The outcomes in single-case experimental designs (SCEDs) are often counts or proportions. In our study, we provided a colloquial illustration for a new class of generalized linear mixed models (GLMMs) to fit count and proportion data from SCEDs. We also addressed important aspects in the GLMM framework including overdispersion, estimation methods, statistical inferences, model selection methods by detecting overdispersion, and interpretations of regression coefficients. We then demonstrated the GLMMs with two empirical examples with count and proportion outcomes in SCEDs. In addition, we conducted simulation studies to examine the performance of GLMMs in terms of biases and coverage rates for the immediate treatment effect and treatment effect on the trend. We also examined the empirical Type I error rates of statistical tests. Finally, we provided recommendations about how to make sound statistical decisions to use GLMMs based on the findings from simulation studies. Our hope is that this article will provide SCED researchers with the basic information necessary to conduct appropriate statistical analysis of count and proportion data in their own research and outline the future agenda for methodologists to explore the full potential of GLMMs to analyze or meta-analyze SCED data. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

中文翻译：

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使用计数和比例数据的单案例研究中的多级建模：演示和评估。

单例实验设计 (SCED) 的结果通常是计数或比例。在我们的研究中，我们为一类新型广义线性混合模型 (GLMM) 提供了通俗说明，以拟合来自 SCED 的计数和比例数据。我们还讨论了 GLMM 框架中的重要方面，包括过度离散、估计方法、统计推断、通过检测过度离散的模型选择方法以及回归系数的解释。然后，我们通过两个经验示例演示了 GLMM，其中包含 SCED 中的计数和比例结果。此外，我们还进行了模拟研究，以检验 GLMM 在即时治疗效果和趋势治疗效果的偏差和覆盖率方面的表现。我们还检查了统计测试的经验第一类错误率。最后，我们提供了有关如何根据模拟研究的结果做出使用 GLMM 的合理统计决策的建议。我们希望本文能够为 SCED 研究人员提供必要的基本信息，以便对他们自己的研究中的计数和比例数据进行适当的统计分析，并概述方法学家探索 GLMM 分析或荟萃分析 SCED 的全部潜力的未来议程数据。（PsycInfo 数据库记录 (c) 2023 APA，保留所有权利）。