Inference for Predictor Comparisons: Dominance Analysis and the Distribution of R(2) Differences

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Psychology

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Azen, Razia

Contributors dc:contributor

• David Budescu

• Statistics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9989935

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/82312