In educational and psychological research, it is common to use latent factors to represent constructs and then to examine covariate effects on these latent factors. Using empirical data, this study applied three approaches to covariate effects on latent factors: the multiple-indicator multiple-cause (MIMIC) approach, multiple group confirmatory factor analysis (MG-CFA) approach, and the structural equation model trees (SEM Trees) approach. The MIMIC approach directly models covariate effects on latent factors. The MG-CFA approach allows testing of measurement invariance before latent factor means could be compared. The more recently developed SEM Trees approach partitions the sample into homogenous subsets based on the covariate space; model parameters are estimated separately for each subgroup. We applied the three approaches using an empirical dataset extracted from the eighth-grade U.S. data from the Trends in International Mathematics and Science Study 2019 database. All approaches suggested differences among mathematics achievement categories for the latent factor of mathematics self-concept. In addition, language spoken at home did not seem to affect students' mathematics self-concept. Despite these general findings, the three approaches provided different pieces of information regarding covariate effects. For all models, we appropriately considered the complex data structure and sampling weights following recent recommendations for analyzing large-scale assessment data.