Although traditional methods to collect similarity data (for multidimensional scaling [MDS]) are robust, they share a key shortcoming. Specifically, the possible pairwise comparisons in any set of objects grow rapidly as a function of set size. This leads to lengthy experimental protocols, or procedures that involve scaling stimulus subsets. We…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

A key challenge for cognitive psychology is the investigation of mental representations, such as object categories, subjective probabilities, choice utilities, and memory traces. In many cases, these representations can be expressed as a non-negative function defined over a set of objects. We present a behavioral method for estimating these…

Bayesian multidimensional scaling (MDS) has attracted a great deal of attention because: (1) it provides a better fit than do classical MDS and ALSCAL; (2) it provides estimation errors of the distances; and (3) the Bayesian dimension selection criterion, MDSIC, provides a direct indication of optimal dimensionality. However, Bayesian MDS is not…

A cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two- or three-way dominance data (e.g., preference, choice, consideration) measured on ordered successive category rating scales. The technical description of the proposed model and estimation procedure are discussed, as well as the…

Reading and Mathematics tests of multiple-choice items for grades Kindergarten through 9 were vertically scaled using the three-parameter logistic model and two different scaling procedures: concurrent and separate by grade groups. Item parameters were estimated using Markov chain Monte Carlo methodology while fixing the grade 4 population…

DETECT is a nonparametric "full" dimensionality assessment procedure that clusters dichotomously scored items into dimensions and provides a DETECT index of magnitude of multidimensionality. Four factors (test length, sample size, item response theory [IRT] model, and DETECT index) were manipulated in a Monte Carlo study of bias, standard error,…

Multivariate models for the triangular and duo-trio methods are described, and theoretical methods are compared to a Monte Carlo simulation. Implications are discussed for a new theory of multidimensional scaling which challenges the traditional assumption that proximity measures and perceptual distances are monotonically related. (Author/GDC)

An experimental procedure involving interaction between subject and computer was used to determine an opitmum subset of stimuli for multidimensional scaling (MDS). A computer program evaluated this procedure compared with MDS based on (a) all pairs of stimuli, and (b) on one-third of the possible pairs. The new method was better. (Author/HG)

A multidimensional scaling procedure is introduced that attempts to derive a spatial representation of stimuli unconfounded by the effect of subjects' degrees of familiarity with these stimuli. A Monte Carlo study investigating the extent to which the procedure recovers known parameters shows that the procedure succeeds in adjusting for…

Critical examination is made of the recent controversy over the value of Monte Carlo techniques in nonmetric multidimensional scaling procedures. The case is presented that the major relevance of Monte Carlo studies is not for the local minima problem but for the meaningfulness of the obtained solutions. (Author)

Monte Carlo procedures are used to develop stress distributions using Kruskal's second stress formula. These distributions can be used in multidimensional scaling procedures to determine whether a set of data has other than random structure. (Author/JKS)

Presents an approach to multidimensional unfolding that reduces the occurrence of degenerate solutions and conducts a Monte Carlo study to demonstrate the superiority of the new method to the ALSCAL and KYST nonmetric procedures for student preference data. (SLD)

A Monte Carlo study was carried out to investigate the ability of the ALSCAL multidimensional scaling program to recover true structure inherent in simulated proximity data. The results under varying conditions were mixed. Practical implications and suggestions for further research are discussed. (Author/JKS)

An examination is made concerning the utility and design of studies comparing nonmetric multidimensional scaling algorithms and their initial configurations, as well as the agreement between the results of such studies. Various practical details of nonmetric scaling are also considered. (Author/JKS)