**********************
* Poisson regression *
**********************

log using poisson_negbin.log, replace

use http://fmwww.bc.edu/ec-p/data/wooldridge/CRIME1, clear

* OLS

reg  narr86 pcnv avgsen tottime ptime86 qemp86 inc86 black hispan  born60

* Poisson Regression

poisson  narr86 pcnv avgsen tottime ptime86 qemp86 inc86 black hispan  born60, nolog
mfx compute

scalar loglu=e(ll)
* keep the log-likelihood value evaluated at MLE estimator

* LR test for parameter restriction:
* the null is to exclude: black and hispan
poisson  narr86 pcnv avgsen tottime ptime86 qemp86 inc86  born60, nolog
scalar loglr=e(ll)

scalar LR=2*(loglu-loglr)
dis "the LR statistic is " LR
scalar p_value=chi2tail(2,LR)
dis "the p-value of LR statistic is " p_value

* regression_based test for over-dispersion in the model above
* we need to keep the "stata-score" vector as lamda
quietly poisson  narr86 pcnv avgsen tottime ptime86 qemp86 inc86 black hispan  born60, score(lamda)
gen zi =( (narr86-lamda)^2-narr86)/(sqrt(2)*lamda)
* run the regression of zi on lamda
reg zi lamda, noconstant

*************************************************************
* Negative binomial regression  *
*************************************************************

nbreg narr86 pcnv avgsen tottime ptime86 qemp86 inc86 black hispan  born60, nolog
mfx compute


*************************************************************
*  Zero-inflated Poisson regression model *
*************************************************************

zip narr86 pcnv avgsen tottime ptime86 qemp86 inc86 black hispan born60, inflate(pcnv avgsen tottime ptime86 qemp86 inc86 black hispan born60) vuong probit nolog
mfx compute

*************************************************************
*  Zero-inflated Negative Binomial regression model *
*************************************************************

zinb narr86 pcnv avgsen tottime ptime86 qemp86 inc86 black hispan born60, inflate(pcnv avgsen tottime ptime86 qemp86 inc86 black hispan born60) vuong probit nolog
mfx compute

* Stata example

webuse fish, clear
zip count persons livebait, inflate(child camper) vuong probit nolog
mfx compute
zinb count persons livebait, inflate(child camper) vuong probit nolog
mfx compute


*************************************************************
*  Panel Poisson model (FE, RE) *
*************************************************************

webuse ships.dta, clear

xtpois accident op_75_79 co_65_69 co_70_7 co_75_79, i(ship) ex(service) re nolog
xtpois accident op_75_79 co_65_69 co_70_7 co_75_79, i(ship) ex(service) re normal nolog
xtpois accident op_75_79 co_65_69 co_70_7 co_75_79, i(ship) ex(service) fe nolog