Bayesian methods have been said to solve small sample problems in frequentist methods by reflecting prior knowledge in the prior distribution. However, there are dangers in strongly reflecting prior knowledge or situations where much prior knowledge cannot be used. In order to address the issue, in this article, we considered to apply two Bayesian…

Purpose and Background: Despite the flexibility of multilevel structural equation modeling (MLSEM), a practical limitation many researchers encounter is how to effectively estimate model parameters with typical sample sizes when there are many levels of (potentially disparate) nesting. We develop a method-of-moment corrected maximum likelihood…

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the…

We develop a structural after measurement (SAM) method for structural equation models (SEMs) that accommodates missing data. The results show that the proposed SAM missing data estimator outperforms conventional full information (FI) estimators in terms of convergence, bias, and root-mean-square-error in small-to-moderate samples or large samples…

This study aims to compare the results of the factor analysis performed with Frequentist and Bayesian approaches. The number of sub-dimensions of the measurement tool obtained from different methods, the variation of the items in the sub-dimensions, and the fit statistics' differentiation were examined. 778 students constitute the study sample.…

Weighted least squares (WLS), weighted least squares mean-and-variance-adjusted (WLSMV), unweighted least squares mean-and-variance-adjusted (ULSMV), maximum likelihood (ML), robust maximum likelihood (MLR) and Bayesian estimation methods were compared in mixed item response type data via Monte Carlo simulation. The percentage of polytomous items,…

Latent growth models (LGMs) are an application of structural equation modeling and frequently used in developmental and clinical research to analyze change over time in longitudinal outcomes. Maximum likelihood (ML), the most common approach for estimating LGMs, can fail to converge or may produce biased estimates in complex LGMs especially in…

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

Diffusion-based item response theory models for responses and response times in tests have attracted increased attention recently in psychometrics. Analyzing response time data, however, is delicate as response times are often contaminated by unusual observations. This can have serious effects on the validity of statistical inference. In this…

The aim of this study is to explore the judgments and reasoning in probabilistic tasks that require comparing two probabilities either with or without introducing an additional degree of uncertainty. The reasoning associated with the task having an additional condition of uncertainty has not been discussed in previous studies. The 66 undergraduate…

Piecewise GMM with unknown turning points is a new procedure to investigate heterogeneous subpopulations' growth trajectories consisting of distinct developmental phases. Unlike the conventional PGMM, which relies on theory or experiment design to specify turning points a priori, the new procedure allows for an optimal location of turning points…

This paper studies the influence diagnostics in meta-regression model including case deletion diagnostic and local influence analysis. We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures. The DerSimonian and Laird estimation and maximum…

Multilevel models (MLMs) have proven themselves to be very useful in social science research, as data from a variety of sources is sampled such that individuals at level-1 are nested within clusters such as schools, hospitals, counseling centers, and business entities at level-2. MLMs using restricted maximum likelihood estimation (REML) provide…

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…