On regression analysis with incomplete covariate data

Abstract

Approximate likelihoods are considered for regression analysis with co-variate data missing at random. The methods are based on discrete approxi¬mations to the covariate distribution. In the first approximation, the covari-ate distribution is assumed to be concentrated on the observed complete cases, with kernel averaging used for the likelihood contribution of partially complete cases. The second method places the mass of the covariate distribution on a discrete grid of points, and uses a penalty function to regularize the covari¬ate distribution estimator. Simulations indicate the methods give reasonably good performance for estimated parameters, but that inferences based on large sample approximations may not be reliable.