The Annals of Statistics

Maximum likelihood methods for a generalized class of log-linear models

Joseph B. Lang

Full-text: Open access

Abstract

We discuss maximum likelihood methods for fitting a broad class of multivariate categorical response data models. In particular, we derive the large-sample distributions for maximum likelihood estimators of parameters of product-multinomial generalized log-linear models. The large-sample behavior of other relevant likelihood-based statistics such as goodness-of-fit statistics and adjusted residuals is also described. The asymptotic results are derived within the framework of the constraint specification, rather than the more common freedom specification, of the model. We also outline an improved fitting algorithm for computing parameter maximum likelihood estimates and other relevant statistics. The broad class of multivariate categorical response data models, which are referred to as generalized log-linear models, can imply structure on several response configuration distributions (e.g., joint and marginal distributions). These models, which include as special cases log-linear, logit and cumulative-logit models, enjoy a wide breadth of application including longitudinal, rater-agreement and crossover data analyses.

Article information

Source
Ann. Statist., Volume 24, Number 2 (1996), 726-752.

Dates
First available in Project Euclid: 24 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032894462

Digital Object Identifier
doi:10.1214/aos/1032894462

Mathematical Reviews number (MathSciNet)
MR1394985

Zentralblatt MATH identifier
0859.62061

Subjects
Primary: 62H17: Contingency tables 62E20: Asymptotic distribution theory

Keywords
Asymptotics constraint equation freedom equation marginal model multinomial distribution multivariate categorical data simultaneous model

Citation

Lang, Joseph B. Maximum likelihood methods for a generalized class of log-linear models. Ann. Statist. 24 (1996), no. 2, 726--752. doi:10.1214/aos/1032894462. https://projecteuclid.org/euclid.aos/1032894462


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