Chapter 14: Multidimensional Scaling: British Water Voles and Voting in US Congress

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Chapter 14 Multidimensional Scaling British
Water Voles and Voting in US Congress

• By Laila, Rozie, Vimal

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Introduction

• The aim of the study was to compare British
  populations of water voles with those in Europe.
• To investigate whether more than one species
  might be present in Britain.

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Introduction

• Table 14.1
• Gives a distance matrix derived from their voles
  data. Measures distance between populations of
  water voles.
• Table 14.2
• Shows number of times 15 congressmen voted
  differently in the house of representatives on 19
  bills. So similarity of voting behavior of
  congressmen is measured.

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Multidimensional Scaling

• What is it?
• How it does it?

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Example
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Example-Map produced by MDS
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Multidimensional Scaling

• So both 14.1 and 14.2 are examples of proximity
  matrices.
• Which attempt to quantify how similar are
  stimuli, objects, or individuals.
• How proximity data can be best displayed to aid
  in uncovering of an interesting structure.

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Multidimensional Scaling

• The model consist of q dimensional coordinate
  values, with nnumber of rows and columns of
  proximity matrix, and measure of distance between
  pairs of points.
• Q provides information about the adequate fit.

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Euclidean distance

• One of the inter-point distance measures used in
  MDS.