Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

We present a method for Bayesian structural equation modeling of sample correlation matrices as correlation structures. The method transforms the sample correlation matrix to an unbounded vector using the matrix logarithm function. Bayesian inference about the unbounded vector is performed assuming a multivariate-normal likelihood, with a mean…

Teaching statistics to generalist students oriented toward a profession, rather than academic merits, may be challenging. As statistics courses also tend to have a low student appeal, tailoring a course toward this type of audience is demanding. Framed within the theory of statistical thinking and literacy, this article shows how an investigative…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite requirement on correlation matrices, from sign indeterminacy of factor loadings, and from order constraints on…

The product Bayes factor (PBF) synthesizes evidence for an informative hypothesis across heterogeneous replication studies. It can be used when fixed- or random effects meta-analysis fall short. For example, when effect sizes are incomparable and cannot be pooled, or when studies diverge significantly in the populations, study designs, and…

Effect sizes are important because they are an accessible way to indicate the practical importance of observed associations or differences. Standardized mean difference (SMD) effect sizes, such as Cohen's d, are widely used in education and the social sciences -- in part because they are relatively easy to calculate. However, SMD effect sizes…

In recent years, proponents of configurational comparative methods (CCMs) have advanced various dimensions of robustness as instrumental to model selection. But these robustness considerations have not led to computable robustness measures, and they have typically been applied to the analysis of real-life data with unknown underlying causal…

Seeking to leverage students' interests into mathematical tasks and noticing how their students excitedly discussed the NCAA's Division 1-A football rankings every year, the authors devised a mathematical modeling task in which students could use mathematics to justify their rankings. The task takes students on a journey to consider the complexity…

Policymakers and institutional leaders in higher education too often make decisions based on descriptive data analyses or even anecdote when better analysis options could produce more nuanced and more valuable results. Employing the setting of higher education program evaluation at a midwestern regional public university, for this study we…

Examples of the impact of statistical theory on assessment practice are provided from the perspective of a statistician trained in theoretical statistics who began to work on assessments. Goodness of fit of item-response models is examined in terms of restricted likelihood-ratio tests and generalized residuals. Minimum discriminant information…

This study proposes a two-stage causal modeling with instrumental variables to mitigate selection bias, provide correct standard error estimates, and address nonnormal and missing data issues simultaneously. Bayesian methods are used for model estimation. Robust methods with Student's "t" distributions are used to account for nonnormal…

Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or…

This supplement concerns Appendix E of the "What Works Clearinghouse (WWC) Procedures Handbook, Version 4.1." The supplement extends the range of designs and analyses that can generate effect size and standard error estimates for the WWC. This supplement presents several new standard error formulas for cluster-level assignment studies,…

This article develops a set-theoretic approach to Bayes's theorem and Bayesian process tracing. In the approach, hypothesis testing is the procedure whereby one updates beliefs by narrowing the range of states of the world that are regarded as possible, thus diminishing the domain in which the actual world can reside. By explicitly connecting…

In this response, we first show that Simpson's proposed analysis answers a different and less interesting question than ours. We then justify the choice of prior for our Bayes factors calculations, but we also demonstrate that the substantive conclusions of our article are not substantially affected by varying this choice.