Inference for Predictor Comparisons: Dominance Analysis and the Distribution of R(2) Differences
Azen, Razia
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Permalink
https://hdl.handle.net/2142/82312
Description
Title
Inference for Predictor Comparisons: Dominance Analysis and the Distribution of R(2) Differences
Author(s)
Azen, Razia
Issue Date
2000
Doctoral Committee Chair(s)
David Budescu
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
Dominance analysis is a procedure that determines, for each pair of predictors in the general linear (for example, multiple regression) model, the relative importance based on differences between the R2 values of relevant subset models. Depending on the subset models compared, the dominance measure is defined as either complete, average or global dominance. It is shown that predictor comparisons based on these measures will be unaffected by the use of other model fit criteria that rely on the error sum of squares (for example, adjusted-R2, C p or AIC). Four methods are proposed to construct confidence intervals for the dominance measures. Three of these methods rely on examining the distribution of R2 differences by using (1) the asymptotic estimate of its covariance matrix, (2) the bootstrap estimate of its covariance matrix, or (3) the full empirical distribution (obtained using the bootstrap). The fourth inference method relies on examining the distribution of the probability that one predictor dominates another. These methods are compared to each other in simulations applied to data generated using different multivariate distributions (namely, the normal and lognormal) as well as different sample sizes. The methods are also applied to real data samples. The fourth method is shown to be overly sensitive to the detection of dominance. Extensions of these procedures to the multivariate multiple regression model are proposed.
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