Beyond spatial representation

The correspondence between theory and observation is often evaluated by a comparison between a hypothesized constraint matrix and the spatial representation of a pxp similarity matrix. This comparison of constraint and proximity matrices assumes the accurate translation of similarities to proximities. If the translation is not exact (i.e., a stress or alienation coefficient greater than zero), the hypothesized structure is evaluated using a false representation of the observed data. The proposed model eliminates the need for spatial representation by making a direct comparison between the hypothesized constraint matrix and the multivariate structure of the bivariate similarities. Goodness of fit indices are used for three model comparisons; (1) single data set, one hypothesized structure; (2) single data set, two hypothesized structures; and (3) two data sets, one hypothesized structure.