Title: Descriptive Discriminant Analysis of Multivariate Repeated Measures Data: A Use Case Show Chinese title

Title: 多变量重复测量数据的描述性判别分析：一个案例应用

Abstract: Psychological research often focuses on examining group differences in a set of numeric variables for which normality is doubtful. Longitudinal studies enable the investigation of developmental trends. For instance, a recent study (Voormolen et al (2020), https://doi.org/10.3390/jcm9051525) examined the relation of complicated and uncomplicated mild traumatic brain injury (mTBI) with multidimensional outcomes measured at three- and six-months after mTBI. The data were analyzed using robust repeated measures multivariate analysis of variance (MANOVA), resulting in significant differences between groups and across time points, then followed up by univariate ANOVAs per variable as is typically done. However, this approach ignores the multivariate aspect of the original analyses. We propose descriptive discriminant analysis (DDA) as an alternative, which is a robust multivariate technique recommended for examining significant MANOVA results and has not yet been applied to multivariate repeated measures data. We provide a tutorial with annotated R code demonstrating its application to these empirical data. Show Chinese abstract

Abstract: 心理研究经常关注一组数值变量中的群体差异，这些变量的正态性存疑。 纵向研究能够调查发展趋势。 例如，一项近期的研究 (Voormolen等，2020年，https://doi.org/10.3390/jcm9051525) 考察了复杂性和非复杂性轻度创伤性脑损伤(mTBI)与在mTBI后三和六个月测量的多维结果之间的关系。 数据使用稳健的重复测量多元方差分析(MANOVA)进行分析，结果显示组间和时间点之间存在显著差异，随后按照通常的做法对每个变量进行了单变量ANOVAs。 然而，这种方法忽略了原始分析的多变量特性。 我们建议使用描述性判别分析(DDA)作为替代方法，这是一种推荐用于检查显著MANOVA结果的稳健多变量技术，尚未应用于多变量重复测量数据。 我们提供了一个带有注释R代码的教程，展示了其在这些实证数据中的应用。