Bayesian Analysis of Multivariate Latent Curve Models With Nonlinear Longitudinal Latent Effects.

In longitudinal studies, investigators often measure multiple variables at multiple time points and are interested in investigating individual differences in patterns of change on those variables. Furthermore, in behavioral, social, psychological, and medical research, investigators often deal with latent variables that cannot be observed directly and should be measured by 2 or more manifest variables. Longitudinal latent variables occur when the corresponding manifest variables are measured at multiple time points.

Bayesian semiparametric analysis of structural equation models with mixed continuous and unordered categorical variables.

Recently, structural equation models (SEMs) have been applied for analyzing interrelationships among observed and latent variables in biological and medical research. Latent variables in these models are typically assumed to have a normal distribution. This article considers a Bayesian semparametric SEM with covariates, and mixed continuous and unordered categorical variables, in which the explanatory latent variables in the structural equation are modeled via an appropriate truncated Dirichlet process with a stick-breaking procedure.

Robust model fitting for the non linear structural equation model under normal theory.

Structural equation modelling has been widely applied in behavioural, educational, medical, social, and psychological research. The classical maximum likelihood estimate is vulnerable to outliers and non-normal data. In this paper, a robust estimation method for the nonlinear structural equation model is proposed.

Longitudinal analysis of quality of life for stroke survivors using latent curve models.

Background And Purpose: For the survivors, activities of daily living, handicap, and depression have a significant impact on health-related quality of life (HRQOL). How the dynamic changes of these variables relate to HRQOL over time in the subacute phase of stroke recovery has not been investigated. The objective of this study was to study longitudinal behaviors of HRQOL of the stroke survivors in relation to the changes in activities of daily living, handicap, and depression after stroke.

Non-linear structural equation models with correlated continuous and discrete data.

Structural equation models (SEMs) have been widely applied to examine interrelationships among latent and observed variables in social and psychological research. Motivated by the fact that correlated discrete variables are frequently encountered in practical applications, a non-linear SEM that accommodates covariates, and mixed continuous, ordered, and unordered categorical variables is proposed. Maximum likelihood methods for estimation and model comparison are discussed.

A two-level structural equation model approach for analyzing multivariate longitudinal responses.

The analysis of longitudinal data to study changes in variables measured repeatedly over time has received considerable attention in many fields. This paper proposes a two-level structural equation model for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables. The first-level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that are changed with time.

Semiparametric Bayesian analysis of structural equation models with fixed covariates.

Latent variables play the most important role in structural equation modeling. In almost all existing structural equation models (SEMs), it is assumed that the distribution of the latent variables is normal. As this assumption is likely to be violated in many biomedical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper.

Bayesian analysis of structural equation models with multinomial variables and an application to type 2 diabetic nephropathy.

There is now increasing evidence proving that many complex diseases can be significantly influenced by correlated phenotype and genotype variables, as well as their interactions. Effective and rigorous assessment of such influence is difficult, because the number of phenotype and genotype variables of interest may not be small, and a genotype variable is an unordered categorical variable that follows a multinomial distribution. To address the problem, we establish a novel nonlinear structural equation model for analysing mixed continuous and multinomial data that can be missing at random.

Bayesian Analysis of Structural Equation Models With Nonlinear Covariates and Latent Variables.

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the proposed model.

Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data.

Structural equation models are very popular for studying relationships among observed and latent variables. However, the existing theory and computer packages are developed mainly under the assumption of normality, and hence cannot be satisfactorily applied to non-normal and ordered categorical data that are common in behavioural, social and psychological research. In this paper, we develop a Bayesian approach to the analysis of structural equation models in which the manifest variables are ordered categorical and/or from an exponential family.

Bayesian analysis of latent variable models with non-ignorable missing outcomes from exponential family.

To provide a comprehensive framework for analysing complex non-normal medical and biological data, we propose a Bayesian approach for a non-linear latent variable model with covariates, and non-ignorable missing data, under the exponential family of distributions. The non-ignorable missing mechanism is defined via a logistic regression model. Based on conjugate prior distributions, full conditional distributions for the implementation of Markov chain Monte Carlo methods in simulating observations from the joint posterior distribution are derived.

Model comparison of generalized linear mixed models.

Generalized linear mixed models (GLMMs) have been widely appreciated in biological and medical research. Maximum likelihood estimation has received a great deal of attention. Comparatively, not much has been done on model comparison or hypotheses testing.

Maximum Likelihood Analysis of Nonlinear Structural Equation Models With Dichotomous Variables.

In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the development is to augment the observed dichotomous data with the hypothetical missing data that involve the latent underlying continuous measurements and the latent variables in the model.

Evaluation of the Bayesian and Maximum Likelihood Approaches in Analyzing Structural Equation Models with Small Sample Sizes.

The main objective of this article is to investigate the empirical performances of the Bayesian approach in analyzing structural equation models with small sample sizes. The traditional maximum likelihood (ML) is also included for comparison. In the context of a confirmatory factor analysis model and a structural equation model, simulation studies are conducted with the different magnitudes of parameters and sample sizes n = da, where d = 2, 3, 4 and 5, and a is the number of unknown parameters.

Maximum likelihood analysis of a general latent variable model with hierarchically mixed data.

A general two-level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels. Nonlinear relationships among the latent variables in the structural equations at both levels, as well as the effects of fixed covariates in the measurement and structural equations at both levels, can be analyzed within the framework. Moreover, the methodology can be applied to hierarchically mixed continuous, dichotomous, and polytomous data.

Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data.

Missing data are very common in behavioural and psychological research. In this paper, we develop a Bayesian approach in the context of a general nonlinear structural equation model with missing continuous and ordinal categorical data. In the development, the missing data are treated as latent quantities, and provision for the incompleteness of the data is made by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm.

Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data.

Two-level structural equation models with mixed continuous and polytomous data and nonlinear structural equations at both the between-groups and within-groups levels are important but difficult to deal with. A Bayesian approach is developed for analysing this kind of model. A Markov chain Monte Carlo procedure based on the Gibbs sampler and the Metropolis-Hasting algorithm is proposed for producing joint Bayesian estimates of the thresholds, structural parameters and latent variables at both levels.

Local influence analysis of structural equation models with continuous and ordinal categorical variables.

This paper proposes a method to assess the local influence of minor perturbations for a structural equation model with continuous and ordinal categorical variables. The key idea is to treat the latent variables as hypothetical missing data and then apply Cook's approach to the conditional expectation of the complete-data log-likelihood function in the corresponding EM algorithm for deriving the normal curvature and the conformal normal curvature. Building blocks for achieving the diagnostic measures are computed via observations generated by the Gibbs sampler.

Bayesian analysis of structural equation models with dichotomous variables.

Structural equation modelling has been used extensively in the behavioural and social sciences for studying interrelationships among manifest and latent variables. Recently, its uses have been well recognized in medical research. This paper introduces a Bayesian approach to analysing general structural equation models with dichotomous variables.

Case-Deletion Diagnostics for Nonlinear Structural Equation Models.

In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the computational burden.

Bayesian model selection for mixtures of structural equation models with an unknown number of components.

This paper considers mixtures of structural equation models with an unknown number of components. A Bayesian model selection approach is developed based on the Bayes factor. A procedure for computing the Bayes factor is developed via path sampling, which has a number of nice features.

Full Maximum Likelihood Estimation of Polychoric and Polyserial Correlations With Missing Data.

This article develops a full maximum likelihood method for obtaining joint estimates of variances and correlations among continuous and polytomous variables with incomplete data which are missing at random with an ignorable missing mechanism. The approach for obtaining the maximum likelihood estimate of the covariance matrix is via a simple confirmatory analysis model with a fixed identity loading matrix and a fixed diagonal matrix with small of unique variances. A Monte Carlo Expectation-Maximization (MCEM) algorithm is constructed to obtain the solution, in which the E-step is approximated by observations simulated by the Gibbs sampler.

Estimating the covariance function with functional data.

This paper describes a two-step procedure for estimating the covariance function and its eigenvalues and eigenfunctions in situations where the data are curves or functions. The first step produces initial estimates of eigenfunctions using a standard principal components analysis. At the second step, these initial estimates are smoothed via local polynomial fitting, with the bandwidth in the kernel function being selected by a data-driven procedure.