Penalized Multinomial Logistic Regression
Description
Extends the approach proposed by Firth (1993) for bias
reduction of MLEs in exponential family models to the
multinomial logistic regression model with general covariate
types. Modification of the logistic regression score function
to remove first-order bias is equivalent to penalizing the
likelihood by the Jeffreys prior, and yields penalized maximum
likelihood estimates (PLEs) that always exist. Hypothesis
testing is conducted via likelihood ratio statistics. Profile
confidence intervals (CI) are constructed for the PLEs.