* W.H. Greene, Econometric Analysis, Fourth Edition, 2000. 
SAMPLE 1 40
* Table A19.3 - Data on ship accidents 
READ (ship.shd) / NAMES
* Missing values are assigned the code -999.
SET MISSVALU=-999
SET SKIPMISS
SET NOWARNMISS 

* Example 19.22 - Poisson Regression, pp. 881-882.

* Generate the "Log service" variable.
GENR lserv=LOG(Months)
* An unrestricted model 
MLE Acc B C D E p6569 p7074 p7579 c7579 lserv / TYPE=EPOISSON COEF=BETA

* The results reported in the first column of Table 19.18, p. 882
* impose the restriction of 1 for the coefficient of lserv.
* (See Footnote 61, p. 881 for explanation about this restriction).

* The NL command is used below to estimate the Poisson regression
* model with restrictions.
* The LGAM(x) function with the GENR command generates a log gamma function. 
GENR CONST = LGAM(Acc+1)
GEN1 BETA:9=BETA:10
* Estimation of a Poisson regression model by maximum likelihood.
* Specify the log-density for a single observation based on the
* formula for lnL on p. 880.
XB: (B1*B+B2*C+B3*D+B4*E+B5*p6569+B6*p7074+B7*p7579+B8*c7579+lserv+B0)
NL 1 / NCOEF=9 LOGDEN START=BETA 
EQ -EXP([XB])+ &
   Acc*[XB] - CONST
END
STOP