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

被引:1145
作者
Smithson, M [1 ]
Verkuilen, J
机构
[1] Australian Natl Univ, Sch Psychol, Canberra, ACT 0200, Australia
[2] Univ Illinois, Dept Psychol, Urbana, IL 61801 USA
关键词
beta distribution; regression; variance; generalized linear model; heteroscedasticity;
D O I
10.1037/1082-989X.11.1.54
中图分类号
B84 [心理学];
学科分类号
04 ; 0402 ;
摘要
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.
引用
收藏
页码:54 / 71
页数:18
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