6 rotation rotation in the context of factor analysis

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extracted factors account for all the groups, the index will then approach unity. 6) Rotation : Rotation, in the context of factor analysis, is something like staining a microscope slide. Just as different stains on it reveal different strictures in the tissue, different rotations reveal different structures in the data. Though different rotations give results that appear to be entirely different, but from a statistical point of view, all results are taken as equal, none superior or inferior to others. However, from the standpoint of making sense of the results of factor analysis, one must select the right rotation. If the factors are independent orthogonal rotation is done and if the factors are correlated, an oblique rotation is made. Communality for each variable will remain undisturbed regardless of rotation but the Eigen values will change as result of rotation. 7) Factor scores : Factor score represents the degree to which each respondent gets high scores on the group of items that load high on each factor. Factor scores can help explain what the factors mean. With such scores, several other multivariate analyses can be performed. We can now take up the important methods of factor analysis. 23.3.1.3. Centroid Method This method of factor analysis, developed by L.L. Thurstone, was quited frequently used until about 1950 before the advent of large capacity high speed computers. The centroid method tends to maximize the sum of loadings, disregarding signs; it is the method which extracts the largest sum of absolute loadings for each factor in turn. It is defined by linear combinations in which all weights are either 1.0 1.0 or . The main merit of this method is that it is relatively simple, can be easily understood and involves simplex computations. If one understands this method, it becomes easy to understand the mechanics involved in other methods of factor analysis. Various steps involved in this method are as follows: 1) This method starts with the computation of a matrix of correlations, R , wherein unities are place in the diagonal spaces. The product moment formula is used for working out the correlation coefficients. 2) If the correlation matrix so obtained happens to be positive manifold (i.e., disregarding the diagonal elements each variable has a large sum of positive correlations than of negative correlations), the centroid method requires that the weights for all variables be 01 . In other words, the variables are not weighted; they are simply summed. But in case the correlation matrix is not a positive manifold, than reflections must be made before the first centroid factor is obtained.
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219 3) The first cetroid factor is determined as under: i. The sum of the coefficients (including the diagonal unity) in each column of the correlation matrix is worked out. ii. Then the sum of these column sums ( ) T is obtained.
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