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

By Spencer Bennett, David Bowers

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Extra resources for An Introduction to Multivariate Techniques for Social and Behavioural Sciences

Sample text

This 'contamination' is not too serious from the factor analytic point 37 Principal Factor Analysis of view in the first few factors extracted (the proportion of common variance extracted decreases with each factor), although the contribution of unique variance to later factors (and its extraction) becomes more serious. Whether or not we get different results from using unities or communality estimates in the principal diagonal depends on the amount of common variance that exists between the original variables, as we shall see later.

3. 2 Oblique rotation of the two factors emerging from the factor analysis of five variables oblique rotation is simply to enable us to locate clusters of similar variables, and thus aid interpretation of factors. The cosine of the angle between the axes representing factors is equal to the correlation between them; thus, for orthogonal axes, cos 90° =0, indicating zero correlation between them. The smaller the angle between axes, the larger the cosine and, hence, the correlation. 31. How this affects the interpretation of the analysis had best be left until the next chapter, and all that need be said here is that oblique rotation has helped locate clusters of similar variables, and thus aided interpretation of the factors.

91) + {0. 57. e. Otf1 = Q/1 /Q/1 (max). e. 3) until successive sets of values for et11 agree to the desired degree (in our case, to two places of decimals). In our example, the procedure only has to be carried out once. 8 gives details of the calculations. 8, F11 , gives the values for the first factor loadings. jt which equals unity. 57. 1) (re-stated here for convenience), r;i = L F;kFik k relates the original correlations between variables, r;j, to the correlations between the variables and factors.

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