One of the most important developments in the current era of social sciences is the growing availability and diversity of data, big and small. Social scientists increasingly combine information from multiple data sets in their research. While conducting statistical analyses with linked data is relatively straightforward, borrowing information…

While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality…

In sample survey analysis, accurate population mean estimation is an important task, but traditional approaches frequently ignore the intricacies of real-world data, leading to biassed results. In order to handle uncertainties, indeterminacies, and ambiguity, this work presents an innovative approach based on neutrosophic statistics. We proposed…

A central theme in the field of survey statistics is estimating population-level quantities through data coming from potentially non-representative samples of the population. Multilevel regression and poststratification (MRP), a model-based approach, is gaining traction against the traditional weighted approach for survey estimates. MRP estimates…

The various empirical models built for enrollment management, operations, and program evaluation purposes may have lost their predictive power as a result of the recent collective impact of COVID restrictions, widespread social upheaval, and the shift in educational preferences. This statistical artifact is known as model drifting, data-shift,…

Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this article, we present a simple-to-use method for generating multiple imputations (MIs) using a Gaussian copula. The…

Partial correlation coefficients are often used as effect sizes in the meta-analysis and systematic review of multiple regression analysis research results. There are two well-known formulas for the variance and thereby for the standard error (SE) of partial correlation coefficients (PCC). One is considered the "correct" variance in the…

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

The conventional Q statistic, using estimated inverse-variance (IV) weights, underlies a variety of problems in random-effects meta-analysis. In previous work on standardized mean difference and log-odds-ratio, we found superior performance with an estimator of the overall effect whose weights use only group-level sample sizes. The Q statistic…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

This article describes an extension to the use of heteroskedastic ordered probit (HETOP) models to estimate latent distributional parameters from grouped, ordered-categorical data by pooling across multiple waves of data. We illustrate the method with aggregate proficiency data reporting the number of students in schools or districts scoring in…

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…

There is a need for effect sizes that are readily interpretable by a broad audience. One index that might fill this need is [pi], which represents the proportion of scores in one group that exceed the mean of another group. The robustness of estimates of [pi] to violations of normality had not been explored. Using simulated data, three estimates…

This dissertation is composed of a study of estimation methods in classical and test theories and the elaboration and application of a cluster-robust variance estimator. Variance estimators derived from generalized estimating equations are known to be robust to most covariance structures and are therefore well suited for psychometric analysis of…