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

A Comparison of ML, WLSMV, and Bayesian Methods for Multilevel Structural Equation Models in Small Samples: A Simulation Study

Multilevel structural equation models are increasingly applied in psychological research. With increasing model complexity, estimation becomes computationally demanding, and small sample sizes pose further challenges on estimation methods relying on asymptotic theory. Recent developments of Bayesian estimation techniques may help to overcome the shortcomings of classical estimation techniques. The use of potentially inaccurate prior information may, however, have detrimental effects, especially in small samples. The present Monte Carlo simulation study compares the statistical performance of classical estimation techniques with Bayesian estimation using different prior specifications for a two-level SEM with either continuous or ordinal indicators. Using two software programs (Mplus and Stan), differential effects of between- and within-level sample sizes on estimation accuracy were investigated. Moreover, it was tested to which extent inaccurate priors may have detrimental effects on parameter estimates in categorical indicator models. For continuous indicators, Bayesian estimation did not show performance advantages over ML. For categorical indicators, Bayesian estimation outperformed WLSMV solely in case of strongly informative accurate priors. Weakly informative inaccurate priors did not deteriorate performance of the Bayesian approach, while strong informative inaccurate priors led to severely biased estimates even with large sample sizes. With diffuse priors, Stan yielded better results than Mplus in terms of parameter estimates.

Modeling error distributions of growth curve models through Bayesian methods

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

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. This method gives more weight to data that are likely to occur based on the structure of the posited model, and effectively downweights the influence of outliers. An algorithm is proposed to obtain the robust estimator. Asymptotic properties of the proposed method are investigated, which include the asymptotic distribution of the estimator, and some statistics for hypothesis testing. Results from a simulation study and a real data example show that our procedure is effective.

Phenotype-genotype interactions on renal function in type 2 diabetes: an analysis using structural equation modelling

AIMS/HYPOTHESIS

Cardiovascular and renal diseases share common risk factors. We used structural equation modelling (SEM) to evaluate the independent and combined effects of phenotypes and genotypes implicated in cardiovascular diseases on renal function in type 2 diabetes.

METHODS

1,188 type 2 diabetic patients were stratified into high-risk and low-risk groups according to bimodal distributions of the logarithmically transformed (log(e)) urinary albumin:creatinine ratio and plasma creatinine levels. Models for these groups, comprising continuous and non-ranking categorical data, were developed separately to evaluate the inter-relationships among measured variables and latent factors using non-linear SEMs, Bayesian estimation and model selection as assessed by a goodness-of-fit statistic.

RESULTS

Inter-correlated measured variables (obesity, glycaemia, lipid, blood pressure) and variants of the genes encoding endothelial nitric oxide synthase (NOS), beta-adrenergic receptor (ADRB), components of the renin-angiotensin system (RAS) and lipid metabolism were loaded onto their respective latent factors of phenotypes and genotypes. In addition to direct and indirect effects, latent factors of obesity, lipid and BP interacted with latent factors of ADRB and RAS genotypes to influence renal function. Together with variants of the genes encoding peroxisome proliferator-activated receptor gamma, atrial natriuretic peptide, adducin, G protein beta(3) subunit, epithelial sodium channel alpha subunit and matrix metallopeptidase 3, these parameters explained 39-80% of the variance in renal function in the high-risk and low-risk models.

CONCLUSIONS/INTERPRETATION

SEM is a useful tool for confirming and quantifying multiple interactions of biological pathways with genetic determinants. The combined and interactive effects of blood pressure, lipid and obesity on renal function may have therapeutic implications, especially in type 2 diabetic individuals with genetic risk factors.

The Rise of Markov Chain Monte Carlo Estimation for Psychometric Modeling

Markov chain Monte Carlo (MCMC) estimation strategies represent a powerful approach to estimation in psychometric models. Popular MCMC samplers and their alignment with Bayesian approaches to modeling are discussed. Key historical and current developments of MCMC are surveyed, emphasizing how MCMC allows the researcher to overcome the limitations of other estimation paradigms, facilitates the estimation of models that might otherwise be intractable, and frees the researcher from certain possible misconceptions about the models.