Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, interpreting these functional principal components (PCs) can sometimes be challenging due to issues such as roughness and sparsity. In this dissertation,…

Testing for differential item functioning (DIF) has undergone rapid statistical developments recently. Moderated nonlinear factor analysis (MNLFA) allows for simultaneous testing of DIF among multiple categorical and continuous covariates (e.g., sex, age, ethnicity, etc.), and regularization has shown promising results for identifying DIF among…

The large scale expansion of online courses has led to the crisis of course quality issues. In this study, we first established an evaluation index system for online courses using factor analysis, encompassing three key constructs: course resource construction, course implementation, and teaching effectiveness. Subsequently, we employed factor…

In confirmatory factor analysis (CFA), model parameters are usually estimated by iteratively minimizing the Maximum Likelihood (ML) fit function. In optimal circumstances, the ML estimator yields the desirable statistical properties of asymptotic unbiasedness, efficiency, normality, and consistency. In practice, however, real-life data tend to be…

We develop a "latent variable forest" (LV Forest) algorithm for the estimation of latent variable scores with one or more latent variables. LV Forest estimates unbiased latent variable scores based on "confirmatory factor analysis" (CFA) models with ordinal and/or numerical response variables. Through parametric model…

We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter…

Psychology originally defined parent-child conflict in terms of interpersonal relationships, where parent-child conflict is a process of inconsistent attitudes between parents and children that occurs in a family setting. For this end, we aims to investigate the influence of parental awareness on preschoolers' perception of parent-child conflict…