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…

Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

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…

Performance Factors Analysis (PFA) is considered one of the most important Knowledge Tracing (KT) approaches used for constructing adaptive educational hypermedia systems. It has shown a high prediction accuracy against many other KT approaches. While, the desire to estimate more accurately the student level leads researchers to enhance PFA by…

Massive open online courses (MOOCs) have evolved rapidly in recent years due to their open and massive nature. However, MOOCs suffer from a high dropout rate, since learners struggle to stay cognitively and emotionally engaged. Learner feedback is an excellent way to understand learner behaviour and model early decision making. In the presented…

The new Croatian Informatics curriculum, which introduces computational thinking concepts into learning outcomes has been put into practice. A computational thinking assessment model reflecting the learning outcomes of the Croatian curriculum was created using an evidence-centered design approach. The possibility of assessing the computational…

Principal component analysis is an important statistical technique for dimension reduction and exploratory data analysis. However, it is not robust to outliers and may obfuscate important data structure such as clustering. We propose a version of principal component analysis based on the robust L2E method. The technique seeks to find the principal…

Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class…

The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)

The method proposed by Harman and Fukuda to treat the so-called Heywood case in the minres method in factor analysis (i.e., the case where the resulting communalities are greater than one) involves the frequent solution of eigenvalue problems. A simple method to treat this problem is presented. (Author/JKS)