Interval estimation of latent correlations in structural equation models with A Priori restricted parameters

Abstract

We propose a procedure for estimating standard errors and confidence intervals (CIs) for particular latent variable correlations. Our approach is based on a utilization of the generally applicable delta method and can be used to evaluate precision of estimation of factor correlations in structural equation models with factor loadings a priori restricted to given constants. This procedure allows comparison of strengths of interrelation across pairs of latent constructs. Similarly, the approach can be used to evaluate standard errors and CIs or parametric expressions of substantive interest in covariance structure models, which are not directly accessible as parameters of the latter. The outlined interval evaluation method is illustrated with a numerical example.