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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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slide3

* 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

slide4

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

------------------------------------------------------------------------------

slide5

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

slide6

-2 log likelihood test

    • LL for Poisson = -22275.351
    • LL for NB = 14519.721
    • -2 LL difference = -15511
cond c ount data models
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?
covariates
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
slide13

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

summarize
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
slide17

Results similar to cond.

model but w/ smaller

std errors

Easily reject delta=0

ad