Latent class and finite mixture models for multilevel data sets

2008 ◽  
Vol 17 (1) ◽  
pp. 33-51 ◽  
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.

Modeling the crashes count using finite mixture models

2019 ◽  
Vol 7 (1) ◽  
pp. 13-27
Author(s):  
Safaa K. Kadhem ◽  
Sadeq A. Kadhim
Keyword(s):  
Bayesian Inference ◽  
Mixture Models ◽  
Gibbs Sampler ◽  
Simulation Study ◽  
Finite Mixture Models ◽  
Synthetic Data ◽  
Finite Mixture Model ◽  
Finite Mixture ◽  
Model Parameters ◽  
Mcmc Method

"This paper aims at the modeling the crashes count in Al Muthanna governance using finite mixture model. We use one of the most common MCMC method which is called the Gibbs sampler to implement the Bayesian inference for estimating the model parameters. We perform a simulation study, based on synthetic data, to check the ability of the sampler to find the best estimates of the model. We use the two well-known criteria, which are the AIC and BIC, to determine the best model fitted to the data. Finally, we apply our sampler to model the crashes count in Al Muthanna governance.

scholarly journals Hybridizing Machine Learning Methods and Finite Mixture Models for Estimating Heterogeneous Treatment Effects in Latent Classes

2020 ◽  
pp. 107699862095198
Author(s):  
Youmi Suk ◽  
Jee-Seon Kim ◽  
Hyunseung Kang
Keyword(s):  
Machine Learning ◽  
Treatment Effects ◽  
Latent Class ◽  
Finite Mixture Models ◽  
Likelihood Estimation ◽  
Study Data ◽  
Latent Class Models ◽  
Finite Mixture ◽  
Latent Classes ◽  
Heterogeneous Treatment Effects

There has been increasing interest in exploring heterogeneous treatment effects using machine learning (ML) methods such as causal forests, Bayesian additive regression trees, and targeted maximum likelihood estimation. However, there is little work on applying these methods to estimate treatment effects in latent classes defined by well-established finite mixture/latent class models. This article proposes a hybrid method, a combination of finite mixture modeling and ML methods from causal inference to discover effect heterogeneity in latent classes. Our simulation study reveals that hybrid ML methods produced more precise and accurate estimates of treatment effects in latent classes. We also use hybrid ML methods to estimate the differential effects of private lessons across latent classes from Trends in International Mathematics and Science Study data.

Forecasting Financial Products Acquisition via Dynamic Segmentation: An Application to the Italian Market

2015 ◽  
Vol 57 (6) ◽  
pp. 909-930
Author(s):  
Francesca Bassi
Keyword(s):  
Mixture Models ◽  
Latent Class ◽  
Finite Mixture Models ◽  
Longitudinal Component ◽  
Marketing Strategies ◽  
Finite Mixture ◽  
Dynamic Segmentation ◽  
Financial Products ◽  
Italian Market ◽  
Product Choices

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.

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

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.

Latent Class (Finite Mixture) Models

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
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