RESUMO
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. Results obtained from a simulation study and an analysis of a real medical data set are presented to illustrate the methodology.
Assuntos
Teorema de Bayes , Modelos Estatísticos , Biometria , Nefropatias Diabéticas/genética , Nefropatias Diabéticas/fisiopatologia , Genótipo , Humanos , Funções Verossimilhança , FenótipoRESUMO
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.