Coxe Stefany, West Stephen G, Aiken Leona S
Department of Psychology, Arizona State University, USA.
J Pers Assess. 2009 Mar;91(2):121-36. doi: 10.1080/00223890802634175.
Count data reflect the number of occurrences of a behavior in a fixed period of time (e.g., number of aggressive acts by children during a playground period). In cases in which the outcome variable is a count with a low arithmetic mean (typically < 10), standard ordinary least squares regression may produce biased results. We provide an introduction to regression models that provide appropriate analyses for count data. We introduce standard Poisson regression with an example and discuss its interpretation. Two variants of Poisson regression, overdispersed Poisson regression and negative binomial regression, are introduced that may provide more optimal results when a key assumption of standard Poisson regression is violated. We also discuss the problems of excess zeros in which a subgroup of respondents who would never display the behavior are included in the sample and truncated zeros in which respondents who have a zero count are excluded by the sampling plan. We provide computer syntax for our illustrations in SAS and SPSS. The Poisson family of regression models provides improved and now easy to implement analyses of count data. [Supplementary materials are available for this article. Go to the publisher's online edition of Journal of Personality Assessment for the following free supplemental resources: the data set used to illustrate Poisson regression in this article, which is available in three formats-a text file, an SPSS database, or a SAS database.].
计数数据反映了在固定时间段内某种行为发生的次数（例如，儿童在操场活动期间的攻击性行为次数）。在结果变量为算术平均值较低（通常<10）的计数数据的情况下，标准的普通最小二乘法回归可能会产生有偏差的结果。我们介绍了一些回归模型，这些模型为计数数据提供了适当的分析方法。我们通过一个例子介绍标准泊松回归，并讨论其解释。还介绍了泊松回归的两种变体，即过度分散泊松回归和负二项回归，当标准泊松回归的一个关键假设被违反时，它们可能会提供更优的结果。我们还讨论了零值过多的问题，即在样本中包含了永远不会表现出该行为的受访者子群体，以及截断零值的问题，即在抽样计划中排除了计数为零的受访者。我们提供了在SAS和SPSS中进行示例说明的计算机语法。泊松回归模型家族为计数数据提供了改进且易于实施的分析方法。[本文提供补充材料。请访问《人格评估杂志》出版商的在线版本，获取以下免费补充资源：本文用于说明泊松回归的数据集，有三种格式可供选择——文本文件、SPSS数据库或SAS数据库。]
