Abstract：
Generalized linear mixed models (GLMMs) have great potential to deal with count data in single-case experimental designs (SCEDs). However, applied researchers have faced challenges in making various statistical decisions when using such advanced statistical techniques in their own research. This study focused on a critical issue by investigating the selection of an appropriate distribution to handle different types of count data in SCEDs due to overdispersion and/or zero-inflation. To achieve this, I proposed two model selection frameworks, one based on calculating information criteria (AIC and BIC) and another based on utilizing a multistage-model selection procedure. Four data scenarios were simulated including Poisson, negative binominal (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB). The same set of models (i.e., Poisson, NB, ZIP, and ZINB) were fitted for each scenario. In the simulation, I evaluated 10 model selection strategies within the two frameworks by assessing the model selection bias and its consequences on the accuracy of the treatment effect estimates and inferential statistics. Based on the simulation results and previous work, I provide recommendations regarding which model selection methods should be adopted in different scenarios. The implications, limitations, and future research directions are also discussed.
摘要：
广义线性混合模型（GLMM）在处理单案例实验设计（SCED）中的计数数据方面具有巨大的潜力。然而,应用研究人员在自己的研究中使用这种先进的统计技术时，在做出各种统计决策时面临挑战。这项研究通过研究选择适当的分布来处理由于过度分散和/或零膨胀而导致的SCED中不同类型的计数数据，从而专注于一个关键问题。为了实现这一点，我提出了两个模型选择框架，一个基于计算信息标准（AIC和BIC），另一个基于利用多阶段模型选择程序。模拟了四种数据场景，包括泊松，负二项（NB），零膨胀泊松（ZIP），和零膨胀负二项式(ZINB)。同一组模型(即，Poisson,NB,ZIP,和ZINB)适用于每种情况。在模拟中,通过评估模型选择偏差及其对治疗效果估计和推论统计的准确性的影响，我评估了两个框架内的10种模型选择策略。根据仿真结果和前期工作,我提供了关于在不同情况下应采用哪些模型选择方法的建议。的影响，局限性,并对未来的研究方向进行了展望。
