By Bartholomew, David J.
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Additional info for Analysis of Multivariate Social Science Data, Second Edition
However, some care should be taken because 1 and 0 may have diﬀerent meanings for diﬀerent variables. Sometimes, we may only wish to consider (1, 1) as a match. For example, suppose we have a binary variable for nationality where x = 1 if a person is a UK citizen, and x = 0 otherwise. In this case, if we are really interested in nationality (rather than just whether UK or not), we cannot tell whether two people with x = 0 match on nationality. If we do not wish to consider (0, 0) as a match, a suitable measure of similarity is a/p.
Adam and Donna are separated by a distance of 11, Adam and Eve are 10 units apart, but Brian is 9 units away from both Donna and Eve. 3. 3 is 6 indicating that at the next stage we should amalgamate Carmen with the group (Donna, Eve). 3 Second stage distance table for nearest neighbour clustering (A,B) C (D,E) (A,B) C (D,E) – 7 9 – 6 – is to amalgamate them into a single cluster. 4). 4 Agglomeration table for nearest neighbour clustering Stage Number of clusters Clusters Distance level Initial 1 2 3 4 5 4 3 2 1 (A) (B) (C) (D) (E) (A,B) (C) (D) (E) (A,B) (C) (D,E) (A,B) (C,D,E) (A,B,C,D,E) 0 3 5 6 7 What we have achieved by this operation is not quite what we set out to produce.
14, the relative frequency of 0 for item 1 is 213/379 and the relative frequency of 1 for item 4 is 234/379. 40 . 37 . 138 234 Thus, patterns 7 and 8 are judged to be more similar than patterns 7 and 6, because x3 = 0 is a rarer response than x1 = 0. You could consider the appropriateness of this measure of similarity which gives a larger weight to less frequent responses than to more frequent responses. Another feature of this measure is that the diagonal elements of the similarity matrix are not all equal, but, of course, they do not aﬀect the clustering process.
Analysis of Multivariate Social Science Data, Second Edition by Bartholomew, David J.