoissonNegative Binomial VariableParameterStd. error.ParameterStd. error. age Chronic excel female mcaid incomel Some Results 7

Cond. count data models State level data on deaths of motor cycle drivers/riders, for people aged Over this period, tremendous changes in motor cycle helmet laws Do laws reduce mortality? 8

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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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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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Summarize Coefficients (std errors) on helmet law – Cond. Poisson (0.032) – Cond. NB (0.045) Log likelihood – Cond. Poisson – Cond. NB log likelihood = 49.2 =χ 2 (1) – Reject Poisson is the correct model 16

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

Notice that stand errors increase by a factor of