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st: Modeling Options Overdispersion and "excess zeros"
I am working with data that gives clear evidence of both overdispersion
and excess zeros. Accordingly, I have been examining the viability of
modelling it using zero-inflated models (ZIP and ZINB) as well as
negative binomial regression (NBRM). Vuong tests tell me that ZIP is
preferred to the standard Poisson; on the other hand, ZINB does not
give a significant improvement over NBRM, implying (as I understand it)
that either a zero-inflating process or between-subject heterogeneity
may account for both the overdispersion and the excess zeros in the raw
data. At the same time (and similar to the the example given in David
Dukker's reponse to an issue like this in FAQ), standard errors for
ZINB are large, suggesting a poor fit of this model. Subsequently, I
followed that procedures given in Long and Freese (2e: 2003, pp.
283-84) and graphed the differences between the observed probabilities
and mean predictions for the different models. The results indicate
that NBRM performing more poorly than ZIP, with ZIP and ZINB performing
in an almost identical manner. Subsequently (and again following Long
and Freese) I have compared the models using BIC', with ZIP emerging as
overall best. From this, I have concluded that ZIP is my best option.
At the same time, it also fits with where I am at substantively with
these data. To those who actually have knowledge of the underlying
processes associate with this, does all this seem reasonable? Have I
left something out or made a leap I shouldn't have? Thanks.
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