Chapter 14: Multidimensional Scaling: British Water Voles and Voting in US Congress By: Laila, Rozie, Vimal.

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Chapter 14: Multidimensional Scaling: British Water Voles and Voting in US Congress By: Laila, Rozie, Vimal

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

Introduction Table 14.1 Table 14.1 Gives a distance matrix derived from their voles data. Measures distance between populations of water voles. Gives a distance matrix derived from their voles data. Measures distance between populations of water voles. Table 14.2 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. 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.

Multidimensional Scaling What is it? What is it? How it does it? How it does it?

Example

Example-Map produced by MDS

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

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

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