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A Stochastic Multidimensional Scaling Procedure for the Spatial Representation of Three-Mode, Three-Way Pick Any/J Data

Published online by Cambridge University Press:  01 January 2025

Kamel Jedidi  and
Wayne S. DeSarbo
Kamel Jedidi
Affiliation:
Marketing Department Graduate School of Business, Columbia University
Wayne S. DeSarbo*
Affiliation:
Marketing and Statistics Department, Graduate School of Business, University of Michigan
*
Request for reprints should be sent to Wayne S. DeSarbo, Marketing and Statistics Departments, School of Business Administration, University of Michigan, Ann Arbor, MI 48109-1234.
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Abstract

This paper presents a new stochastic multidimensional scaling procedure for the analysis of three-mode, three-way pick any/J data. The method provides either a vector or ideal-point model to represent the structure in such data, as well as “floating” model specifications (e.g., different vectors or ideal points for different choice settings), and various reparameterization options that allow the coordinates of ideal points, vectors, or stimuli to be functions of specified background variables. A maximum likelihood procedure is utilized to estimate a joint space of row and column objects, as well as a set of weights depicting the third mode of the data. An algorithm using a conjugate gradient method with automatic restarts is developed to estimate the parameters of the models. A series of Monte Carlo analyses are carried out to investigate the performance of the algorithm under diverse data and model specification conditions, examine the statistical properties of the associated test statistic, and test the robustness of the procedure to departures from the independence assumptions. Finally, a consumer psychology application assessing the impact of situational influences on consumers' choice behavior is discussed.

Keywords

multidimensional scalingbinary data analysismaximum likelihood estimationstochastic modelsconsumer psychology
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 3 , September 1991 , pp. 471 - 494
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The authors acknowledge the helpful comments on previous versions of this manuscript made by the editor, associate editor, and anonymous reviewers.

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