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…

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…

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…

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…

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…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

The analysis of cross-lagged relationships is a popular approach in prevention research to explore the dynamics between constructs over time. However, a limitation of commonly used cross-lagged models is the requirement of equally spaced measurement occasions that prevents the usage of flexible longitudinal designs and complicates cross-study…

Commonly used machine learning applications seem to relate to big data. This article provides a gentle review of machine learning and shows why machine learning can be applied to small data too. An example of applying machine learning to screen irregularity reports is presented. In the example, the support vector machine and multinomial naïve…