Open Access
April 1996 Maximum likelihood methods for a generalized class of log-linear models
Joseph B. Lang
Ann. Statist. 24(2): 726-752 (April 1996). DOI: 10.1214/aos/1032894462


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.


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Joseph B. Lang. "Maximum likelihood methods for a generalized class of log-linear models." Ann. Statist. 24 (2) 726 - 752, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0859.62061
MathSciNet: MR1394985
Digital Object Identifier: 10.1214/aos/1032894462

Primary: 62E20 , 62H17

Keywords: asymptotics , constraint equation , freedom equation , marginal model , multinomial distribution , multivariate categorical data , simultaneous model

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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