Factor analysis as data matrix decomposition: a new approach for quasi-sphering in noisy ICA

In this paper, a new approach for quasi-sphering in noisy ICA by means of exploratory factor analysis (EFA) is introduced. The EFA model is considered as a novel form of data matrix decomposition. By factoring the data matrix, estimates for all EFA model parameters are obtained simultaneously. After the preprocessing, an existing ICA algorithm can be used to rotate the sphered factor scores towards independence. An application to climate data is presented to illustrate the proposed approach

On the construction of all factors of the model for factor analysis

indeterminacy, factor scores, confirmatory factor analysis, exploratory factor analysis, distance between factors,

Rotational uniqueness conditions under oblique factor correlation metric

In an addendum to his seminal 1969 article J\"{o}reskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix. These condition sets, formulated under factor correlation and factor covariance metrics, respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and hence, that the condition sets are not equivalent in terms of unicity of the solution.Comment: Postprint, 5 page