Only in the case of principal components analysis is it possible to compute exact factor scores.

Question

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In principal components analysis (PCA), it is possible to compute exact factor scores because PCA assumes that the observed variables are linear combinations of the underlying factors, and the factor loadings are obtained as orthogonal transformations of the original variables. Thus, the factor scores can be computed as weighted sums of the original variables, with the weights given by the factor loadings. However, in other factor analysis methods, such as exploratory factor analysis (EFA), it is not possible to compute exact factor scores because EFA assumes that the observed variables are linear combinations of the underlying factors plus a unique error term, and the factor loadings are estimated as correlations between the observed variables and the underlying factors. Thus, the factor scores can only be estimated, not computed exactly.

Only in the Case of Principal Components Analysis Is It