Simple estimation of hidden correlation in repeated measures

In medical and social studies, it is often desirable to assess the correlation between characteristics of interest that are not directly observable. In such cases, repeated measures are often available, but the correlation between the repeated measures is not the same as that between the true characteristics that are confounded with the measurement errors. The latter is called the hidden correlation. Previously, the problem has been treated by assuming prior knowledge about the measurement errors or by using relatively complex statistical models, such as the mixed-effects models, with no closed-form expression for the estimated hidden correlation. We propose a simple estimator of the hidden correlation that is very much like the Pearson correlation coefficient, with a closed-form expression, under assumptions much weaker than the mixed-effects model. Simulation results show that the proposed simple estimator performs similarly as the restricted maximum likelihood (REML) estimator in mixed models but is computationally much more efficient than REML. We also made simulation comparison with the Pearson correlation. We considered a real data example.