Overdispersion: Detection and Modeling Approaches

What Is Overdispersion

Overdispersion occurs when the observed variance exceeds the variance implied by the assumed model. For Poisson data, the mean equals the variance; overdispersion means Var(Y) > E[Y]. Common causes include unobserved heterogeneity (omitted variables), clustering, and excess zeros. Detection methods include comparing the Pearson chi-squared or deviance to the degrees of freedom (ratio significantly above 1 indicates overdispersion), and formal tests like the Dean-Lawless test. Ignoring overdispersion leads to underestimated standard errors and overly optimistic significance tests.

Modeling Solutions

Several approaches address overdispersion. Quasi-Poisson models introduce a dispersion parameter phi so Var(Y) = phi*mu, adjusting standard errors without changing point estimates. The negative binomial model adds a parameter making Var(Y) = mu + mu^2/k, naturally accommodating overdispersion. Mixed models with random effects capture unobserved heterogeneity. Zero-inflated models handle excess zeros specifically. The choice depends on the suspected cause: heterogeneity favors negative binomial or mixed models, while excess zeros favor zero-inflated approaches. Exam MAS-I tests detection, consequences, and remedies for overdispersion.