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Summary: Usually in latent class (LC) analysis, external predictors are taken to be cluster conditional probability predictors (LC models with external predictors), and/or score conditional probability predictors (LC regression models). In such cases, their distribution is not of interest. Class‐specific distribution is of interest in the distal outcome model, when the distribution of the external variables is assumed to depend on LC membership. In this paper, we consider a more general formulation, that embeds both the LC regression and the distal outcome models, as is typically done in cluster‐weighted modelling. This allows us to investigate (1) whether the distribution of the external variables differs across classes, (2) whether there are significant direct effects of the external variables on the indicators, by modelling jointly the relationship between the external and the latent variables. We show the advantages of the proposed modelling approach through a set of artificial examples, an extensive simulation study and an empirical application about psychological contracts among employees and employers in Belgium and the Netherlands. [ABSTRACT FROM AUTHOR]

Cluster-weighted models (CWMs) extend finite mixtures of regressions (FMRs) in order to allow the distribution of covariates to contribute to the clustering process. In this article, we introduce 24 matrix-variate CWMs which are obtained by allowing both the responses and covariates in each cluster to be modelled by one of four existing skewed matrix-variate distributions or the matrix-variate normal distribution. Endowed with greater flexibility, our matrix-variate CWMs are able to handle this kind of data in a more suitable manner. As a by-product, the four skewed matrix-variate FMRs are also introduced. Maximum likelihood parameter estimates are derived using an expectation-conditional maximization algorithm. Parameter recovery, classification assessment, and the capability of the Bayesian information criterion to detect the underlying groups are investigated using simulated data. Lastly, our matrix-variate CWMs, along with the matrix-variate normal CWM and matrix-variate FMRs, are applied to two real datasets for illustrative purposes. [ABSTRACT FROM AUTHOR]

Cluster-weighted models represent a convenient approach for model-based clustering, especially when the covariates contribute to defining the cluster-structure of the data. However, applicability may be limited when the number of covariates is high and performance may be affected by noise and outliers. To overcome these problems, common/uncommon $$t$$ -factor analyzers for the covariates, and a $$t$$ -distribution for the response variable, are here assumed in each mixture component. A family of twenty parsimonious variants of this model is also presented and the alternating expectation-conditional maximization algorithm, for maximum likelihood estimation of the parameters of all models in the family, is described. Artificial and real data show that these models have very good clustering performance and that the algorithm is able to recover the parameters very well. [ABSTRACT FROM AUTHOR]