An Index of Local Sensitivity to Nonignorability for a Pseudolikelihood Method

Abstract

For regression analysis of data with non response, sensitivity analysis is usually recommended. An index of local sensitivity to non ignorability (ISNI) (Troxel et al., 2004) was derived to detect the sensitivity of maximum likelihood estimates to small departures from ignorability. However, ISNI requires specification of a parametric model for the missing-data mechanism. In this article, a local sensitivity index for a pseudolikelihood (PL) method that does not require specification of the mechanism is proposed. For bivariate data (x, y), when the non response mechanism is an arbitrary function of x + λy, this new index is defined as the first derivative of the PL estimate with respect to λ at λ = 0. The closed form was derived for normal regression data when the density function of the predictor x approximated by a kernel estimator in the PL method. The utility of this new local sensitivity index was illustrated through application on one dataset.

Keywords:

• Missing data
• Pseudolikelihood
• Sensitivity analysis

Mathematics Subject Classification:

• 62F35
• 62J86