An algorithm for assessing the correspondence of one or more attribute rating variables to a symmetric matrix of dissimilarities is presented. It is useful as an alternative to fitting property variables into a multidimensional scaling space. The relation between the matrix and the variables is determined by evaluating pairs of pairs relations.…

Using an infinite item test framework, it is argued that the usual assumption of local independence should be replaced by a weaker assumption--essential independence. The usual assumption of unidimensionality is replaced by a weaker and more appropriate statistically testable assumption of essential unidimensionality. (TJH)