چکیده :
In the behavioral, social, psychological, and the medical sciences, the most widely used
models in assessing latent variables are the structural equation models (SEMs). However,
most of the existing statistical methods for analyzing SEMs have been developed for
normally distributed data. Transformation SEMs are useful tools for tackling the nonnormality
of multidimensional data and simultaneously revealing the interrelationships
among latent variables. The main objective of this paper is to develop a Bayesian
diagnostic procedure for transformation SEMs. The first- and second-order local inference
measures are established with the objective functions that are defined based on the
logarithm of Bayes Factor. Markov chain Monte Carlo (MCMC) methods with the Bayesian
P-splines approach are developed to compute the local influence measures and to
estimate nonparametric transformations, latent variables, and unknown parameters.
Compared with conventional maximum likelihood-based diagnostic procedures, the
Bayesian diagnostic approach could detect outliers and/or influential points in the observed
data, as well as conduct model comparison and sensitivity analysis through various
perturbations of the data, sampling distributions, or prior distributions of the model
parameters. Simulation studies reveal the empirical performance of the proposed Bayesian
diagnostic procedure. An actual data set that is extracted from a study based on the Hong
Kong Diabetes Registry is used to illustrate the application of our methodology
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