This paper describes the implementation in R of a method for tabular or graphical display of terms in a complex generalised linear model. By complex, I mean a model that contains terms related by marginality or hierarchy, such as polynomial terms, or main effects and interactions. These displays, called effect displays, are constructed by identifying high-order terms in a generalised linear model. Fitted values under the model are computed for each such term. The lower-order 'relatives' of a high-order term are absorbed into the term, allowing the predictors appearing in the high-order term to range over their values. The values of other predictors are fixed at typical values: for example, a covariate could be fixed at its mean or median, a factor at its proportional distribution in the data, or to equal proportions in its several levels. Variations of effect displays are also described, including representation of terms higher-order to any appearing in the model.
The paper discusses the implementation of effect displays in the R package 'effects'. The function 'effect' returns an object of class 'effect', containing information for constructing an effect display. The essential input includes a linear or generalised-linear model object and a term for which the effect is to be computed. The function 'all.effects' identifies all high-order terms in a model and returns a list of effects corresponding to these terms. The package also provides print, summary, and plot methods for effect objects and effect.list objects. Effect plots are created using Trellis graphics (via the lattice package in R). The plot method for effect.list objects presents a text menu from which the user can select effects to graph.
The paper illustrates the use of effect displays with examples from the 'Arrests' and 'Cowles' datasets. It discusses the interpretation of effects on the scale of the linear predictor and the response scale. The paper also addresses the issue of safe prediction for terms in a linear or generalised linear model with bases that depend upon the data, such as orthogonal polynomial regressors or regression splines. The paper concludes with a discussion of the importance of effect displays in interpreting complex generalised linear models.This paper describes the implementation in R of a method for tabular or graphical display of terms in a complex generalised linear model. By complex, I mean a model that contains terms related by marginality or hierarchy, such as polynomial terms, or main effects and interactions. These displays, called effect displays, are constructed by identifying high-order terms in a generalised linear model. Fitted values under the model are computed for each such term. The lower-order 'relatives' of a high-order term are absorbed into the term, allowing the predictors appearing in the high-order term to range over their values. The values of other predictors are fixed at typical values: for example, a covariate could be fixed at its mean or median, a factor at its proportional distribution in the data, or to equal proportions in its several levels. Variations of effect displays are also described, including representation of terms higher-order to any appearing in the model.
The paper discusses the implementation of effect displays in the R package 'effects'. The function 'effect' returns an object of class 'effect', containing information for constructing an effect display. The essential input includes a linear or generalised-linear model object and a term for which the effect is to be computed. The function 'all.effects' identifies all high-order terms in a model and returns a list of effects corresponding to these terms. The package also provides print, summary, and plot methods for effect objects and effect.list objects. Effect plots are created using Trellis graphics (via the lattice package in R). The plot method for effect.list objects presents a text menu from which the user can select effects to graph.
The paper illustrates the use of effect displays with examples from the 'Arrests' and 'Cowles' datasets. It discusses the interpretation of effects on the scale of the linear predictor and the response scale. The paper also addresses the issue of safe prediction for terms in a linear or generalised linear model with bases that depend upon the data, such as orthogonal polynomial regressors or regression splines. The paper concludes with a discussion of the importance of effect displays in interpreting complex generalised linear models.