A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables

Michael Smithson*, Jay Verkuilen

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1034 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)54-71
    Number of pages18
    JournalPsychological Methods
    Issue number1
    Publication statusPublished - Mar 2006


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