| Abstract: | A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable
missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and
the Metropolis–Hastings algorithm is used to produce the joint Bayesian estimates of structural parameters, latent variables,
parameters in the nonignorable missing model, as well as their standard errors estimates. A goodness-of-fit statistic for
assessing the plausibility of the posited nonlinear structural equation model is introduced, and a procedure for computing
the Bayes factor for model comparison is developed via path sampling. Results obtained with respect to different missing data
models, and different prior inputs are compared via simulation studies. In particular, it is shown that in the presence of
nonignorable missing data, results obtained by the proposed method with a nonignorable missing data model are significantly
better than those that are obtained under the missing at random assumption. A real example is presented to illustrate the
newly developed Bayesian methodologies.
This research is fully supported by a grant (CUHK 4243/03H) from the Research Grant Council of the Hong Kong Special Administration
Region. The authors are thankful to the editor and reviewers for valuable comments for improving the paper, and also to ICPSR
and the relevant funding agency for allowing the use of the data.
Requests for reprints should be sent to Professor S.Y. Lee, Department of Statistics, The Chinese University of Hong Kong,
Shatin, N.T., Hong Kong. |
