A b k a w a w b w k are obtained by any method of

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a b k A W a W b W k ) are obtained (by any method of factoring). After this, we work out factor loadings (i.e., factor-variable correlations). Then communality, symbolized as 2 h , the Eigen value and the total sum of squares are obtained and the result interpreted. For realistic results, we resort to the technique of rotation, because such rotations reveal different structures in the data. Finally, factor scores are obtained which help in explaining what the factors mean. They also facilitate comparison among groups of items as groups. With factor scores, one can also perform several other multivariate analyses such as multivariate analyses such as multiple regressions, cluster analysis, multiple discriminant analysis, etc. 23.3.1.2. Important Methods of Factor Analysis There are several methods of factor analysis, but they do not necessarily give same results. As such factor analysis is not a single unique method but a set of techniques. Important methods of factor analysis are: i. The centroid method; ii. The principal components method; iii. The maximum likelihood method. Before we describe theses different methods of factor analysis, it seems appropriate that some basic terms relating to factor analysis be well understood. 1) Factor : A factor is an underlying dimension that account for several observed variables. There can be one or more factors, depending upon the nature of the study and the number of variables involved in it. 2) Factor-loadings : Factor loadings are those values which explain how closely the variables are related to each one of the factors discovered. They are also known as factor-variable correlations. In fact, factor-loadings work as key to understanding what the factors mean. It is the absolute size (rather than the signs, plus or minus) of the loadings that is important is the interpretation of a factor. 3) Communality ( 2 h ) : Communality, symbolized as 2 h shows how much of each variable is accounted for the underlying factors taken together. A high value of communality mean that not much of the variable is left over after whatever the factors represent is taken into consideration. It is worked out in respect of each variable as under: 2 2 2 var ( ) ( ) ...... th th th h of the i iable i factor loading of factor A i factor loading of factor B 4) Eigen value (or latent root) : When we take the sum of squared values of factor loadings relating to a factor, then such sum is referred to as Eigen Value
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218 or latent root. Eigen value indicates the relative importance of each factor in accounting for the particular set of variables being analyzed. 5) Total sum of squares : When Eigen values of all factors are totaled, the resulting value is termed as the total sum of squares. This value, when divided by the number of variables (involved in a study), results in an index that shows how the particular solution accounts for what all the variables taken together represent. If the variables are all very different from each other, this index will be low. If they fall into one or more highly redundant groups, and if the extracted factors account for all the groups, the index will then approach unity.
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