Regressors In Models Research Articles

A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression

AbstractFor the model y = α + βx + ϵ (model I) of linear regression we dealt with in KUHNERT and HORN (1980) the determination of a confidence interval for that x0 where the expectation Ey reaches a given value y0. Here we start with realizations of random variables y (i = 1,…, m) being independent of x which are given in addition to the realizations of‐y. Now y0 denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ciEy and x0 the x‐value where the expectation Ey reaches that value y0. For this x0 we give a confidence interval. Applications stem from dose response assays.

Collinearity, Ridge Regression, and Investigator Judgment

Several recent articles have suggested that ridge regression may provide an "optimal" procedure for dealing with the problems created by highly collinear regressors in linear models. In this article, we review the consequences of collinearity among the regressors in a well-specified structural equation model and the several variants of ridge regression that may be considered as possible responses to such collinearity. Based on thts review and on application of several ridge regression methods to an actual structural equation model in which collinearity is high, it becomes clear that one or another form of investigator judgment is unavoidable when any specific estimates are obtained via a ridge adjustment. The article indicates how the several ridge techniques implicitly involve distinct criteria whereby an estimator should be judged and some of the complications involved in each.