Latent Class and Finite Mixture Models

The topic of market segmentation is still one of the most pervasive in marketing. Among clustering techniques, finite mixture models have gained recognition as a method of segmentation with several advantages over traditional methods; one variant of finite mixture models – the latent class (LC) model – is probably the most popular. The LC approach is innovative and flexible, and can provide suitable solutions to several problems regarding the definition and development of marketing strategies, because it takes into account specific features of the collected data, such as their scale of measure (often ordinal or categorical, rather than continuous), their hierarchical structure and their longitudinal component. Dynamic segmentation is of key importance in many markets where it is unrealistic to assume stationary segments due to the dynamics in consumers' needs and product choices. In this paper, a mixture latent class Markov model is proposed to dynamically segment Italian households with reference to financial products ownership. The mixture approach is compared with the standard one in terms of its ability to forecast customers' behaviour in the reference market.

Download Full-text

Model Fit and Comparison in Finite Mixture Models: A Review and a Novel Approach

Frontiers in Education ◽

10.3389/feduc.2021.613645 ◽

2021 ◽

Vol 6 ◽

Author(s):

Kevin J. Grimm ◽

Russell Houpt ◽

Danielle Rodgers

Keyword(s):

Mixture Models ◽

Model Comparison ◽

Latent Class ◽

Finite Mixture Models ◽

Model Simulation ◽

Information Criteria ◽

Finite Mixture ◽

Model Fit ◽

Future Research ◽

Novel Approach

One of the greatest challenges in the application of finite mixture models is model comparison. A variety of statistical fit indices exist, including information criteria, approximate likelihood ratio tests, and resampling techniques; however, none of these indices describe the amount of improvement in model fit when a latent class is added to the model. We review these model fit statistics and propose a novel approach, the likelihood increment percentage per parameter (LIPpp), targeting the relative improvement in model fit when a class is added to the model. Simulation work based on two previous simulation studies highlighted the potential for the LIPpp to identify the correct number of classes, and provide context for the magnitude of improvement in model fit. We conclude with recommendations and future research directions.

Download Full-text

Latent Class (Finite Mixture) Models

Statistical and Econometric Methods for Transportation Data Analysis ◽

10.1201/9780429244018-21 ◽

2020 ◽

pp. 361-371

Author(s):

Simon Washington ◽

Matthew Karlaftis ◽

Fred Mannering ◽

Panagiotis Anastasopoulos

Keyword(s):

Mixture Models ◽

Latent Class ◽

Finite Mixture Models ◽

Finite Mixture

Download Full-text

Latent class and finite mixture models for multilevel data sets

Statistical Methods in Medical Research ◽

10.1177/0962280207081238 ◽

2008 ◽

Vol 17 (1) ◽

pp. 33-51 ◽

Cited By ~ 117

Author(s):

Jeroen K Vermunt

Keyword(s):

Mixture Models ◽

Random Effects ◽

Latent Class ◽

Finite Mixture Models ◽

Expectation Maximization Algorithm ◽

Likelihood Estimation ◽

Finite Mixture ◽

Model Parameters ◽

Data Sets ◽

Special Cases

An extension of latent class (LC) and finite mixture models is described for the analysis of hierarchical data sets. As is typical in multilevel analysis, the dependence between lower-level units within higher-level units is dealt with by assuming that certain model parameters differ randomly across higher-level observations. One of the special cases is an LC model in which group-level differences in the logit of belonging to a particular LC are captured with continuous random effects. Other variants are obtained by including random effects in the model for the response variables rather than for the LCs. The variant that receives most attention in this article is an LC model with discrete random effects: higher-level units are clustered based on the likelihood of their members belonging to the various LCs. This yields a model with mixture distributions at two levels, namely at the group and the subject level. This model is illustrated with three rather different empirical examples. The appendix describes an adapted version of the expectation—maximization algorithm that can be used for maximum likelihood estimation, as well as providing setups for estimating the multilevel LC model with generally available software.

Download Full-text

A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

Risks ◽

10.3390/risks9060115 ◽

2021 ◽

Vol 9 (6) ◽

pp. 115

Author(s):

Despoina Makariou ◽

Pauline Barrieu ◽

George Tzougas

Keyword(s):

Decision Making ◽

Mixture Models ◽

Finite Mixture Models ◽

Risk Measures ◽

Finite Mixture ◽

Parametric Family ◽

Collective Decision Making ◽

Multiple Sources ◽

Mixture Modelling ◽

Expert Opinions

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.

Download Full-text