Maximal reliability and power in covariance structure models.

In covariance structure modelling, the non-centrality parameter of the asymptotic chi-squared distribution is typically used as an indicator of asymptotic power for hypothesis tests. When a latent linear regression is of interest, the contribution to power by the maximal reliability coefficient, which is associated with used latent variable indicators, is examined and this relationship is further explicated in the case of congeneric measures. It is also shown that item parcelling may reduce power of tests of latent regression parameters. Recommendations on weights for parcelling to avoid power loss are provided, which are found to be those of optimal linear composites with maximal reliability.