Multidimensional Scaling (MDS). Angelina Anastasova Natalia Jaworska. PSY5121 March 18/2008. Multidimensional Scaling (MDS): What Is It?. Generally regarded as exploratory data analysis (Ding, 2006). Reduces large amounts of data into easy-to-visualize structures.
PSY5121 March 18/2008
Similar objects: Close points Dissimilar objects: Far apart points
Dissimilarity scale: Low #=high similarity &
High #=high dissimilarity.
Similarity scale: Opposite of dissimilarity.
# of pairs = n(n-1)/2, n = # of objects/cases
Can be tedious and inefficient process.
Facilitation of pairwise comparison task:
1) Incomplete similarity task: random or cyclic deletion of comparison pairs.
2) Simplification of pair comparisons (binary scale).
3) Choosing grouping/sorting tasks(Tsogo et al., 2000).
Pre-specified # of groups or not specified.
1) Type of proximities:
2) Number of proximity matrices (distance, dis/similarity matrix).
1) Decompositional MDS: Subjects rate objects on an overall basis, an “impression,” without reference to objective attributes.
2) Compositional MDS: Subjects rate objects
on a variety of specific, pre-specified attributes
xi and xj specify coordinates of points i and j on dimension a, respectively.
ij = f(dij)
1) Clusters: Groupings in a MDS spatial representation.
2) Dimensions: Hidden structures in data. Ordered groupings that explain similarity between items.
that the following is true: f(δij) ≈ dij(X)
Proportion of variance of disparities
not accounted for by the model:
number of dimensions.
E.g. cities distance
Assessing whether MDS solution (dimensionality extraction) changes in a substantial way.
If Data are distances (e.g. cities distances) option is selected, click on the Shape button to define characteristic of the dissimilarities/proximity matrices.
In the Multidimensional Scaling dialog box, click on the Model button to control the level of measurement, conditionality, dimensions, and the scaling model.
“Multidimensional scaling modelling approach to latent profile analysis in psychological research” (Ding, 2006)
BI=body image, PR=peer relations, FR=family relations, MC=mastery & coping, VE=vocational & educational goal, SA=superior adjustment, PMI-1=profile match index for Profile 1, PMI-2=profile match index for Profile 2, LS=life satisfaction, Dep=depression, PL=psychological loneliness
PMI-1=profile match index for Profile 1, PMI-2=profile match index for Profile 2, LS=life satisfaction, Dep=depression, PL=psychological loneliness
Profile 1: -High scores on Body Image - higher degree of life satisfaction.
-High scores on the Vocational-Educational Goal - higher degree of depression.
Profile 2: -Higher scores on the family relationships profile - higher degree of psychological loneliness.
Level: -Average scores of individuals’ psychosocial adjustment.
-Overall positive psychosocial adjustment scores suggest less depression or psychological loneliness and higher degree of life satisfaction.