Multidimensional analysis of successive categories (rating) data by dual scaling

The collection of data by rating questionnaires is so commonplace in the behavioural sciences that the problem of quantifying the stimuli (items) rated has a long and varied history. Traditional Thurstonian sealing, based an the method of successive categories, provides a model for psychological judgement that estimates stimulus scale values and category boundaries. However, methods based on this model assume that all the raters are interchangeable and that all stimuli and categories are ordered on a unidimensional scale. In this thesis, the problem of finding multidimensional solutions for both stimuli and raters is addressed by a data analytic technique called dual scaling. A major purpose of the study has been to propose a way to deal with the difficulties caused by category boundary scale values that violate the assumed unidimensional ordering.; To illustrate the problem, consider rating students' performance using the categories "Poor," "Mediocre," "Average," "Good," "Excellent." Such ratings exemplify "successive categories data" the kind of data considered in this study. The category boundaries ({dollar}tausb{lcub}k{rcub}, k = 1,2,3,4){dollar} are introduced as response variables such that {dollar}tausb1{dollar} is between "Poor" and "Mediocre," {dollar}tausb2{dollar} between "Mediocre" and "Average," {dollar}tausb3{dollar} between "Average" and "Good," {dollar}tausb4{dollar} between "Good" and "Excellent" and {dollar}tausb1 < tausb2 < tausb3 < tausb4.{dollar} If different raters (respondents) do not completely agree on how the students rank in their overall performance, then summarizing the ratings in a single dimension of performance, with the category boundaries ordered as expected, would not be possible.; A two-step procedure is proposed in which the subjects (raters) are clustered into more homogeneous groups and a separate dual scaling solution for each cluster is found. The proposed method (DSMASC) is illustrated with artificial and real data. The major conclusion is that DSMASC provides multidimensional solutions for the stimuli with the category boundaries ordered as required. Limitations of the study and directions for future are discussed.