A Stochastic Multidimensional Scaling Vector Threshold Model for the Spatial Representation of 'Pick Any/N' Data

Psychometrika, Volume 54, Issue 1, pp 105-129

25 Pages Posted: 30 May 2016

See all articles by Wayne S. DeSarbo

Wayne S. DeSarbo

Pennsylvania State University

Jaewun Cho

Arizona State University (ASU)

Date Written: March 1989

Abstract

This paper presents a new stochastic multidimensional scaling vector threshold model designed to analyze “pick any/n” choice data (e.g., consumers rendering buy/no buy decisions concerning a number of actual products). A maximum likelihood procedure is formulated to estimate a joint space of both individuals (represented as vectors) and stimuli (represented as points). The relevant psychometric literature concerning the spatial treatment of such binary choice data is reviewed. The nonlinear probit type model is described, as well as the conjugate gradient procedure used to estimate parameters. Results of Monte Carlo analyses investigating the performance of this methodology with synthetic choice data sets are presented. An application concerning consumer choices for eleven competitive brands of soft drinks is discussed. Finally, directions for future research are presented in terms of further applications and generalizing the model to accommodate three-way choice data.

Keywords: binary data analysis, multidimensional scaling, nonlinear probit model

Suggested Citation

DeSarbo, Wayne S. and Cho, Jaewun, A Stochastic Multidimensional Scaling Vector Threshold Model for the Spatial Representation of 'Pick Any/N' Data (March 1989). Psychometrika, Volume 54, Issue 1, pp 105-129, Available at SSRN: https://ssrn.com/abstract=2785857

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Jaewun Cho

Arizona State University (ASU)

Farmer Building 440G PO Box 872011
Tempe, AZ 85287
United States

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