Someone asked me privately if exponentiating the linear predictor produces
the fitted value for all maximum likelihood models. No it does not -- only for
those models that are members of the exponential family of distributions
having a log link. For example, you would exponentiate the linear predictor to
obtain the fitted values, mu, for the log-normal, canonical Poisson, and
log-negative binomial (the log link is not canonical for the NB distribution).
Read the reference manual for GLM to get more information.
Joe Hilbe
--------------------
trpois0 and trnbin0 are simliar to other ML based programs in Stata. When
you type predict after modeling, you get the linear predictor, XB. To
obtain
the fitted values, type
predict lp
gen mu=exp(lp)
Note that Stata's -poisson- and nbreg commands have been written so that
using predict afterwards generates the fitted value rather than the standard
ML
linear predictor.
You can check this out yourself by comparing output; e.g.
use cancer
tab drug, gen(drug)
poisson studytim age drug2 drug3
predict mu_p
trpois0 studytim age drug2 drug3
predict lp
gen mu_tr = exp(lp)
l mu_p lp mu_tr
You'll find that mu_p and mu_tr are the same. Type
gen lp_p = ln(mu_p)
to obtain the poisson command linear predictors
The same is the case with negative binomial: nbreg and trnbin0.
I nearly always use the glm version of poisson since it displays BIC and
AIC
GOF statistics, along with other GOF values and statistical diagnostics, as
well as allowing you to immediately calculate lp, mu, and 11 types of
residuals. With the -glm- command you can also obtain standard errors using
jacknife
and bootstrap -- and a variety of robust techniques.
With the negative binomial it is a bit different. I use nbreg to obtain an
estimate of the ancillary parameter and then use that value for alpha in the
glm version. I can then utilize the above mentioned modeling utilities that
glm
offers, and obtain the many residual statistics for
model assessment.
Joe Hilbe
I believe -trnbin0- is producing the linear prediction. Exponentiate the
values to get the predicted number of events.
Scott
>
> Dear all,
> I have used a truncated negative binomial model (trbin0) for the
> conditional number of visits to the doctor. I have found out that the
> predictions after the estimation of the positive number of visits is
> sometimes negative. Is there any one who could help me to understand why
> that happens?
>
> Many thanks in advance,
>
> Dolores
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