The Error in Variables (EIV) Regression Approach as a Means of Identifying Unbiased Physical Parameter Estimates: Application to Chiller Performance Data

Abstract

Classical linear regression analysis by the method of Ordinary Least Squares (OLS) considers errors to affect the dependent variable only, while it is implicitly assumed that the independent or regressor variables are free of error. This assumption is frequently unrealistic, because measurement inaccuracies in the regressor variables are sometimes very large. If these variables are correlated, which is often the case, model coefficients identified by OLS will be biased. This issue may be of secondary concern if the model is used for predictive purposes only, but it is problematic if the model coefficients are to be interpreted as physical quantities and used for diagnostic purposes. A modeling approach that can overcome this deficiency is the Error-InVariable (EIV) regression approach, which can provide unbiased parameter estimates even in the presence of errors in the regressor variables (under the assumption that the errors are unbiased and normally distributed) and when the regressor variables are correlated. This paper describes this method, and, based on precise chiller performance data measured in a laboratory, illustrates the benefit and advantage of the EIV method over the OLS method in the framework of the Gordon and Ng (GN) chiller model. It is found that biased parameter estimates are very likely to occur when OLS is used for identification using the GN model even when well-maintained field instrumentation is used. This bias in parameter estimates can be minimized or even eliminated when the EIV method is used instead.