After the second centroid factor is obtained cross

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After the second centroid factor is obtained, cross products are computed forming, matrix, 2 Q . This is then subtracted from 1 R (and not from ' 1 R ) resulting in 2 R . To obtain a third factor (C), one should operate on 2 R in the same way as on 1 R . First, some of the variables would have to be reflected to maximize the sum of loadings, which would produce ' 2 R . Loadings would be computed from ' 2 R as they were from ' 1 R . Again, it would be necessary to give negative sigs to the loadings of variables which were reflected which would result in third centroid factor (C) 23.3.1.4. Maximum Likelihood Method The maximum likelihood (ML) method consists in obtaining sets of factor loadings successively in such a way that each, in turn, explains as much as possible of the population correlation matrix as estimated from the sample correlation matrix. If R stands for the correlation matrix actually obtained from the data in a sample, R stands for the correlation matrix that would be obtained if the entire population were tested, then the ML method seeks to extrapolate what is known from R, in the best possible way to estimate R (but the PC method only maximizes the variance explained in R). Thus, the ML method is a statistical approach in which one maximizes some relationship between the sample of data and the population from which the sample was drawn. The arithmetic underlying the ML method is relatively difficult in comparison to that involved in the Principal Components (PC) method and as such is understandable when one has adequate grounding in calculus, higher algebra and matrix algebra in particular. Iterative approach is employed in ML method also to find each factor, but the iterative procedures have proved much more difficult than what we find in the case of PC method. Hence the ML method is generally not used for factor analysis in practice. The loadings obtained on the first factor are employed in the usual way to obtain a matrix of the residual coefficients. A significance test is then applied to indicate whether it would be reasonable to extract a second factor. This goes on repeatedly in search of one factor after another. One stops factoring after the significance test fails to reject the null hypothesis for the residual matrix. The final product is a matrix of factor loadings. The ML factor loadings can be interpreted in a similar fashion as we have explained in case on the centroid or the PC method.
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221 23.3.1.5. Rotation in Factor Analysis One often talks about the rotated solutions in the context of factor analysis. This is done (i.e., a factor matrix is subjected to rotation) to attain what is technically called “simple structure” in data. Rotation constitutes the geometric aspects of factor analysis. Only the axes of the graph (wherein the points representing variables have been shown) are rotated keeping the location these points relative to each other understood. Simple structure is obtained by rotating the axes until: i. Each row of the factor matrix has one zero.
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