Comparing the squared multiple correlation coefficients of non-nested models: An examination of confidence intervals and hypothesis testing

The performance of the asymptotic method for comparing the squared multiple correlations of non-nested models was investigated. Specifically, the increase in a given regression model's R-2 when one predictor is added was compared to the increase in the same model's R-2 when another predictor is added. This comparison can be used to determine predictor importance and is the basis for procedures such as Dominance Analysis. Results indicate that the asymptotic procedure provides the expected coverage rates for sample sizes of 200 or more, but in many cases much higher sample sizes are required to achieve adequate power. Guidelines and computations are provided for the determination of adequate sample sizes for hypothesis testing.