When what is wrong seems right: A Monte Carlo simulation investigating the robustness of coefficient omega to model misspecification

Coefficient omega is a model-based reliability estimate that is unrestricted by assumptions of a unidimensional essentially tau equivalent model. Rather, omega can be adapted to suit the underlying factor structure of a given population. A Monte Carlo simulation was used to investigate the performance of unidimensional omega and omega-hierarchical under circumstances of model misspecification for high and low reliability measures and different scale lengths. In general, bias increased with the amount of unmodeled complexity (i.e. unspecified multidimensionality or error correlations). When models were misspecified, observed bias was higher when true population reliability was lower, and increased with scale length. Less variable estimates were observed when true reliability and sample size were higher.