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Multi-dimensional scaling (image (image (Kruskal, distance of the…
Multi-dimensional scaling
subjective interpretation
based on your knowledge of the variables
Goal of MDS is to reduce number of dimensions
1 or 2 preferred as easy to represent on paper
Djk is not the data it is a function of the original data point
move data points around to minimise stress and match rank order of original data the best
badness of fit
Kruskal
distance of the proximity matrix used to create rank order
low values= better fit (<.15)
types
Classical
only 1 proximity matrix
interval or ratio data
function is a simple linear regression
Non-metric MDS
assumes only an ordinal level of measurement
one distance matrix
based on rank order rather than linear function
transformed data points are in the same rank order
When to stop
stress value does not change by greater than a pre-set criterion
stress value reaches a preset mimimum value
program has reached a set no. of iterations
assumptions
assumes relationship between proximity data and derived distances is smooth
degeneracy
points of the representation are located in a few tight clusters
