By Spencer Bennett, David Bowers
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Extra resources for An Introduction to Multivariate Techniques for Social and Behavioural Sciences
1 Rotation of Factors Introduction: orthogonal rotation The results of a factor analysis may be represented graphically as points in n-dimensional space where the factors represent the axes and the factor loadings the co-ordinates of each point. This is only conveniently realisable graphically when an analysis yields a two-factor solution. 1. e. orthogonal, to it. It is because of this that the first factor always appears a general one and the second factor always appears bipolar. Each additional factor will also be orthogonal to preceding ones and hence will be bipolar.
Principal Factor Analysis 49 Another approach is to estimate the number of common factors at the start, rather than the communalities. One such method is the maximum-likelihood solution devised originally by Lawley  which produces the communalities as a by-product, and a test of significance is available which enables one to test whether the number of common factors assumed initially was sufficient. Another method of this type, described in detail in Harman [ 196 7) , is called the 'minres' solution.
E. the variable) and the 1 refers to the fact that we are dealing with the r;j Principal Factor Analysis 41 frrst factor. ;t = Sii/S;t (max). That is, dividing each column sum by the maximum value of S; 1 (regardless of sign). 6. ; 1 values form the basis from which the first factor loadings are calculated. However, they are only approximations to the final values. The next step is to produce a new matrix 1 A (the prefix 1 indicating the first factor), using the values in the inter-correlation matrix R.