Likelihood Analysis and Flexible Structural Modeling for Measurement Error Model Regression
Daniel W. Schafer · Journal of Statistical Computation and Simulation · 2002
A computational approach is presented for likelihood analysis of regression models with measurement errors in explanatory variables. If y, x, and w represent the response, an unobservable true value of an explanatory variable, and an observable measurement of x, then the likelihood function is based on the density of the observable variables: @(y,w) = ∫ƒ(y,w|x)ƒ(x)dx. For realistic model specifications the integral must be approximated numerically. While one could conceivably use a general-purpose optimization routine for finding estimates that maximize the approximate likelihood, that tends not to work very well. The approximate density, however, has the form of a finite mixture model so that the standard EM Algorithm for that problem can be applied. The resulting approach is practically important since it easily permits realistic distributional modeling and can be accomplished through iterative application of readily available routines.