[Limdep Nlogit List] On overdispersion in random effects panel Poisson models

[Bjorn Lardner]

Greetings, 

This is a post from a wildlife ecologist with a data set that I'm trying 
to analyze in LIMDEP. I?m looking for advice on correction for 
overdispersion in random effects panel Poisson models. 

Somewhat simplified, we have subjected a population of animals (snakes) to 
different trap types. It?s a factorial design with 3 factors, each taking 
either of 2 states (effect coded as -1 or 1), hence 2^3 = 8 discrete 
combinations. We recorded how many times each animal entered each of the 
eight trap type combinations over a period of time. We released animals 
after each capture, and they could enter different trap types in no 
particular order. Each animal also had a set of individual covariates such 
as size, weight, and sex, and these did not change during the study. In 
our input file, 8 rows constitute one panel or one cluster. 

We?ve been trying to decide whether a cluster or a panel specification 
would be best suited to analyze this data with a Poisson model. Because we 
were interested in addressing latent heterogeneity - using a latent class 
model (LCM) specification - we lean towards a panel model. [That?s because 
when using a cluster specification and LCM, the class assignment is done 
for each trap type-by-animal (i.e., each row in the data set); not for 
each individual animal (i.e., each cluster) as would be the logical class 
stratum.] By specifying the panel as a random effect, we overcome the 
problem with invariant covariates within a panel. So far, so good. An 
example of a simple candidate model is? 

POISSON;Lhs=COUNT;Rhs=ONE,T,B,A,S,TB,TS,BS;Pds=8;Random effects$ 

?where T, B, and A are our factorial variables, S is a continuous 
variable, and TB, TS, and BS are biologically plausible interactions. 

However, I am confused about corrections for overdispersion in the data in 
a panel context. I have noticed that the commands HC1 (scaling the 
asymptotic covariance matrix; manual p. E24-14) and HC2 (robust covariance 
matrix; manual p. E24-12) will only affect the *first* Poisson step in the 
output, but *not* the table of effects (or rather, the SE estimates) in 
the second table of the output ? the table resulting from invoking the 
panel specification. Why is that the case? 
   In my mind, there could potentially be overdispersion attributed to 
effects other than the panel stratification. One such source of 
overdispersion could be overlooked but relevant covariates, causing 
apparent (as opposed to real, sensu Hilbe 2007) overdispersion. Yet, 
adding the HC1 or HC2 commands produce exactly the same standard errors as 
a panel model omitting any HC-command. 

Somewhat related to this is the fact that only the *first* step in the 
analysis (the one before the panel adjustment kicks in) has statistics on 
overdispersion and, if HC1 or HC2 is requested, a scale factor for 
overdispersion. 
   How do I tell if there is still overdispersion after the panel effect 
has been accounted for in the second step of the analysis? 


If anybody cares to shed some light on this in terms that can be 
understood by a non-statistician, I would be most grateful! 

Sincerely, 
Bjorn Lardner / snake wrangler