Note: numbers in brackets refer to Publications list.
Multidimensional Scaling
Some early work on Thurstonian scaling [5, 10], Guttman's simplex theory [7], and Coombsian metric multidimensional unfolding [9]. An algebraic solution for Horan's subjective metrics model (which underlies "INDSCAL" [15]) was subsequently extended into a computationally efficient and robust scaling algorithm (COSPA, [25, 29]). Later [9] was extended (with Wang) into a multidimensional scaling model for preference data that combines the Bradley-Terry-Luce model with Coombs' unfolding model [14, 19]. A common characteristic all these metric MDS models share is that they all have exact algebraic solutions and are, at least in principle, testable [35, 39].
Later empirical work with similarity data on rectangles followed up on Krantz and Tversky's (1970) lead [36, 37]). On closer scrutiny we found that dissimilarity ratings often violate some basic assumptions required by the conventional metric models, notably the Archimedean axiom, which underlies all Minkowski metrics, in particular, the euclidean and the city-block metric [38, 41, 42, 46, 48, 59, 73].
More generally, such findings cast doubt on the research promise of prepackaged scaling programs that ignore the actual judgement behavior of the subjects. In hindsight, the few nontrivial insights produced during the MDS craze of the 70s seem to have been mostly artifacts [36, 38, 59].
Naively, one might think that both scaling and test theory ought to relate to measurement theory in some way since all three profess to be concerned with the problem of assigning numbers to objects or subjects. Our earlier, still relatively upbeat thoughts on these issues are summarized in [33, with I. Borg]. However, as time went on, and the anticipated empirical support of axiomatic measurment theories never materialized, we found it increasingly harder to maintain our earlier optimism about the prospective utility of such abstract theories. Eventually, this scepticism extended to mathematics more generally as a tool for solving non-ficticious problems in psychology [73].