Sufficiency criteria for factor variances complementing model fit criteria in confirmatory factor analysis

Sufficiency criteria enable the evaluation of the sizes of factor variances of latent variables observed in confirmatory factor analysis with respect to the intended purposes of measurement. They complement model fit criteria that enable researchers to evaluate the correspondence of data and model. While fit information is basic regarding the quality of a model, it does not consider intended purposes, as sufficiency criteria do. Following the lead of exploratory factor analysis, the possibility of establishing sufficiency criteria is explored, which are based on factor variances reflecting the amount of explained common systematic variation. Three sufficiency criteria are described and investigated: salience-based, internal consistency-based, and Kaiser-Guttman-based criteria. A simulation study manipulating the amount of common systematic variation confirms that fit estimates and factor variances are basically independent of each other, meaning that considering factor variances in combination with sufficiency criteria can deepen the researcher’s insight into the properties of data. In another simulation study, the suitability of the three criteria is investigated. Most importantly, given the present design, the salience-based criterion appears to mark the lower boundary of the range where a good model fit based on technically correct structural investigations can be expected.