RE: more on PREDvsDV

From: "Bonate, Peter, Quintiles" <pbonate@qkcm.quintiles.com> Subject: RE: more on PREDvsDV Date: Tue, 2 Feb 1999 09:28:26 -0600 Chuanpu Hu is correct when he states that regression models assume that the independent variable is fixed and the dependent variable has errors, not vice-versa. That is correct for classical functional models, but this is a structural model where both X and Y are random and have error associated with them. That is why plotting one vs. the other is really quite arbitrary. Ordinary regression models will result in artifactual parameter estimates. Any type of fitted line should be simply a visual aid to examine goodness-of-fit and no attempt should be made to do any type of hypothesis testing on the values of the parameter estimates, unless the parameter estimates have been "corrected" for errors in X. If a regression line must be fitted using a linear model, it is best to keep the variable with the smallest error as the independent variable. In this case that is DV. To test whether the errors in X are sufficient to significantly affect the values of the ordinary regression parameter estimates, see the papers by Davies and Hutton (1975) Biometrics 62: 383-391 and Hodges and Moore (1972) Applied Statistics 21: 185-195. Also, the paper by Linnet (1990) Stat Med 9: 1463-1470 is a useful exposition for how to perform error in variables regression for the simple linear model. PETER L. BONATE, PhD. Clinical Pharmacokinetics Quintiles POB 9627 (F4-M3112) Kansas City, MO 64134 phone: 816-966-3723 fax: 816-966-6999