Comparison of goodness measures for linear factor structures

Linear factor structures often exist in empirical data, and they can be mapped by factor analysis. It is, however, not straightforward how to measure the goodness of a factor analysis solution since its results should correspond to various requirements. Instead of a unique indicator, several goodness measures can be defined that all contribute to the evaluation of the results. This paper aims to find an answer to the question whether factor analysis outputs can meet several goodness criteria at the same time. Data aggregability (measured by the determinant of the correlation matrix and the proportion of explained variance) and the extent of latency (defined by the determinant of the antiimage correlation matrix, the maximum partial correlation coefficient and the Kaiser–Meyer–Olkin measure of sampling adequacy) are studied. According to the theoretical and simulation results, it is not possible to meet simultaneously these two criteria when the correlation matrices are relatively small. For larger correlation matrices, however, there are linear factor structures that combine good data aggregability with a high extent of latency.