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Lang, Joseph B.

Maximum likelihood methods for a generalized class of log-linear models. (English) Zbl 0859.62061

Ann. Stat. 24, No. 2, 726-752 (1996).
Summary: 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 applications including longitudinal, rater-agreement and cross-over data analyses.

Cited in 29 Documents

MSC:

62H17 Contingency tables
62J12 Generalized linear models (logistic models)
62H12 Estimation in multivariate analysis
62E20 Asymptotic distribution theory in statistics

Keywords:

constraint equation; freedom equation; marginal model; multinomial distribution; simultaneous model; multivariate categorical response data models; large-sample distributions; maximum likelihood estimators; product-multinomial generalized log-linear models; goodness-of-fit statistics; adjusted residuals; fitting algorithm; generalized log-linear models
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References:

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