Growing scholarship on the pedagogical applications of statistical modeling is currently taking place to create adaptations of this practice to introduce novices to statistics. These are intended to promote novices' reasoning, and are typically void of formal mathematical procedures and calculations. In this article, we define the potential…

Data modeling is an essential activity in a data-driven society, but such a topic and how the context shapes it has received limited attention. This paper reports on research that investigated the role of context in supporting early statistical reasoning in the data modeling process. The data were collected throughout sessions in which young…

This report aims to showcase the value of implementing a Bayesian framework to analyse and report results from international large-scale surveys and provide guidance to users who want to analyse the data using this approach. The motivation for this report stems from the recognition that Bayesian statistical inference is fast becoming a popular…

Employing nested sequences of models is a common practice when exploring the extent to which one set of variables mediates the impact of another set. Such an analysis in the context of logistic regression models confronts two challenges: (1) direct comparisons of coefficients across models are generally biased due to the changes in scale that…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

In this article, we extend Liao's test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be…

Employing a statistical modeling inspired pedagogy is becoming a widespread practice in the statistics education community. Many have incorporated the practice of formulating conjectures in their modeling-enhanced educational designs and have reported on its benefits. We further elucidate the mechanism through which students' conjecturing may be…

The purpose of this article is to illustrate the dynamic process involved in developing and utilizing a theoretical model in a mixed methods study. Specifically, I illustrate how the theoretical model can serve as the starting point in framing the study, as a lens for guiding the data collection and analysis, and as the end point in explaining the…

Multidimensional Item Response Theory (MIRT) is widely used in assessment and evaluation of educational and psychological tests. It models the individual response patterns by specifying functional relationship between individuals' multiple latent traits and their responses to test items. One major challenge in parameter estimation in MIRT is that…

Respondent-driven sampling (RDS), a link-tracing sampling and inference method for studying hard-to-reach populations, has been shown to produce asymptotically unbiased population estimates when its assumptions are satisfied. However, some of the assumptions are prohibitively difficult to reach in the field, and the violation of a crucial…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels--one for the responses and one for the response times--that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a…

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard good-ness-of-fit statistics. Limited-information fit…

This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…