Embedding latent class regression and latent class distal outcome models into cluster‐weighted latent class analysis: a detailed simulation experiment

Australian & New Zealand Journal of Statistics, vol. 65, pp. 213–233

Abstract

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.

Authors 3

1. Roberto Di Mari corresponding

   University of Catania

   Affiliation as printed

   Department of Economics and Business University of Catania Corso Italia 55 Catania 95128 Italy

   Department of Economics and Business, University of Catania, Corso Italia 55, Catania, 95128 Italy

2. Antonio Punzo

   University of Catania

   Affiliation as printed

   Department of Economics and Business University of Catania Corso Italia 55 Catania 95128 Italy

   Department of Economics and Business, University of Catania, Corso Italia 55, Catania, 95128 Italy

3. Zsuzsa Bakk Aachen Statistics Unit

   Leiden University

   Affiliation as printed

   Statistics Unit, Methodology Institute of Psychology Leiden University Wassenaarseweg 52 Leiden 2333 AK The Netherlands

   Statistics Unit, Methodology Institute of Psychology, Leiden University, Wassenaarseweg 52, Leiden, 2333 AK The Netherlands