Gardner W, Mulvey E P, Shaw E C
Western Psychiatric Institute and Clinic, University of Pittsburgh School of Medicine, Pennsylvania 15213, USA.
Psychol Bull. 1995 Nov;118(3):392-404. doi: 10.1037/0033-2909.118.3.392.
The regression models appropriate for counted data have seen little use in psychology. This article describes problems that occur when ordinary linear regression is used to analyze count data and presents 3 alternative regression models. The simplest, the Poisson regression model, is likely to be misleading unless restrictive assumptions are met because individual counts are usually more variable ("overdispersed") than is implied by the model. This model can be modified in 2 ways to accomodate this problem. In the overdispersed model, a factor can be estimated that corrects the regression model's inferential statistics. In the second alternative, the negative binomial regression model, a random term reflecting unexplained between-subject differences is included in the regression model. The authors compare the advantages of these approaches.
适用于计数数据的回归模型在心理学中很少被使用。本文描述了使用普通线性回归分析计数数据时出现的问题，并提出了3种替代回归模型。最简单的泊松回归模型，除非满足严格的假设，否则可能会产生误导，因为个体计数通常比模型所暗示的更具变异性（“过度分散”）。该模型可以通过两种方式进行修改以适应这个问题。在过度分散模型中，可以估计一个因子来校正回归模型的推断统计量。在第二种替代方法，即负二项回归模型中，回归模型中包含一个反映受试者间无法解释差异的随机项。作者比较了这些方法的优点。
