A Model Fit Comparative Study of K-Component Mixture of One Parameter Univariate Distributions (original) (raw)

Editorial: recent developments in mixture models

Computational Statistics & Data Analysis, 2003

Recent developments in the area of mixture models are introduced, reviewed and discussed. The paper introduces this special issue on mixture models, which touches upon a diversity of developments which were the topic of a recent conference on mixture models, taken place in Hamburg, July 2001. These developments include issues in nonparametric maximum likelihood theory, the number of components problem, the non-standard distribution of the likelihood ratio for mixture models, computational issues connected with the EM algorithm, several special mixture models and application studies.

Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling

Communications in Statistics - Theory and Methods, 2017

In this paper, we propose mixtures of skew Laplace normal distributions to model both skewness and heavy-tailedness in the heterogeneous data set as an alternative to mixtures of skew Studentt-normal distributions. We give the EM algorithm to obtain the maximum likelihood estimators for the parameters of interest. We also analyze the mixture regression model based on the skew Laplace normal distribution and provide the maximum likelihood estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.

A Bayesian predictive approach to determining the number of components in a mixture distribution

Statistics and Computing, 1995

This paper describes a Bayesian approach to mixture modelling and a method based on predictive distribution to determine the number of components in the mixtures. The implementation is done through the use of the Gibbs sampler. The method is described through the mixtures of normal and gamma distributions. Analysis is presented in one simulated and one real data example. The Bayesian results are then compared with the likelihood approach for the two examples.

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

2021

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.

Mixture Modeling Using the Multivariate Restricted Skew-Normal Scale Mixture of Birnbaum–Saunders Distributions

Iranian Journal of Science and Technology, Transactions A: Science, 2020

Mixture models are promising statistical tools aiming to modeling and clustering data arisen from a heterogeneous population. This paper presents a mixture model based on the assumption that the mixing components follow the multivariate restricted skew-normal scale mixture of Birnbaum–Saunders (SNBS) distributions. A computationally feasible expectation-maximization algorithm is developed to carry out maximum likelihood estimation of the new model. Simulation studies are carried out to check the clustering performance and classification accuracy. Finally, illustrative example is presented by analyzing a real-world data set.

Assessing the Number of Components in Mixture Models: an Overview

RePEc: Research Papers in Economics, 2005

Despite the widespread application of finite mixture models, the decision of how many classes are required to adequately represent the data is, according to many authors, an important, but unsolved issue. This work aims to review, describe and organize the available approaches designed to help the selection of the adequate number of mixture components (including Monte Carlo test procedures, information criteria and classification-based criteria); we also provide some published simulation results about their relative performance, with the purpose of identifying the scenarios where each criterion is more effective (adequate).

Parameter Estimation in Linear and Quadratic Mixture Models: A Review

2010

In this article, the problems of unbiased estimation of parameters in linear and quadratic mixture models have been revisited. We have studied some standard mixture designs for this purpose. The information matrices of the parameters involved in the linear and quadratic mixture models have been displayed for these standard designs. Some generalizations of the axial designs have been proposed and

Estimation Of Regression Parameters of Two Dimensional Probability Distribution Mixtures

2016

We use two methods of estimation parameters in a mixture regression: maximum likelihood (MLE) and the least squares method for an implicit interdependence. The most popular method for maximum likelihood esti-mation of the parameter vector is the EM algorithm. The least squares method for an implicit interdependence is based solving systems of nonlinear equations. Most frequently used method in the estimation of parameters mixtures regression is the method of maximum likelihood. The article presents the possibility of using a different the least squares method for an implicit interdependence and compare it with the maximum likelihood method. We compare accuracy of two methods of estimation by simulation using bias: root mean square error and bootstrapping standard errors of estimation.

Determining the number of components in mixture regression models: an experimental design

Economics Bulletin, 2020

Despite the popularity of mixture regression models, the decision of how many components to retain remains an open issue. This study thus sought to compare the performance of 26 information and classification criteria. Each criterion was evaluated in terms of that component's success rate. The research's full experimental design included manipulating 9 factors and 22 levels. The best results were obtained for 5 criteria: Akaike information criteria 3 (AIC3), AIC4, Hannan-Quinn information criteria, integrated completed likelihood (ICL) Bayesian information criteria (BIC) and ICL with BIC approximation. Each criterion's performance varied according to the experimental conditions.

Parameter Estimation in Linear and Quadratic Mixture Models

Lecture Notes in Statistics, 2014

In this article, the problems of unbiased estimation of parameters in linear and quadratic mixture models have been revisited. We have studied some standard mixture designs for this purpose. The information matrices of the parameters involved in the linear and quadratic mixture models have been displayed for these standard designs. Some generalizations of the axial designs have been proposed and a comparative study of these designs, in respect of their information matrices, has been considered. Other types of mixture models viz. Becker's homogeneous model and Draper-St. John's model have also been briefly studied and the estimation problems have been addressed by using some axial type designs.