Flexible Mixture Modeling with the Polynomial Gaussian Cluster-Weighted Model

In the mixture modeling frame, this paper presents the polynomial Gaussian cluster-weighted model (CWM). It extends the linear Gaussian CWM, for bivariate data, in a twofold way. Firstly, it allows for possible nonlinear dependencies in the mixture components by considering a polynomial regression. Secondly, it is not restricted to be used for model-based clustering only being contextualized in the most general model-based classification framework. Maximum likelihood parameter estimates are derived using the EM algorithm and model selection is carried out using the Bayesian information criterion (BIC) and the integrated completed likelihood (ICL). The paper also investigates the conditions under which the posterior probabilities of component-membership from a polynomial Gaussian CWM coincide with those of other well-established mixture-models which are related to it. With respect to these models, the polynomial Gaussian CWM has shown to give excellent clustering and classification results when applied to the artificial and real data considered in the paper

KernSmoothIRT: An R Package for Kernel Smoothing in Item Response Theory

Item response theory (IRT) models are a class of statistical models used to describe the response behaviors of individuals to a set of items having a certain number of options. They are adopted by researchers in social science, particularly in the analysis of performance or attitudinal data, in psychology, education, medicine, marketing and other fields where the aim is to measure latent constructs. Most IRT analyses use parametric models that rely on assumptions that often are not satisfied. In such cases, a nonparametric approach might be preferable; nevertheless, there are not many software applications allowing to use that. To address this gap, this paper presents the R package KernSmoothIRT. It implements kernel smoothing for the estimation of option characteristic curves, and adds several plotting and analytical tools to evaluate the whole test/questionnaire, the items, and the subjects. In order to show the package's capabilities, two real datasets are used, one employing multiple-choice responses, and the other scaled responses