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An Introduction to Multivariate Techniques for Social and by Spencer Bennett, David Bowers

By Spencer Bennett, David Bowers

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90 0. 71 0. 64 0. 3, in which the significant loadings are shown in italic, shows how rotation of the factors has caused the three separate variable clusters to emerge quite sharply and agree with our original guesses. 2, it can be seen that the separate clusters are much more easily defmed. It is now possible to re-interpret these factors following rotation. Factor one, corresponding to variables 6, 7, 8 and 9, might be referred to as 'body bulk'; factor two (ignoring variable I for the moment) has high loadings for variables 4 and 5 and may be referred to as 'leg length'; and factor three (corresponding to variables I, 2 and 3) perhaps as 'trunk length'.

6 is re-arranged (for a reason to be explained later), and the communalities estimated. 14) have been employed in the present example. 17. 85, in this case. ht, where the suffix j denotes the variable number. 18 gives the complete set of first factor loadings. 61 %variance extracted 33 What in effect this procedure achieves is to explain all the common variance of variable 1 in terms of one factor. 1)). The first row of the first residual matrix will therefore consist entirely of zeros. e. 19. 20.

If there are n factors, there should ben non-significant loadings in each factor. For every pair of factors there should be several variables with non-significant loadings in one, but significant loadings in the other. Where there are four or more variables for every pair of factors, a large proportion of loadings should have non-significant values in both. For every pair of factors there should be only a small proportion of significant loadings in both. 1 suggests that a clockwise rotation through 45° might improve the situation.

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