By Bartholomew, David J.
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Extra resources for Analysis of Multivariate Social Science Data, Second Edition
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. 16. This is an extreme example of chaining. The ﬁrst two patterns that merge, numbers 1 and 5, have pattern 11 as their nearest neighbour so 11 then merges.
Ij = k=1 Another common measure is the so-called “city block” measure, which is the sum of the absolute diﬀerences between the pairs of points. Compared to Euclidean distance, this gives less relative weight to large diﬀerences. A large diﬀerence for a single variable can easily have a dominating eﬀect on the Euclidean distance. Sometimes the most relevant information for the substantive issues under investigation may be in the comparison of the “shapes” or the proﬁles of the objects rather than of their “sizes”.
There are two types of diagrams which are frequently used for this purpose, the dendrogram, or tree diagram, and the icicle plot. The dendrogram This has a tree structure with respect to a scale of distances, with individuals, or groups of individuals, located on branches emanating from stems higher up the scale. It can be drawn with the distance scale either horizontal or vertical. Drawn vertically, it resembles an artistic “mobile”. It has the property that any two branches hanging from the same stem can be interchanged without affecting the structure (as if the two branches of the mobile were rotated through 180 degrees).
Analysis of Multivariate Social Science Data, Second Edition by Bartholomew, David J.