IJPAM: Volume 88, No. 3 (2013)
IMPORTANCE IN LINEAR REGRESSION MODEL
USING DOMINANCE HIERARCHIES
1Department of Mathematics
8000 York Road, Towson, MD 21252, USA
2Department of Marketing
3The Conrad Business, Entrepreneurship and Technology Centre
University of Waterloo
Abstract. Regression analysis is perhaps the most frequently used statistical tool for the analysis of data in practice. The purpose of regression analysis is to predict or explain response variables from several pre-selected predictive variables. In the model selection stage, the researcher identifies a subset of predictive variables from a full available set. The selected set is chosen to provide the most adequate description of the response variable. Relative importance analysis is a very useful supplement to regression analysis (Tonidandel and LeBreton 2011). The purpose of determining predictor importance is not model selection but rather uncovering the individual contributions of predictors relative to each other within a selected model. The purpose of this article is to extend the current research practice by developing a statistical modeling approach using the Bayesian framework to evaluate the relative importance of each predictor in a multiple regression model. In what follows we will first illustrate the Dominance Analysis procedure, and will then use our critic as a starting point to introduce the Bayesian Dominance Hierarchies approach based on a statistical model of paired comparisons. Simulation studies are conducted to compare with outcomes from the Dominance Analysis procedure, and followed by an empirical example in service research. Finally, the discussion will lead to reviewing potential future research avenues.
Received: February 24, 2013
DOI: 10.12732/ijpam.v88i3.1 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395