Coefficient of Determination for Multiple Measurement Error Models

The coefficient of determination (R2) is used for judging the goodness of fit in a linear regression model. It gives valid results only when the observations are correctly observed without any measurement error. The R2 provides invalid re-sults in the presence of measurement errors in the data in the sense that sample R2 becomes an inconsistent estimator of population multiple correlation coeffi-cient between the study variable and explanatory variables. The corresponding variants of R2 which can be used to judge the goodness of fit in multivariate measurement error model have been proposed in this paper. These variants are based on the utilization of information on known covariance matrix of measure-ment errors and known reliability matrix associated with explanatory variables. The asymptotic properties of the traditional R2 and proposed R2 have been studied. Key Words: Linear regression, ultrastructural model, non-normal distribution.