Education 231C

Applied Categorical & Nonnormal Data Analysis

Complementary Log-Log Models

Complementary log-log models repesent a third altenative to logistic regression and probit analysis for binary response variables. Complementary log-log models are fequently used when the probability of an event is very small or very large. Unlike logit and probit the complementary log-log function is asymmetrical. A graph of the complementary log-log fuanction is given below.

A graph of predicted probabilities is shown next. The log-likelihood function for complementary log-log is, where F(z) = 1-exp(-exp(z)) and wj denotes optional weights.

Examples follow a similar pattern that the ones in logit and probit analyses.

Example 1

Example 2

Categorical Data Analysis Course

Phil Ender