Sik-Yum Lee

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. The performances are evaluated in terms of the goodness-of-fit statistics, and various measures on the accuracy of the estimates. The conclusion is: for data that are normally distributed, the Bayesian approach can be used with small sample sizes, whilst ML cannot.

Local influence for incomplete-data models

This paper proposes a method to assess the local influence in a minor perturbation of a statistical model with incomplete data. The idea is to utilize Cooks approach to the conditional expectation of the complete-data log-likelihood function in the EM algorithm. It is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local influence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods. An application to the generalized linear mixed model is investigated. Some illustrative artificial and real examples are presented.

A Study of Algorithms for Covariance Structure Analysis with Specific Comparisons Using Factor Analysis.

Several algorithms for covariance structure analysis are considered in addition to the Fletcher-Powell algorithm. These include the Gauss-Newton, Newton-Raphson, Fisher Scoring, and Fletcher-Reeves algorithms. Two methods of estimation are considered, maximum likelihood and weighted least squares. It is shown that the Gauss-Newton algorithm which in standard form produces weighted least squares estimates can, in iteratively reweighted form, produce maximum likelihood estimates as well. Previously unavailable standard error estimates to be used in conjunction with the Fletcher-Reeves algorithm are derived. Finally all the algorithms are applied to a number of maximum likelihood and weighted least squares factor analysis problems to compare the estimates and the standard errors produced. The algorithms appear to give satisfactory estimates but there are serious discrepancies in the standard errors. Because it is robust to poor starting values, converges rapidly and conveniently produces consistent standard errors for both maximum likelihood and weighted least squares problems, the Gauss-Newton algorithm represents an attractive alternative for at least some covariance structure analyses.

Structural equation models with continuous and polytomous variables

A two-stage procedure is developed for analyzing structural equation models with continuous and polytomous variables. At the first stage, the maximum likelihood estimates of the thresholds, polychoric covariances and variances, and polyserial covariances are simultaneously obtained with the help of an appropriate transformation that significantly simplifies the computation. An asymptotic covariance matrix of the estiates is also computed. At the second stage, the parameters in the structural covariance model are obtained via the generalized least squares approach. Basic statistical properties of the estimates are derived and some illustrative examples and a small simulation study are reported.

Latent variable models with mixed continuous and polytomous data

Two-level data with hierarchical structure and mixed continuous and polytomous data are very common in biomedical research. In this article, we propose a maximum likelihood approach for analyzing a latent variable model with these data. The maximum likelihood estimates are obtained by a Monte Carlo EM algorithm that involves the Gibbs sampler for approximating the E-step and the M-step and the bridge sampling for monitoring the convergence. The approach is illustrated by a two-level data set concerning the development and preliminary findings from an AIDS preventative intervention for Filipina commercial sex workers where the relationship between some latent quantities is investigated.

Maximum likelihood estimation of nonlinear structural equation models

The existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables. However, models with nonlinear relationships are often encountered in social and behavioral sciences. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model. To avoid computation of the complicated multiple integrals involved, the E-step is completed by a Metropolis-Hastings algorithm. It is shown that the M-step can be completed efficiently by simple conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louiss formula. The methodology is illustrated with results from a simulation study and two real examples.

Basic and advanced Bayesian structural equation modeling : with applications in the medical and behavioral sciences

Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduced, whilst SEM with a nonparametric structural equation to assess unspecified functional relationships among latent variables are also explored.

Statistical analysis of nonlinear structural equation models with continuous and polytomous data

A general nonlinear structural equation model with mixed continuous and polytomous variables is analysed. A Bayesian approach is proposed to estimate simultaneously the thresholds, the structural parameters and the latent variables. To solve the computational difficulties involved in the posterior analysis, a hybrid Markov chain Monte Carlo method that combines the Gibbs sampler and the Metropolis-Hasting algorithm is implemented to produce the Bayesian solution. Statistical inferences, which involve estimation of parameters and their standard errors, residuals and outliers analyses, and goodness-of-fit statistics for testing the posited model, are discussed. The proposed procedure is illustrated by a simulation study and a real example.

A three-stage estimation procedure for structural equation models with polytomous variables

This paper is concerned with the analysis of structural equation models with polytomous variables. A computationally efficient three-stage estimator of the thresholds and the covariance structure parameters, based on partition maximum likelihood and generalized least squares estimation, is proposed. An example is presented to illustrate the method.

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. Methods— This was a prospective cohort study of first disabling patients with stroke. Subjects were interviewed at 3, 6, and 12 months after stroke for modified Barthel Index, London Handicap Scale, Geriatric Depression Scale, and the World Health Organization Quality of Life questionnaire (abbreviated Hong Kong version). A latent curve model was developed to analyze how the dynamic changes in activities of daily living, handicap, and depressive mood related to the changes in HRQOL. Results— Two hundred forty-seven of 303 patients (82%) followed up at 3 months after stroke could complete the quality-of-life questionnaire. Their mean age was 68.8 years. The latent curve model analysis revealed that initial physical health HRQOL was independently associated with activities of daily living, handicap, and depression. The other 3 HRQOL domain scores were primarily associated with depression only. The rates of change in all 4 domains of HRQOL were significantly and inversely associated with rate of change in the Geriatric Depression Scale only. Conclusion— Change in mood in the postacute phase of stroke recovery is the most significant determinant of change in HRQOL. More attention should be paid to the detection and management of poststroke depression.