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date: 15 April 2021

Abstract and Keywords

The general linear model (GLM), which includes multiple regression and analysis of variance, has become psychology’s data analytic workhorse. The GLM can flexibly represent and test a wide variety of relationships between independent variables and a single continuous outcome variable. When the outcome variable takes on other forms (e.g., binary, ordered and unordered categories, counts), GLM may give nonoptimal performance. The generalized linear model (GLiM) extends the well-developed GLM approach to address these types of outcome variables. We describe the basic framework of GLiM and discuss several commonly used exemplars: logistic regression for binary outcomes, multinomial logistic regression for unordered categories, ordinal logistic regression for ordered categories, and Poisson regression for count outcomes. We also consider hurdle and zero-inflated Poisson regression models for data sets in which zero has a special status. Finally, we discuss model estimation, significance testing, measures of model fit, model diagnostics, and residual checking. With the increasing availability of user-friendly software to perform GLiM analyses, we expect the use of these models in psychology will increase dramatically in the coming years.

Keywords: Multiple regression, generalized linear model, logistic regression, ordinal regression, Poisson regression, counts, link function, conditional distribution, zero-inflated Poisson, diagnostics

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