Analyzing latent outcomes via ranks

In this dissertation, we focus on developing techniques for data including a latent outcome variable. Latent variables are variables that are not directly observed, but rather theoretically postulated or empirically inferred from observed variables (i.e. indicators or proxies). Although Structural Equation Modeling (SEM) is a well-known technique, we believe that valuable alternative or complementary techniques can be explored since rank-based methods remained largely unnoticed in the SEM literature despite their attractive properties. Therefore, we introduce and develop rank-based techniques for continuous latent outcome variables in this dissertation. First, we focus on a technique to compare two independent groups. We start from an existing and well-established rank-based method, i.e. the Wilcoxon—Mann—Whitney (WMW) test. We consider the performance of an adaptation of this WMW test in terms of hypothesis testing, the estimation of the probabilistic index and the construction of a confidence interval. Next, we extend our scope and construct a regression framework. By doing so, the inclusion of different observable predictors is possible, both continuous and categorical. After the theoretical justification of this technique, we discuss the results of a simulation study that reveals good finite sample properties. All methods are recurrently demonstrated throughout this dissertation on case studies