The congruence coefficient was first introduced by Burt (1948) under the name of unadjusted correlation as a measure of the similarity of two factorial configurations. The name congruence coefficient was later tailored by Tucker (1951, see also Harman, 1976). The congruence coefficient is also sometimes called a monotonicity coefficient (Borg & Groenen, 1997, p. 203). The congruence coefficient...

The congruence between two configurations of points quantifies their similarity. The configurations to be compared are, in general, produced by factor analytic methods which decompose an “observations by variables” data matrix and produce one set of factor scores for the observations and one set of factor scores (i.e., the “loadings”) for the variables. The congruence between two sets of factor...

Random coe cient regression models have been applied in di erent elds and they constitute a unifying setup for many statistical problems. The nonparametric study of this model started with Beran and Hall (1992) and it has become a fruitful framework. In this paper we propose and study statistics for testing a basic hypothesis concerning this model: the constancy of coe cients. The asymptotic be...

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