Bounded-Bias Robust Estimation in Generalized Linear Latent Variable Models

This paper proposes a robust estimator for a general class of linear latent variable models (GLLVM) (Moustaki and Knott 2000, Bartholomew and Knott 1999). It is based on a weighted score function that is simple to implement numerically and is made consistent using the basic idea of indirect inference. The need of a robust estimator for these models is motivated by the study of the effect of model deviations such as data contamination on the maximum likelihood estimator (MLE). This is done with the use of the influence function (Hampel 1968, 1974) and the gross error sensitivity (Hampel, Ronchetti, Rousseeuw, and Stahel 1986). Simulation studies show that the MLE can be seriously biased by model deviations. The performance of the robust estimator in terms of bias and variance is compared to the MLE estimator with simulation studies and with a real example from a consumption survey.