## Multidimensional Scaling

Multidimensional Scaling is a technique for determining spatial patterns of stimuli and is available in, for example, SPSS and SAS. The input takes the form of a matrix of either similarities or dissimilarities. These can either be calculated by the statistical package from raw data, and expressed in the form of distances, or evaluated directly from a subject by the tester. For example a subject might have their reaction times (RTs) taken for identifying semantic meaning of words from groups of semantic categories such as animals, people and household objects. A pair of stimuli(a,b) would have a value equal to the average RT for stimulus b when it is immediately preceded by stimulus a. The higher the value of the dissimilarity between a pair of stimuli the further that pair of stimuli are apart e.g. distance, RT. Conversely the higher a similarity between a pair of stimuli the closer together they are e.g. correlation.

There is a close similarity between co-ordinates for individuals obtained using Multidimensional Scaling which represent co-ordinates which try to reproduce as accurately as possible the metric Euclidean distance between pairs of sample points (closer agreement between a pairs of points equates to small distances) and using Principal Components Analysis of the covariance matrix of features of these individuals (high covariances across features of pairs of individuals indicates close agreement between individuals). Further details including equations to obtain co-ordinates and the use of singular value decomposition are available in this file which gives an overview of dimensionality reduction taken from this website. Equations for computing co-ordinates using PCA are in this file taken from this website. Equations to compute co-ordinates using MDS are in this file taken from here.

SPSS offer two procedures for MDS (PROXSCAL and ALSCAL). PROXSCAL is recommended (Goodwill, AM, Alison, LJ and Humann M (2009)).

An alternative to MDS: network analysis is available using igraph in R

Reference

Goodwill, AM, Alison, LJ and Humann M (2009) Multidimensional scaling and the analysis of sexual offence behaviour: a reply to Sturidsson et al. *Psychology, Crime & Law* **15(6)** 517-524.