Local influence analysis of structural equation models with continuous and ordinal categorical variables

This paper proposes a method to assess the local influence of minor perturbations for a structural equation model with continuous and ordinal categorical variables. The key idea is to treat the latent variables as hypothetical missing data and then apply Cook's approach to the conditional expectation of the complete‐data log‐likelihood function in the corresponding EM algorithm for deriving the normal curvature and the conformal normal curvature. Building blocks for achieving the diagnostic measures are computed via observations generated by the Gibbs sampler. It is shown that the proposed methodology is relatively simple to implement, computationally efficient, and feasible for a wide variety of perturbation schemes. Two illustrative real examples are presented.