Searching for parsimony in loading patterns with non-zero secondary loadings
Year: 2015
Type: preprint
Abstract: Even when a loading pattern contains a single salient loading for each variable, several nonsalient or secondary loadings are often not close to zero after oblique rotation. The aim of the present study was therefore to propose a criterion for parsimony of non-salient loadings, even when they cannot be reduced to zero. A promising criterion for this purpose is based on ‘buffered scales’, which have been proposed by Cattell and Tsujioka (1964) as optimal indicators of corresponding factors. Variables with positive and negative loadings on an unwanted factor are balanced out in a buffered scale, so that the variance of the unwanted factor is at minimum. It is proposed here to use the balance of positive and negative loadings on unwanted factors as a criterion for finding parsimony in data with non-zero secondary loadings. A rotation method towards this criterion (‘Buffsim-rotation’) is proposed. It is also shown how to specify loadings in confirmatory factor analysis by means of model constraints in order to get buffered simple structure. In a simulation study, Buffsim-rotation performed as well as Geomin-, Oblimin-, and Infomax-rotation with respect to the identification of population simple structure models in the samples. However, a buffered simple structure with a balanced set of positive and negative non-salient loadings could most precisely be identified with Buffsimrotation. An empirical example shows that specifying a buffered simple structure in confirmatory factor analysis results in a more convincing replication of an intended factor structure than methods based on conventional simple structure.
Source: arXiv (Cornell University)
Author: André Beauducel
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W1599639707