Basics of a run of (Non-metric) MULTIDIMENSIONAL SCALING

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Presentation transcript:

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

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

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

RUN: Each iteration:

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

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 !