Methods and Evaluation, Department of Psychology, Bielefeld University, Universitätsstraße 25, D-33501, Bielefeld, Germany.
Clinical Psychology and Psychotherapy, Department of Psychology, Bielefeld University, Universitätsstraße 25, D-33501, Bielefeld, Germany.
Behav Res Methods. 2024 Dec;56(8):8932-8954. doi: 10.3758/s13428-024-02483-4. Epub 2024 Aug 26.
In psychology and the social sciences, researchers often model count outcome variables accounting for latent predictors and their interactions. Even though neglecting measurement error in such count regression models (e.g., Poisson or negative binomial regression) can have unfavorable consequences like attenuation bias, such analyses are often carried out in the generalized linear model (GLM) framework using fallible covariates such as sum scores. An alternative is count regression models based on structural equation modeling, which allow to specify latent covariates and thereby account for measurement error. However, the issue of how and when to include interactions between latent covariates or between latent and manifest covariates is rarely discussed for count regression models. In this paper, we present a latent variable count regression model (LV-CRM) allowing for latent covariates as well as interactions among both latent and manifest covariates. We conducted three simulation studies, investigating the estimation accuracy of the LV-CRM and comparing it to GLM-based count regression models. Interestingly, we found that even in scenarios with high reliabilities, the regression coefficients from a GLM-based model can be severely biased. In contrast, even for moderate sample sizes, the LV-CRM provided virtually unbiased regression coefficients. Additionally, statistical inferences yielded mixed results for the GLM-based models (i.e., low coverage rates, but acceptable empirical detection rates), but were generally acceptable using the LV-CRM. We provide an applied example from clinical psychology illustrating how the LV-CRM framework can be used to model count regressions with latent interactions.
在心理学和社会科学中，研究人员经常对潜在预测因子及其相互作用进行计数结果变量建模。即使在这种计数回归模型（例如泊松或负二项回归）中忽略测量误差可能会产生不利的后果，例如衰减偏差，但这种分析通常是在广义线性模型（GLM）框架中使用不可靠的协变量（例如总和分数）进行的。另一种方法是基于结构方程建模的计数回归模型，它允许指定潜在协变量，从而可以解释测量误差。然而，对于计数回归模型，很少讨论如何以及何时包括潜在协变量之间或潜在协变量与显式协变量之间的交互作用。在本文中，我们提出了一种允许潜在协变量以及潜在和显式协变量之间相互作用的潜在变量计数回归模型（LV-CRM）。我们进行了三项模拟研究，研究了 LV-CRM 的估计准确性，并将其与基于 GLM 的计数回归模型进行了比较。有趣的是，我们发现，即使在可靠性较高的情况下，基于 GLM 的模型的回归系数也可能会严重偏倚。相比之下，即使对于中等样本量，LV-CRM 也提供了几乎无偏的回归系数。此外，基于 GLM 的模型的统计推断结果喜忧参半（即低覆盖率，但可接受的经验检测率），但使用 LV-CRM 通常是可以接受的。我们提供了一个来自临床心理学的应用示例，说明了如何使用 LV-CRM 框架对具有潜在交互作用的计数回归进行建模。
