I am working with count data (number of pregnancies per woman), and using glm Poisson (log-link) to model determinants of the former count variable.
From simple descriptives I observe that my data are overdispersed: Mean = 4.18, Variance = 7.14.
However, after fitting the glm Poisson model with the full set of control, if I run
dispersiontest from the R package
AER I get a statistically significant underdispersion equal to 0.68, p-value=0.000 (to test for underdispersion:
alternative = c("less")).
If some (relevant) controls are omitted from the model (i.e. age, dependency ratio, and dummies for provinces), the model results to be equidispersed (0.98, p-value=0.298).
I see that underdispersion is uncommon, and solution exists to solve for it (e.g., Conway–Maxwell–Poisson regression). In fact, when applying this latter model the equidispersion assumption is satisfied.
However, I am concerned with the reason why I get underdispersion when controlling for such relevant covariates. Given that overdispersion may arise because of omitted variables, or in presence of clustered observations, I am just wondering if in my case controlling for the clustered nature of the data (survey data, 2-stage clustering sampling), is radically "over" reducing the variance.