Browsing by Author "Rodgers, Joseph Lee"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Matrix and stimulus sample sizes in the weighted MDS model: Empirical metric recovery functions
    (1991) Rodgers, Joseph Lee
    The only guidelines for sample size that exist in the multidimensional scaling (MDS) literature are a set of heuristic "rules-of-thumb" that have failed to live up to Young’s (1970) goal of finding functional relationships between sample size and metric recovery. This paper develops answers to two important sample-size questions in nonmetric weighted MDS settings, both of which are extensions of work reported in MacCallum and Cornelius (1977): (1) are the sample size requirements for number of stimuli and number of matrices compensatory? and (2) what type of functional relationships exist between the number of matrices and metric recovery ? The graphs developed to answer the second question illustrate how such functional relationships can be defined empirically in a wide range of MDS and other complicated nonlinear models. Index terms: metnc recovery, monte carlo study, multidimensional scaling, sample size, weighted multidimensional scaling.
  • Thumbnail Image
    Item
    Seriation and multidimensional scaling: A data analysis approach to scaling asymmetric proximity matrices
    (1992) Rodgers, Joseph Lee; Thompson, Tony D.
    A number of model-based scaling methods have been developed that apply to asymmetric proximity matrices. A flexible data analysis approach is proposed that combines two psychometric procedures-seriation and multidimensional scaling (MDS). The method uses seriation to define an empirical ordering of the stimuli, and then uses MDS to scale the two separate triangles of the proximity matrix defined by this ordering. The MDS solution contains directed distances, which define an "extra" dimension that would not otherwise be portrayed, because the dimension comes from relations between the two triangles rather than within triangles. The method is particularly appropriate for the analysis of proximities containing temporal information. A major difficulty is the computational intensity of existing seriation algorithms, which is handled by defining a nonmetric seriation algorithm that requires only one complete iteration. The procedure is illustrated using a matrix of co-citations between recent presidents of the Psychometric Society. Index terms: asymmetric data, cluster analysis, combinatorial data analysis, multidimensional scaling, order analysis, proximity data, seriation, unidimensional scaling.
  • Thumbnail Image
    Item
    Statistical tests of group differences in ALSCAL-derived subject weights: Some monte carlo results
    (1985) Rodgers, Joseph Lee
    Several techniques to test for group differences in weighted multidimensional scaling (MDS) subject weights have recently been proposed. The present study presents monte carlo results to evaluate the operating characteristics of two of these with ALSCAL-derived subject weights. The first uses the analysis of angular variation (ANAVA) on raw subject weights. The second applies the analysis of variance (ANOVA) to the flattened subject weights generated by ALSCAL. The ANOVA on flattened weights was less affected by the presence of error and by distortions caused by ALSCAL’S normalization routine than was the ANAVA.
  • Thumbnail Image
    Item
    Successive unfolding of family preferences
    (1981) Rodgers, Joseph Lee; Young, Forrest W.
    A technique to scale preferences in relation to an externally derived stimulus configuration, called Successive Unfolding, is described. Four steps are involved: (1) computing a matrix of inter-stimulus distances; (2) using ALSCAL to obtain a stimulus configuration from the matrix of distances; (3) using Carroll’s regression procedure to solve for subject ideal points; and (4) using this starting configuration to scale preference rank orders in ALSCAL. The technique is used to analyze family preference data. Results suggest that a number preference, a sex preference, and a balance preference are the components contributing to overall family preferences. Race and sex differences are portrayed by locating subject ideal points along these dimensions. Finally, the relationship of Successive Unfolding to previous techniques for measuring family preferences is discussed, and the decision- making process modeled by Successive Unfolding is outlined.