Pearson's correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman's [rho] is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or…

Data pooling is a powerful strategy in empirical research. However, combining multiple datasets often results in a large amount of missing data, as variables that are not present in some datasets effectively contain missing values for all participants in those datasets. Furthermore, data pooling typically leads to a mix of continuous and…

Multilevel factor mixture modeling (FMM) is a hybrid of multilevel confirmatory factor analysis (CFA) and multilevel latent class analysis (LCA). It allows researchers to examine population heterogeneity at the within level, between level, or both levels. This tutorial focuses on explicating the model specification of multilevel FMM that considers…

The nonequivalent groups with anchor test (NEAT) design is widely used in test equating. Under this design, two groups of examinees are administered different test forms with each test form containing a subset of common items. Because test takers from different groups are assigned only one test form, missing score data emerge by design rendering…

Recently, deep learning has become a pervasive tool in prediction problems for structured and/or unstructured big data in various areas including science and engineering. In particular, deep neural network models (i.e. a basic core model of deep learning) can be viewed as an extension of statistical models by going through the incorporation of…

The use of unidimensional scales that contain both positively and negatively worded items is common in both the educational and psychological fields. However, dimensionality investigations of these instruments often lead to a rejection of the theorized unidimensional model in favor of multidimensional structures, leaving researchers at odds for…

A research question that is of interest across many disciplines is whether and how relationships in a network are related to the attributes of the nodes of the network. In this dissertation, we propose two joint frameworks for modeling the relationship between the network and attributes. In the joint latent space model in Chapter 2, shared latent…

This study proposed a three-stage measurement model utilizing the Latent Growth Curve Modeling and Latent Class Growth Analysis. The measurement model was illustrated using repeated data collected through a four-week prospective study tracking the subjective well-being of volunteer college students (n=154). Firstly, several unconditional growth…

Discrete-time survival analysis (DTSA) models are a popular way of modeling events in the social sciences. However, the analysis of discrete-time survival data is challenged by missing data in one or more covariates. Negative consequences of missing covariate data include efficiency losses and possible bias. A popular approach to circumventing…

This article is concerned with a subset of numerically stable and scalable algorithms useful to support computationally complex psychometric models in the era of machine learning and massive data. The subset selected here is a core set of numerical methods that should be familiar to computational psychometricians and considers whitening transforms…

This article provides a process to carefully evaluate the suitability of a content domain for which diagnostic classification models (DCMs) could be applicable and then optimized steps for constructing a test blueprint for applying DCMs and a real-life example illustrating this process. The content domains were carefully evaluated using a set of…

Economic efficiency demands accurate assessment of individual ability for selection purposes. This study investigates Classical Test Theory (CTT) and Item Response Theory (IRT) for estimating true ability and ranking individuals. Two Monte Carlo simulations and real data analyses were conducted. Results suggest a slight advantage for IRT, but…

The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

Objectively scoring constructed-response items on educational assessments has long been a challenge due to the use of human raters. Even well-trained raters using a rubric can inaccurately assess essays. Unfolding models measure rater's scoring accuracy by capturing the discrepancy between criterion and operational ratings by placing essays on an…

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications of CDMs, certain hierarchical structures among the latent attributes are assumed by researchers to characterize their dependence structure. Specifically, a directed acyclic…