A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables
A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables
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DOI：
10.1037/1082-989x.11.1.54
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发表时间：
2006-03-01
影响因子：
7
通讯作者：
Verkuilen, J
中科院分区：
文献类型：
--
作者：
Smithson, M;Verkuilen, J
不可校正的偏斜和异方差是心理学数据中的“柠檬”，但许多重要的变量自然地表现出这些属性。对于具有下限和上限的尺度，模型的合适候选者是beta分布，它非常灵活，模型的偏斜也很好。作者提出了最大似然回归模型，假设因变量是有条件的β分布，而不是高斯分布。该方法使用其自身不同的预测因子集（连续和/或分类）对均值（位置）和方差（离散）进行建模，从而对异方差性进行建模。位置子模型链接函数是logit，从而类似于逻辑回归，而离散子模型是对数线性的。真实的算例表明，这些模型能很好地处理独立观测值的情况。本文讨论了贝塔回归和替代技术，模型选择和解释，实际估计和软件之间的比较。
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.