Assessing local influence for nonlinear structural equation models with ignorable missing data

Authors:
Sik-Yum Lee;Bin Lu;Xin-Yuan Song
Affiliations:
Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Venue:
Computational Statistics & Data Analysis
Year:
2006

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Abstract

A method is proposed in this paper to assess the local influence of minor perturbations for a nonlinear structural equation model with missing data that are missing at random. The main idea is to apply Zhu and Lee's (J. Roy. Statist. Soc. Ser. B 63 (2001) 111) approach to the conditional expectation of the complete-data log-likelihood function in the corresponding EM algorithm for deriving the conformal normal curvature. Building blocks for achieving the diagnostic measures are computed via latent variables that are generated by the Gibbs sampler and Metropolis-Hastings algorithm. It is shown that the proposed methodology is feasible for a wide variety of perturbation schemes. To illustrate the methodology, results that are obtained from analyses of some artificial examples, a simulation study, and a real example are presented.