A New Constrained Stochastic Multidimensional Scaling Vector Model. An Application to the Perceived Importance of Leadership Attributes

Abstract

Purpose – Multidimensional scaling (MDS) represents a family of various geometric models for the multidimensional representation of the structure in data as well as the corresponding set of methods for fitting such spatial models. Its major uses in business include positioning, market segmentation, new product design, consumer preference analysis, etc. The purpose of this paper is to apply a new stochastic constrained MDS vector model to examine the importance of some 45 different leadership attributes as they impact perceptions of effective leadership practice.

Design/methodology/approach – The authors present a new stochastic constrained MDS vector model for the analysis of two‐way dominance data.

Findings – This constrained vector or scalar products model represents the column objects of the input data matrix by points and row objects by vectors in a T‐dimensional derived joint space. Reparameterization options are available for row and/or column representations so as to constrain or reparameterize such objects as functions of designated features or attributes. An iterative maximum likelihood‐based algorithm is devised for efficient parameter estimation.

Originality/value – The authors present an application to a study conducted to examine the importance of leadership attributes as they impact perceptions of effective leadership practice. Implications for future research and limitations are discussed.

Keywords: Leadership, Data structures, Modelling, Iterative methods