An application of Bayesian factor analysis for evaluation of scale reliability is discussed, which is developed within the framework of latent variable modeling. The method permits direct point and interval estimation of the reliability coefficient of multiple-component measuring instruments using Bayesian inference. The approach allows also point…

A Bayesian statistics-based approach is discussed that can be used for direct evaluation of the popular Cronbach's coefficient alpha as an internal consistency index for multiple-component measuring instruments, as well as for testing its identity to scale reliability. The method represents an application of confirmatory factor analysis within the…

In contemporary societies, the processes of transindividuation by which knowledges are transformed into cycles and rhythms of metastability have been dramatically short-circuited. In turn, this has provoked the spiritual misery and pseudo-fabulations so prevalent all around us, including our educational contexts. For Stiegler, this is nothing…

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…

There are two schools of thought in statistical analysis, frequentist, and Bayesian. Though the two approaches produce similar estimations and predictions in large-sample studies, their interpretations are different. Bland Altman analysis is a statistical method that is widely used for comparing two methods of measurement. It was originally…

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…

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

The article explores the role that subjective evidence of causality and associated counterfactuals and counterpotentials might play in the social sciences where comparative cases are scarce. This scarcity rules out statistical inference based upon frequencies and usually invites in-depth ethnographic studies. Thus, if causality is to be preserved…

Some situations are presented with perplexing properties, which become clearer by looking at contingency tables. This in turn leads to problems that can be solved using conditional frequencies and thus leading to the Bayes formula with natural frequencies or probabilities.

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for…

We present an innovative modelling technique that simultaneously constrains student performance, course difficulty, and the sensitivity with which a course can differentiate between students by means of grades. Grade lists are the only necessary ingredient. Networks of courses will be constructed where the edges are populations of students that…

Reference intervals, or reference ranges, aid medical decision-making by containing a pre-specified proportion (e.g., 95%) of the measurements in a representative healthy population. We recently proposed three approaches for estimating a reference interval from a meta-analysis based on a random effects model: a frequentist approach, a Bayesian…

When a response pattern does not fit a selected measurement model, one may resort to robust ability estimation. Two popular robust methods are biweight and Huber weight. So far, research on these methods has been quite limited. This article proposes the maximum a posteriori biweight (BMAP) and Huber weight (HMAP) estimation methods. These methods…