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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]

Summary: The expectation–maximization (EM) algorithm is a familiar tool for computing the maximum likelihood estimate of the parameters in hidden Markov and semi‐Markov models. This paper carries out a detailed study on the influence that the initial values of the parameters impose on the results produced by the algorithm. We compare random starts and partitional and model‐based strategies for choosing the initial values for the EM algorithm in the case of multivariate Gaussian emission distributions (EDs) and assess the performance of each strategy with different assessment criteria. Several data generation settings are considered with varying number of latent states, of variables as well as of the level of fuzziness in the data, and discussion on how each factor influences the obtained results is provided. Simulation results show that different initialization strategies may lead to different log‐likelihood values and, accordingly, to different estimated partitions. A clear indication of which strategies should be preferred is given. We further include two real‐data examples, widely analysed in the hidden semi‐Markov model literature. [ABSTRACT FROM AUTHOR]

We revisit the generalized hyperbolic (GH) distribution and its nested models. These include widely used parametric choices like the multivariate normal, skew‐t$$ t $$, Laplace, and several others. We also introduce the multiple‐choice LASSO, a novel penalized method for choosing among alternative constraints on the same parameter. A hierarchical multiple‐choice Least Absolute Shrinkage and Selection Operator (LASSO) penalized likelihood is optimized to perform simultaneous model selection and inference within the GH family. We illustrate our approach through a simulation study and a real data example. The methodology proposed in this paper has been implemented in R functions which are available as supplementary material. [ABSTRACT FROM AUTHOR]