Effect Displays inRfor Generalised Linear Models

Abstract

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. I call these tables or graphs effect displays. 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 (e.g., main effects marginal to an interaction) 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. Background and MotivationThis 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 (in the sense of Nelder, 1977), such as polynomial terms, or main effects and interactions. I call these tables or graphs effect displays.I assume that readers are familiar with R, which is a free, open-source implementation of the S statistical programming language and computing environment. Extensive information on R is available at <http://www.r-project.org/>. The software described in the paper is distributed as the effects package for R, available on the Comprehensive R Archive Network (CRAN) at <http://cran.r-project.org/>.The general approach implemented in the effects package is a modest extension of methods introduced by Fox (1987). Similar, if less general, ideas have a long history, dating at least to Fisher's (1936) "adjusted means" in the analysis of covariance. Goodnight and Harvey's (1978) "least-squares means" in analysis of variance and covariance, and Searle, Speed, and Milliken's (1980) "estimated population marginal means" are other examples, though all of these approaches are restricted to interactions among factors (i.e., categorical predictors) in a linear model. Recently King, Tomz, and Wittenberg (2000) and Tomz, Wittenberg, and King (2003) have presented similar ideas, but their approach, based on Monte-Carlo simulation of a model, is much more complicated than the one discussed here.To motivate effect displays, consider the following data on police treatment of individuals arrested in Toronto for simple possession of small quantities of marijuana. (The data discussed here are part of a larger data set featured in a series of articles in the Toronto Star newspaper.) Under these circumstances police have the option of releasing an arrestee with a summons to appear in court -similar to a traffic ticket; altern...

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