Multidimensional Scaling Methods

Introduction

The verb to scale means ‘to arrange in a graduated series’ (Webster's, 1961). Multidimensional scaling means arranging people (or objects) in two or more graduated series. A personality inventory may measure adults on their extroversion and conventionalism, thus yielding two graduated series: extroversion and conventionalism. Each graduated series is a dimension. Hence the term multidimensional scaling.

A scaling model is a statistical function expressing the relationship between location on a psychological dimension, X, and a behavioural response B: B = f(X). The dimension might be psychological extroversion. The behaviour might involve reacting to the statement ‘I like loud parties’ by choosing one of two responses: ‘True of me’; or ‘Not true of me’. The scaling model would express the probability of choosing the response ‘True of me’ as a function of extroversion.

If a good scaling model can be found, dimension X can be measured by observing the behaviour and then computing X: X = f-1 (B). The score X then constitutes our measurement. When the behaviour is a response to a test item, then the scaling model is called an item response theory (see entry on ‘Items Response Theory: Models and Features’).

If the behaviour is a function of two or more dimensions, the scaling model is said to be multidimensional. B becomes a vector of behaviours and X becomes a vector of measurements along two or more dimensions. After observing the several behaviours in vector B, the measurements along the dimensions can be taken by computing X = f-1(B).

Multidimensional assessment methods fall into two categories, semi- and fully multidimensional. Fully multidimensional assessments are multidimensional in three respects. First, they employ complex tasks, each of which is a function of more than one dimension. Second, they employ multidimensional scaling models. Third, they yield a description of people (or objects) along two or more dimensions. Semi-multidimensional methods are multidimensional only in the last of these three respects. In what follows, semi- and fully multidimensional methods are discussed. Within the semi- and fully multidimensional sections, methods designed primarily for measuring attributes of people and methods for measuring perceptions of stimuli are considered separately.

Semi-Multidimensional Methods