A New Parametric Approach to the Analysis of a Bivariate Structural Relationship

• Activity Number: 248
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Fassil Nebebe*+
• Companies: Concordia University
• Keywords: latent variable ; asymptotic bias ; maximum likelihood estimation ; Monte Carlo simulation ; UIC distributions

Abstract

We consider in this paper the analysis of a bivariate linear structural relationship when the ratio of the error variance is known and the errors are normally distributed. It is well known in this case that the maximum likelihood estimator assuming that the unobservable independent variable is normally distributed remains consistent for any other distributional forms. Its efficiency, however, is highly dependent upon the actual form of the distribution of the latent variable. We consider here a more general parametric approach to the analysis of the bivariate structural relationship assuming that latent variable follows an UIC distribution. The advantages of such an approach are discussed, including the availability of a simple test for the normality of the latent variable. Since the normal distribution is a member of the UIC distribution, the maximum likelihood estimator in this new parametric approach remains consistent when the latent variable is normally distributed. The asymptotic bias and the efficiency under the UIC assumption are studied numerically under various distributional forms of the latent variable using Monte Carlo simulation.