The measure of goodness of fit in multidimensional scaling is called S(caled)-Stress! It measures the difference between the observed (dis)similarity matrix e.g. reaction time between semantic pairs and the estimated one using one or more estimated stimuli dimensions. The lower the stress the better the fit.
Dimensions are similar to factors as they give the number of facets of the relationships between stimuli and may be plotted. S-Stress is standardised to take values between 0 and 1. Hair et al(1998) rules of thumb for what values of S-Stress make a good fit.
Dugard, Todman and Staines (2010 p.275) suggest Stress values below 0.15 represent a good fit and also suggest Dispersion Accounted For (DAF) and Tucker's Coefficient of Congruence should have values 'close to 1'.
100 x Stress |
Goodness of Fit |
|
20% or above |
Very Poor (not worth doing) |
|
10%-19.9% |
Fair |
|
5%-9.9% |
Good |
|
2.5%-4.9% |
Excellent |
|
0%-2.4% |
Near Perfect Fit |
|
An R-squared may also be computed in SPSS to determine what proportion of variance of the scaled data can be accounted for by the MDS procedure. R-squared represents the squared correlation coefficient between the estimated distances and the observed distances between data points and is analogous to the R-squared in multiple regression. An R-square of 0.6 is considered the minimum acceptable level (Hair et al, 1998). An R-square of 0.8 is considered good for metric scaling and 0.9 is considered good for non-metric scaling.
References
Dugard P, Todman J and Staines H (2010) Approaching multivariate analysis. A practical introduction. Second Edition. Routledge:New York. This text has example analyses using SPSS.
Hair Jr, JF, Anderson, RE, Tatham, RL and Black WC (1998) Multivariate data analysis. Fifth Edition. Prentice-Hall:New Jersey.
Hair Jr, JF, Black, B, Babin, B, Anderson, RE and Tatham, RL (2005) Multivariate data analysis. Sixth Edition. Prentice-Hall:New Jersey. IN CBSU LIBRARY. A 1995 edition is also in the CBSU LIBRARY.