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EFFECT DISPLAYS FOR MULTINOMIAL AND PROPORTIONAL-ODDS LOGIT MODELS

Authors


  • This is a revised version of a paper read at the ASA Methodology Conference 2004. Please address correspondence to John Fox, Department of Sociology, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M4; jfox@mcmaster.ca. We are grateful to Georges Monette for checking some of the derivations in this paper, and to Michael Ornstein and two anonymous reviewers for helpful suggestions.

Abstract

An “effect display” is a graphical or tabular summary of a statistical model based on high-order terms in the model. Effect displays have previously been defined by Fox (1987, 2003) for generalized linear models (including linear models). Such displays are especially compelling for complicated models—for example, those including interactions or polynomial terms. This paper extends effect displays to models commonly used for polytomous categorical response variables: the multinomial logit model and the proportional-odds logit model. Determining point estimates of effects for these models is a straightforward extension of results for the generalized linear model. Estimating sampling variation for effects on the probability scale in the multinomial and proportional-odds logit models is more challenging, however, and we use the delta method to derive approximate standard errors. Finally, we provide software for effect displays in the R statistical computing environment.

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