To fully represent a theoretical or latent-trait structure of behaviour, it is necessary to model observed variable intercepts and factor means in addition to the familiar factor loadings, factor variances and covariances, and residual variances (Meredith, 1993; Widaman & Reise, 1997). Represented in this way, it is possible to fully examine measurement model invariance across groups. The centrality of assumptions of invariance for fairness in testing, and theoretical equivalence of validity patterns are widely acknowledged (Byrne et al., 1988; Meredith, 1993). Since identification of clinical disorders usually involves interpretations of patterns of means or patterns of validity correlations, it is important to examine the assumptions of invariance.

Bowden, S.; Reilly, R.; Bardenhagen, F.; Cook, M.