Estimation of Generalized Simple Measurement Error Models with Instrumental Variables

• Activity Number: 312
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Jeffrey R. Thompson*+ and Randy L. Carter
• Companies: North Carolina State University and University of Buffalo
• Keywords: measurement error models ; instrumental variables ; nonlinear models ; generalized linear models ; latent class models

Abstract

Measurement Error (ME) Models contain at least one independent variable that is imprecisely measured. This leads to an unidentified model and a bias in the naive estimate of the effect of the variable measured with error. One method to correct these problems is through the use of an instrumental variable (IV). We propose a method for parameter estimation, where an IV provides the identifying information, in simple nonlinear ME models. Our estimation method utilizes a "categorization" step and assumes conditional independence given the latent variable, to arrive at maximum likelihood estimates for the parameters of interest, through solving a resulting system of nonlinear equations using estimated generalized nonlinear least squares. New theorems on the identifiability of a large class of ME models are given. We show our estimators have favorable asymptotic properties and provide methods of inference for them. We show how many commonly studied ME models fit into, and can be solved, using the general method we developed.