A Stabilized Newton-Raphson Algorithm for Log-Linear Models for Frequency Tables Derived by Indirect Observation

A new algorithm is proposed that converges both more quickly and more reliably than currently available alternatives in estimation of asymptotic variances of parameter estimates and may be applied to both grouped and ungrouped data.

Abstract

In a variety of problems involving models from genetics, latent-class analysis, and missing data, I apply a log-linear model to an indirectly observed frequency table. Current algorithms for computation of maximum likelihood estimates for such cases have often been unsatisfactory because they fail to converge at all or they converge at an unacceptable rate. I propose a new algorithm that converges both more quickly and more reliably than currently available alternatives. The algorithm assists in estimation of asymptotic variances of parameter estimates. It may be applied to both grouped and ungrouped data. I illustrate results in two examples from the literature on latent-class analysis.