Bayesian local influence of semiparametric structural equation models

The authors develop a Bayesian local influence method for semiparametric structural equation models. The effects of minor perturbations to individual observations, the prior distributions of parameters, and the sampling distribution on the statistical inference are assessed with various perturbation schemes. A Bayesian perturbation manifold is constructed to characterize such perturbation schemes. The first- and second-order influence measures are proposed to quantify the degree of minor perturbations on different aspects of a statistical model via objective functions, such as Bayes factor. Simulation studies are conducted to evaluate the empirical performance of the Bayesian local influence procedure. An application to a study of bone mineral density is presented.