Hi,

I'd like to replicate the coefficients obtained by 'poisson ; offset' with MLE statements.
Here is an example that shows the differences.
Btw, is there a more efficient way of coding the MLE e.g. in case of 20 regressors?

Cheers
Leon

<hansl>
open rac3d.gdt --quiet
list X = SEX INCOME

# Poisson regression
poisson DVISITS 0 X

# Initial OLS to get starting values for the coefficients
ols DVISITS 0 X --quiet
list xList = $xlist
matrix b = zeros(1,nelem(xList))

mle loglik = DVISITS*Xb - exp(Xb)
    series Xb = lincomb(xList,b)   
    deriv b = {DVISITS - exp(Xb), \
      SEX*(DVISITS - exp(Xb)), \
      INCOME*(DVISITS - exp(Xb))}
end mle --hessian
 
# Poisson regression with Offset
poisson DVISITS 0 X ; AGE

series DVISITS_off = DVISITS/AGE  # try

mle loglik = DVISITS_off*Xb - exp(Xb)
    series Xb = lincomb(xList,b)   
    deriv b = {DVISITS_off - exp(Xb), \
      SEX*(DVISITS_off - exp(Xb)), \
      INCOME*(DVISITS_off - exp(Xb))}
end mle --hessian
<hansl>