Advanced Regression: Tweedie and Zero-Inflated Models

Tweedie Distribution

The Tweedie distribution is an exponential dispersion model with variance function V(mu) = mu^p. Different values of the power parameter p yield different distributions: p=0 (Normal), p=1 (Poisson), 1

Zero-Inflated GLMs

Zero-inflated regression models combine a logistic component for the probability of a structural zero with a GLM for the count process. For a zero-inflated Poisson GLM, E[Y] = (1-pi)*lambda and Var(Y) = (1-pi)*lambda*(1 + pi*lambda). Both pi and lambda can depend on different sets of covariates. The EM algorithm or direct maximum likelihood estimates both components simultaneously. Model selection between standard GLM, zero-inflated, and hurdle models uses AIC, BIC, or Vuong's test. Exam MAS-II tests Tweedie models in pricing contexts and zero-inflated models for data with excess zeros.