A New Diagnostic Test for Regression

A new diagnostic test for regression and generalized linear models is discussed. The test is based on testing if the residuals are close together in the linear space of one of the covariates are correlated. This is a generalization of the famous problem of spurious correlation in time series regression. A full model building approach for the case of regression was developed in Mahdi (2011, Ph.D. Thesis, Western University, ”Diagnostic Checking, Time Series and Regression”) using an iterative generalized least squares algorithm. Simulation experiments were reported that demonstrate the validity and utility of this approach but no actual applications were developed. In this thesis, the application of this hidden correlation paradigm is further developed as a diagnostic check for both regression and more generally for generalized linear models. The utility of the new diagnostic check is demonstrated in actual applications. Some simulation experiments illustrating the performance of the diagnostic check are also presented. It is shown that in some cases, existing well-known diagnostic checks can not easily reveal serious model inadequacy that is detected using the new approach.KEY WORDS: diagnostic test, regression, hidden correlation, generalized linear models