Analysis of Variance and Generalized Linear Models

Abstract

Analysis of variance (ANOVA) models apply to data that occur in groups. The fundamental ANOVA model is the one-way model that specifies a common mean value for the observations in a group. The analysis of variance associated with the one-way model is presented. When the groups in a one-way ANOVA are identified as combinations of two or more factors, models incorporating factor main effects and factor interactions provide a useful device for exploring the underlying structure of the data. The main effects only two-way ANOVA model is discussed along with its interpretation and how it differs from the interaction model. Three factor models and their interpretations are discussed. Appropriate models can be identified by fitting sequences of successively smaller models and using general testing procedures to identify models within each sequence that fit well. ANOVA models are also useful in generalized linear models. These are discussed with examples involving logistic regression. Again, appropriate models can be identified by fitting sequences of models.