Testing equality of reliability and stability with simple linear constraints in multi-wave, multi-variable models

Data from a longitudinal study on school achievement were used to develop new methods for analysing reliability of measurements and stability of behaviour over a long time interval. The proposed method of analysis makes it possible to test hypotheses about equality constraints on reliability and stability. It is known that the use of negative variances for imaginary latent variables with equality constraints between structural parameters produces standardized variances for endogenous latent variables and quality constraints for coefficients of stability. Reparameterization of random errors in measurement models allows equality constraints to be set for coefficients of cross-sectional and of longitudinal reliability. This technique was applied to empirical longitudinal data by using reparameterized three-wave, three-variable models and simplex models.