ERIC Number: EJ735348
Record Type: Journal
Publication Date: 2006-Mar
A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables
Smithson, Michael; Verkuilen, Jay
Psychological Methods, V11 n1 p54-71 Mar 2006
Uncorrectable skew and heteroscedasticity are among the "lemons" of psychological data, yet many important variables naturally exhibit these properties. For scales with a lower and upper bound, a suitable candidate for models is the beta distribution, which is very flexible and models skew quite well. The authors present maximum-likelihood regression models assuming that the dependent variable is conditionally beta distributed rather than Gaussian. The approach models both means (location) and variances (dispersion) with their own distinct sets of predictors (continuous and/or categorical), thereby modeling heteroscedasticity. The location submodel link function is the logit and thereby analogous to logistic regression, whereas the dispersion submodel is log linear. Real examples show that these models handle the independent observations case readily. The article discusses comparisons between beta regression and alternative techniques, model selection and interpretation, practical estimation, and software.
Descriptors: Maximum Likelihood Statistics, Predictor Variables, Mathematical Models, Comparative Analysis, Psychology, Multidimensional Scaling, Discriminant Analysis
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Publication Type: Journal Articles; Reports - Evaluative
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