Wiley Robert W, Rapp Brenda
Department of Cognitive Science, Johns Hopkins University, Baltimore, MD, USA.
Aphasiology. 2019;33(1):1-30. doi: 10.1080/02687038.2018.1454884. Epub 2018 Mar 21.
Advances in statistical methods and computing power have led to a renewed interest in addressing the statistical analysis challenges posed by Small-N Designs (SND). Linear mixed-effects modeling (LMEM) is a multiple regression technique that is flexible and suitable for SND and can provide standardized effect sizes and measures of statistical significance.
Our primary goals are to: 1) explain LMEM at the conceptual level, situating it in the context of treatment studies, and 2) provide practical guidance for implementing LMEM in repeated measures SND.
METHODS & PROCEDURES: We illustrate an LMEM analysis, presenting data from a longitudinal training study of five individuals with acquired dysgraphia, analyzing both binomial (accuracy) and continuous (reaction time) repeated measurements.
OUTCOMES & RESULTS: The LMEM analysis reveals that both spelling accuracy and reaction time improved and, for accuracy, improved significantly more quickly under a training schedule with distributed, compared to clustered, practice. We present guidance on obtaining and interpreting various effect sizes and measures of statistical significance from LMEM, and include a simulation study comparing two -value methods for generalized LMEM.
We provide a strong case for the application of LMEM to the analysis of training studies as a preferable alternative to visual analysis or other statistical techniques. When applied to a treatment dataset, the evidence supports that the approach holds up under the extreme conditions of small numbers of individuals, with repeated measures training data for both continuous (reaction time) and binomially distributed (accuracy) dependent measures. The approach provides standardized measures of effect sizes that are obtained through readily available and well-supported statistical packages, and provides statistically rigorous estimates of the expected average effect size of training effects, taking into account variability across both items and individuals.
统计方法和计算能力的进步使得人们重新关注解决小样本设计（SND）带来的统计分析挑战。线性混合效应建模（LMEM）是一种多元回归技术，它灵活且适用于小样本设计，能够提供标准化效应量和统计显著性度量。
我们的主要目标是：1）在概念层面解释线性混合效应建模，将其置于治疗研究的背景中；2）为在重复测量小样本设计中实施线性混合效应建模提供实用指导。
我们展示了一个线性混合效应建模分析，呈现了一项针对五名获得性书写障碍个体的纵向训练研究的数据，分析了二项式（准确性）和连续性（反应时间）重复测量数据。
线性混合效应建模分析表明，拼写准确性和反应时间均有所提高，而且就准确性而言，与集中练习相比，在分散练习的训练计划下提高得明显更快。我们提供了关于从线性混合效应建模中获取和解释各种效应量及统计显著性度量的指导，并纳入了一项模拟研究，比较了广义线性混合效应建模的两种p值方法。
我们有力地论证了将线性混合效应建模应用于训练研究分析，作为视觉分析或其他统计技术的更优替代方法。当应用于治疗数据集时，有证据支持该方法在个体数量极少的极端条件下依然适用，同时具备针对连续性（反应时间）和二项分布（准确性）相关测量的重复测量训练数据。该方法通过易于获取且有充分支持的统计软件包提供标准化的效应量度量，并在考虑项目和个体变异性的情况下，对训练效果的预期平均效应量进行严格的统计估计。
