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

Psychometrika, Volume 56, Issue 3, pp 471-494

24 Pages Posted: 3 Jun 2016

See all articles by Kamel Jedidi

Kamel Jedidi

Columbia Business School - Marketing

Wayne S. DeSarbo

Pennsylvania State University

Date Written: September 1991

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 scaling, binary data analysis, maximum likelihood estimation, stochastic models, consumer psychology

Suggested Citation

Jedidi, Kamel and DeSarbo, Wayne S., A Stochastic Multidimensional Scaling Procedure for the Spatial Representation of Three-Mode, Three-Way Pick Any/J Data (September 1991). Psychometrika, Volume 56, Issue 3, pp 471-494. Available at SSRN: https://ssrn.com/abstract=2788146

Kamel Jedidi

Columbia Business School - Marketing ( email )

New York, NY 10027
United States

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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