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

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.     

A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance with the more common maximum likelihood-based model selection for simulated and real market data. All five MCMC methods proved reliable in the simulation study, although differing in their computational demands. Results on simulated data also show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favor of the true model than maximum likelihood. Results on market data show the instability of the harmonic mean estimator and reliability of the advanced model selection methods.     

Bayesian testing of restrictions on vector autoregressive models

In this study, we propose a prior on restricted Vector Autoregressive (VAR) models. The prior setting permits efficient Markov Chain Monte Carlo (MCMC) sampling from the posterior of the VAR parameters and estimation of the Bayes factor. Numerical simulations show that when the sample size is small, the Bayes factor is more effective in selecting the correct model than the commonly used Schwarz criterion. We conduct Bayesian hypothesis testing of VAR models on the macroeconomic, state-, and sector-specific effects of employment growth.     

Bayesian analysis of latent Markov models with non-ignorable missing data

Latent Markov models (LMMs) are widely used in the analysis of heterogeneous longitudinal data. However, most existing LMMs are developed in fully observed data without missing entries. The main objective of this study is to develop a Bayesian approach for analyzing the LMMs with non-ignorable missing data. Bayesian methods for estimation and model comparison are discussed. The empirical performance of the proposed methodology is evaluated through simulation studies. An application to a data set derived from National Longitudinal Survey of Youth 1997 is presented.     

Model selection information criteria in latent class models with missing data and contingency question

Latent class analysis (LCA) has been found to have important applications in social and behavioural sciences for modelling categorical response variables, and non-response is typical when collecting data. In this study, the non-response mainly included ‘contingency questions’ and real ‘missing data’. The primary objective of this study was to evaluate the effects of some potential factors on model selection indices in LCA with non-response data. We simulated missing data with contingency question and evaluated the accuracy rates of eight information criteria for selecting the correct models. The results showed that the main factors are latent class proportions, conditional probabilities, sample size, the number of items, the missing data rate and the contingency data rate. Interactions of the conditional probabilities with class proportions, sample size and the number of items are also significant. From our simulation results, the impact of missing data and contingency questions can be amended by increasing the sample size or the number of items.     

Bayesian analysis of the Box-Cox transformation model based on left-truncated and right-censored data

In this paper, we discuss the inference problem about the Box-Cox transformation model when one faces left-truncated and right-censored data, which often occur in studies, for example, involving the cross-sectional sampling scheme. It is well-known that the Box-Cox transformation model includes many commonly used models as special cases such as the proportional hazards model and the additive hazards model. For inference, a Bayesian estimation approach is proposed and in the method, the piecewise function is used to approximate the baseline hazards function. Also the conditional marginal prior, whose marginal part is free of any constraints, is employed to deal with many computational challenges caused by the constraints on the parameters, and a MCMC sampling procedure is developed. A simulation study is conducted to assess the finite sample performance of the proposed method and indicates that it works well for practical situations. We apply the approach to a set of data arising from a retirement center.     

Female athletic participation and income: evidence from a latent class model

This paper introduces and applies an EM algorithm for the maximum-likelihood estimation of a latent class version of the grouped-data regression model. This new model is applied to examine the effects of college athletic participation of females on incomes. No evidence for an “athlete” effect in the case of females has been found in the previous work by Long and Caudill [12], Henderson et al. [10], and Caudill and Long [5]. Our study is the first to find evidence of a lower wage for female athletes. This effect is present in a regime characterizing 42% of the sample. Further analysis indicates that female athletes in many otherwise low-paying jobs actually get paid less than non-athletes.     

Inverse Gaussian process models for bivariate degradation analysis: A Bayesian perspective

This article conducts a Bayesian analysis for bivariate degradation models based on the inverse Gaussian (IG) process. Assume that a product has two quality characteristics (QCs) and each of the QCs is governed by an IG process. The dependence of the QCs is described by a copula function. A bivariate simple IG process model and three bivariate IG process models with random effects are investigated by using Bayesian method. In addition, a simulation example is given to illustrate the effectiveness of the proposed methods. Finally, an example about heavy machine tools is presented to validate the proposed models.     

Bayesian penalized B-spline estimation approach for epidemic models

Ordinary differential equations (ODEs) are normally used to model dynamic processes in applied sciences such as biology, engineering, physics, and many other areas. In these models, the parameters are usually unknown, and thus they are often specified artificially or empirically. Alternatively, a feasible method is to estimate the parameters based on observed data. In this study, we propose a Bayesian penalized B-spline approach to estimate the parameters and initial values for ODEs used in epidemiology. We evaluated the efficiency of the proposed method based on simulations using the Markov chain Monte Carlo algorithm for the Kermack–McKendrick model. The proposed approach is also illustrated based on a real application to the transmission dynamics of hepatitis C virus in mainland China.     

A Bayesian analysis on time series structural equation models

Structural equation models (SEM) have been extensively used in behavioral, social, and psychological research to model relations between the latent variables and the observations. Most software packages for the fitting of SEM rely on frequentist methods. Traditional models and software are not appropriate for analysis of the dependent observations such as time-series data. In this study, a structural equation model with a time series feature is introduced. A Bayesian approach is used to solve the model with the aid of the Markov chain Monte Carlo method. Bayesian inferences as well as prediction with the proposed time series structural equation model can also reveal certain unobserved relationships among the observations. The approach is successfully employed using real Asian, American and European stock return data.     

Latent class analysis for measuring Turkish People's future expectations for Turkey

The aim of this study is to classify the Turkish People and measure the probability of their positive or negative expectations according to their 5-year expectations on Turkish Economy, Social Rights and Freedom, Rendering of the Public Services, Government Transparency and Turkey's Reputation. For this purpose latest data from the Turkish Statistical Institute's Life Satisfaction Survey 2011 was used and latent class analysis (LCA) was utilized on this data. For this study, unrestricted and restricted models of LCAs were performed, and it is observed that the three-class unrestricted model was found to be the best fit. Latent Class probabilities were interpreted and each class was named based on the calculated conditional probabilities.     

Bayesian analysis of generalized elliptical semi-parametric models

In this paper, we study the statistical inference based on the Bayesian approach for regression models with the assumption that independent additive errors follow normal, Student-t, slash, contaminated normal, Laplace or symmetric hyperbolic distribution, where both location and dispersion parameters of the response variable distribution include nonparametric additive components approximated by B-splines. This class of models provides a rich set of symmetric distributions for the model error. Some of these distributions have heavier or lighter tails than the normal as well as different levels of kurtosis. In order to draw samples of the posterior distribution of the interest parameters, we propose an efficient Markov Chain Monte Carlo (MCMC) algorithm, which combines Gibbs sampler and Metropolis–Hastings algorithms. The performance of the proposed MCMC algorithm is assessed through simulation experiments. We apply the proposed methodology to a real data set. The proposed methodology is implemented in the R package BayesGESM using the function gesm().     

Bayesian analysis of censored linear regression models with scale mixtures of normal distributions

As is the case of many studies, the data collected are limited and an exact value is recorded only if it falls within an interval range. Hence, the responses can be either left, interval or right censored. Linear (and nonlinear) regression models are routinely used to analyze these types of data and are based on normality assumptions for the errors terms. However, those analyzes might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored linear regression models by replacing the Gaussian assumptions for the random errors with scale mixtures of normal (SMN) distributions. The SMN is an attractive class of symmetric heavy-tailed densities that includes the normal, Student-t, Pearson type VII, slash and the contaminated normal distributions, as special cases. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is introduced to carry out posterior inference. A new hierarchical prior distribution is suggested for the degrees of freedom parameter in the Student-t distribution. The likelihood function is utilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influence diagnostics based on the q-divergence measure. The proposed Bayesian methods are implemented in the R package BayesCR. The newly developed procedures are illustrated with applications using real and simulated data.     

Bayesian predictive densities based on latent information priors

Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data is assumed to belong to a parametric submodel of a multinomial model. Future observables and data are possibly dependent. The discrepancy of a predictive density to the true conditional density of future observables given observed data is evaluated by the Kullback-Leibler divergence. It is proved that limits of Bayesian predictive densities form an essentially complete class. Latent information priors are defined as priors maximizing the conditional mutual information between the parameter and the future observables given the observed data. Minimax predictive densities are constructed as limits of Bayesian predictive densities based on prior sequences converging to the latent information priors.     

An evaluation of the Bayesian approach to fitting the N-mixture model for use with pseudo-replicated count data

The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.     

Bayesian model averaging in longitudinal regression models with AR(1) errors with application to a myopia data set

We propose a new iterative algorithm, called model walking algorithm, to the Bayesian model averaging method on the longitudinal regression models with AR(1) random errors within subjects. The Markov chain Monte Carlo method together with the model walking algorithm are employed. The proposed method is successfully applied to predict the progression rates on a myopia intervention trial in children.     

Bayesian change points analysis on the seismic activity in northeastern Taiwan

Bayesian change points analysis on the seismic activity in northeastern Taiwan is studied via the reversible jump Markov chain Monte Carlo simulation. An epidemic model is considered with Gamma prior distributions for the parameters. The prior distributions are essentially determined based on an earlier period of the seismic data in the same region. It is investigated that there exist two change points during the time period considered. This result is also confirmed by the BIC criteria.     

Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population

We present a new class of models to fit longitudinal data, obtained with a suitable modification of the classical linear mixed-effects model. For each sample unit, the joint distribution of the random effect and the random error is a finite mixture of scale mixtures of multivariate skew-normal distributions. This extension allows us to model the data in a more flexible way, taking into account skewness, multimodality and discrepant observations at the same time. The scale mixtures of skew-normal form an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-Student-t, skew-slash and the skew-contaminated normal distributions as special cases, being a flexible alternative to the use of the corresponding symmetric distributions in this type of models. A simple efficient MCMC Gibbs-type algorithm for posterior Bayesian inference is employed. In order to illustrate the usefulness of the proposed methodology, two artificial and two real data sets are analyzed.     

A multiple group item response theory model with centered skew-normal latent trait distributions under a Bayesian framework

Very often, in psychometric research, as in educational assessment, it is necessary to analyze item response from clustered respondents. The multiple group item response theory (IRT) model proposed by Bock and Zimowski [12] provides a useful framework for analyzing such type of data. In this model, the selected groups of respondents are of specific interest such that group-specific population distributions need to be defined. The usual assumption for parameter estimation in this model, which is that the latent traits are random variables following different symmetric normal distributions, has been questioned in many works found in the IRT literature. Furthermore, when this assumption does not hold, misleading inference can result. In this paper, we consider that the latent traits for each group follow different skew-normal distributions, under the centered parameterization. We named it skew multiple group IRT model. This modeling extends the works of Azevedo et al. [4], Bazán et al. [11] and Bock and Zimowski [12] (concerning the latent trait distribution). Our approach ensures that the model is identifiable. We propose and compare, concerning convergence issues, two Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation. A simulation study was performed in order to evaluate parameter recovery for the proposed model and the selected algorithm concerning convergence issues. Results reveal that the proposed algorithm recovers properly all model parameters. Furthermore, we analyzed a real data set which presents asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of negative asymmetry for some latent trait distributions.