Suppose that we rank-order the conditional probabilities for a group of subjects that are provided from a Bayesian network (BN) model of binary variables. The conditional probability is the probability that a subject has a certain attribute given an outcome of some other variables and the...

Probabilistic feature models (PFMs) can be used to explain binary rater judgements about the associations between two types of elements (e.g., objects and attributes) on the basis of binary latent features. In particular, to explain observed object-attribute associations PFMs assume that...

Multiple choice items on tests and Likert items on surveys are ubiquitous in educational, social and behavioral science research; however, methods for analyzing of such data can be problematic. Multidimensional item response theory models are proposed that yield structured Poisson regression...

We consider correspondence analysis (CA) and taxicab correspondence analysis (TCA) of relational datasets that can mathematically be described as weighted loopless graphs. Such data appear in particular in network analysis. We present CA and TCA as relaxation methods for the graph partitioning...

Over the past decade, diagnostic classification models (DCMs) have become an active area of psychometric research. Despite their use, the reliability of examinee estimates in DCM applications has seldom been reported. In this paper, a reliability measure for the categorical latent variables of...

Based on the notion of mutual information between the components of a random vector, we construct, for data reduction reasons, an optimal quantization of the support of its probability measure. More precisely, we propose a simultaneous discretization of the whole set of the components of the...

A trend in educational testing is to go beyond unidimensional scoring and provide a more complete profile of skills that have been mastered and those that have not. To achieve this, cognitive diagnosis models have been developed that can be viewed as restricted latent class models. Diagnosis of...

Model selection is an important component of data analysis. This study focuses on issues of model selection for the trend vector model, a model for the analysis of longitudinal multinomial outcomes. The trend vector model is a so-called marginal model, focusing on population averaged evolutions...

Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of distances from a given point, a probability distribution mapping...