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Log‐linear modeling
Author(s) -
von Eye Alexander,
Mun EunYoung,
Mair Patrick
Publication year - 2011
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.203
Subject(s) - log linear model , linear model , categorical variable , dependency (uml) , hierarchical generalized linear model , marginal model , logarithm , mathematics , generalized linear model , interpretation (philosophy) , generalized linear mixed model , design matrix , computer science , statistics , algorithm , regression analysis , artificial intelligence , mathematical analysis , programming language
This article describes log‐linear models as special cases of generalized linear models. Specifically, log‐linear models use a logarithmic link function. Log‐linear models are used to examine joint distributions of categorical variables, dependency relations, and association patterns. Three types of log‐linear models are discussed, hierarchical models, nonhierarchical models, and nonstandard models. Emphasis is placed on parameter interpretation. It is demonstrated that parameters are best interpretable when they represent the effects specified in the design matrix of the model. Parameter interpretation is illustrated first for a standard hierarchical model, and then for a nonstandard model that includes structural zeros. In a data example, the relationships among race of defendant, race of victim, and death penalty sentence are examined using a log‐linear model with all three two‐way interactions. Recent developments in log‐linear modeling are discussed. WIREs Comput Stat 2012, 4:218–223. doi: 10.1002/wics.203 This article is categorized under: Statistical Models > Generalized Linear Models