Master of Science
Dr. G.Y. Zou
Dr. John Koval
Multiple linear regression analysis is used widely to evaluate how an outcome or responsevariable is related to a set of predictors. Once a final model is specified, the interpretation of predictors can be achieved by assessing the relative importance of predictors.
A common approach to predictor importance is to compare the increase in squared multiple correlation for a given model when one predictor is added to the increase when another predictor is added to the same model.
This thesis proposes asymmetric confidence-intervals for a difference between two correlated squared multiple correlation coefficients of non-nested models. These new proceduresare developed by recovering variance estimates needed for the difference from asymmetric confidence limits for single multiple correlation coefficients. Simulation resultsshow that the new procedure based on confidence limits obtained from the two-moment scaled central F approximation performs much better than the traditional Wald approach. Two examples are used to illustrate the methodology. The application of the procedure indominance analysis and commonality analysis is discussed.
Tan, Li Jr., "Confidence Intervals for Comparison of the Squared Multiple Correlation Coefficients of Non-nested Models" (2012). Electronic Thesis and Dissertation Repository. 384.