Disjoint factor analysis with cross-loadings

Disjoint factor analysis with cross-loadings Disjoint factor analysis (DFA) is a new latent factor model that we propose here to identify factors that relate to disjoint subsets of variables, thus simplifying the loading matrix structure. Similarly to exploratory factor analysis (EFA), the DFA does not hypothesize prior information on the number of factors and on the relevant relations between variables and factors. In DFA the population variance–covariance structure is hypothesized block diagonal after the proper permutation of variables and estimated by Maximum Likelihood, using an Coordinate Descent type algorithm. Inference on parameters on the number of factors and to confirm the hypothesized simple structure are provided. Properties such as scale equivariance, uniqueness, optimal simplification of loadings are satisfied by DFA. Relevant cross-loadings are also estimated in case they are detected from the best DFA solution. DFA has also the option to constrain a variable to load on a pre-specified factor so that the researcher can assume, a priori, some relations between variables and loadings. A simulation study shows performances of DFA and an application to optimally identify the dimensions of well-being is used to illustrate characteristics of the new methodology. A final discussion concludes the paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Data Analysis and Classification Springer Journals

Disjoint factor analysis with cross-loadings

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistical Theory and Methods; Data Mining and Knowledge Discovery
ISSN
1862-5347
eISSN
1862-5355
D.O.I.
10.1007/s11634-016-0263-9
Publisher site
See Article on Publisher Site

Abstract

Disjoint factor analysis (DFA) is a new latent factor model that we propose here to identify factors that relate to disjoint subsets of variables, thus simplifying the loading matrix structure. Similarly to exploratory factor analysis (EFA), the DFA does not hypothesize prior information on the number of factors and on the relevant relations between variables and factors. In DFA the population variance–covariance structure is hypothesized block diagonal after the proper permutation of variables and estimated by Maximum Likelihood, using an Coordinate Descent type algorithm. Inference on parameters on the number of factors and to confirm the hypothesized simple structure are provided. Properties such as scale equivariance, uniqueness, optimal simplification of loadings are satisfied by DFA. Relevant cross-loadings are also estimated in case they are detected from the best DFA solution. DFA has also the option to constrain a variable to load on a pre-specified factor so that the researcher can assume, a priori, some relations between variables and loadings. A simulation study shows performances of DFA and an application to optimally identify the dimensions of well-being is used to illustrate characteristics of the new methodology. A final discussion concludes the paper.

Journal

Advances in Data Analysis and ClassificationSpringer Journals

Published: Aug 5, 2016

References

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