When the factor analysis model holds, component loadings are linear combinations of factor loadings, and vice versa. This interrelation permits us to define new optimization criteria and estimation methods for exploratory factor analysis. Although this article is primarily conceptual in nature, an illustrative example and a small simulation show the methodology to be promising.

The objective of the present study was to assess the reproducibility of data-driven dietary patterns in different samples extracted from similar populations. Dietary patterns were extracted by applying principal component analyses to the dietary information collected from a sample of 3550 women recruited from seven screening centres belonging to the Spanish breast cancer (BC) screening network (Determinants of Mammographic Density in Spain (DDM-Spain) study). The resulting patterns were compared with three dietary patterns obtained from a previous Spanish case–control study on female BC (Epidemiological study of the Spanish group for breast cancer research (GEICAM: grupo Español de investigación en cáncer de mama)) using the dietary intake data of 973 healthy participants. The level of agreement between patterns was determined using both the congruence coefficient (CC) between the pattern loadings (considering patterns with a CC≥0·85 as fairly similar) and the linear correlation between patterns scores (considering as fairly similar those patterns with a statistically significant correlation). The conclusions reached with both methods were compared. This is the first study exploring the reproducibility of data-driven patterns from two studies and the first using the CC to determine pattern similarity. We were able to reproduce the EpiGEICAM Western pattern in the DDM-Spain sample (CC=0·90). However, the reproducibility of the Prudent (CC=0·76) and Mediterranean (CC=0·77) patterns was not as good. The linear correlation between pattern scores was statistically significant in all cases, highlighting its arbitrariness for determining pattern similarity. We conclude that the reproducibility of widely prevalent dietary patterns is better than the reproducibility of more population-specific patterns. More methodological studies are needed to establish an objective measurement and threshold to determine pattern similarity.