A covariance analysis of multiple paired comparisons

In the method of multiple paired comparisons the dominance of objectj over objectk is observed uponp attributes. The present paper develops a covariance analysis for these paired comparisons in terms of a linear model which includes scale, bias, and interaction effects, along withs covariants upon which the comparisons are presumably dependent. The covariance model gives rise to adjusted parameter estimates and hypothesis tests for the residual pairwise layout from which the effects of thes covariants have been removed. These estimation and testing procedures are illustrated with an analysis of political judgment data, and their relevance to the general problem of residual scaling is discussed.This research was supported by National Institute of Mental Health grants MH 12972 and MH 15506. The author would like to express his appreciation to Jerry Solomon and Wei-Ching Chang of the Oregon Research Institute for the data analysis reported at the end of the paper. Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by N.I.H. Grant FR-3.