1. Basics of a run of (Non-metric) MULTIDIMENSIONAL SCALING
Data = Function [Model]
Dis/ Ordinal Euclidean
Similarities (Monotonic) Distance
Any measure that Kruskal: Weak Mon (Triangle
satisfies simple Guttman: Strong Inequality)
requirements Transformations
(includes, but much
more than, PM)
aka Proximities

2. Basics of a run of non-metricMDS INPUT SPECIFICATION
Given a [SSM/LTM/LTD] data matrix of [non-negative] dis/similarities between p objects
SPECIFY:
dimensionality/ies of solution (5 ->1!)
Options for details of type of transformation (default is weak mon; primary ties)
Options for model (Minkowski: Euclidean)
CHECK: Adequacy of constraints:
DCR (Data Compression Ratio)
(#data / #params)>2

3. MULTIDIMENSIONAL SCALING: The Run
How does it work? It’s iterative
Current trial configuration
Distances in current configuration are calculated
See how well they fit data –
by monotone regression
And calculate b-o-f measure, Stress
Look at each point and its residuals
And see how (and how far) it needs to be moved
Move configuration into one of better fit
How? Method of steepest descent.
Well, there was this aviator, see? …
Back to next iteration

4. RUN: Each iteration:

5. Run of MULTIDIMENSIONAL SCALING
to understand in detail, you need to know about:
How and why of MONOTONE / Isotonic / Ordinal Regression
How to interpret “Stress” (fit)
How to decide whether the fit of solution/configuration is acceptably low
If so, how to interpret a configuration
How to compare configurations

6. OUTPUT from Run of MULTIDIMENSIONAL SCALING
(this does NOT follow the order of output!)
Look at ADEQUACY OF FIT:
Stress value (compare to simulation values)
Shepard Diagram. To see form of transformation
Signs of more regular transformation? Re-run with another transformation
Residuals/Point contribution to Stress to locate ill-fitting pts
If not acceptable, don’t even bother looking at “Solution”!
ONLY THEN… LOOK AT Solution Configuration
Consider fixed vs arbitrary aspects (rotation …)
And then …
GET INTO THE SERIOUS BUSINESS OF INTERPRETATION !