Problems of Domain Factors with Small Factor Loadings in Bi-Factor Models

Many measurement designs produce domain factors with small variances and factor loadings. The current study investigates the cause, prevalence, and problematic consequences of such domain factors. We collected a meta-analytic sample of empirical applications, conducted a simulation study on statistical power and estimation precision, and provide a reanalysis of an empirical example. The meta-analysis shows that about a quarter of all standardized domain factor loadings is in the range of $$ and about a third of all domains is measured by five or fewer indicators, resulting in small factor variances. The simulation study examines the associated difficulties concerning statistical power, trait recovery, irregular estimates, and estimation precision for a range of such realistic cases. The empirical example illustrates the challenge to develop measures that produce clearly interpretable domain factors. Study planning and interpretation need to take the (expected) sum of squared factor loadings per domain factor into account. This is relevant even if influences of domain factors are desired to be small, and equally applies to different model variants. We propose several strategies for how researchers may better unlock the bifactor model's full potential and clarify its interpretation.