[Estimation of reliability and stability in the data where test-retest intervals change over subjects]

Models for the test-retest situation are proposed, in which an interval between a test and a retest changes over subjects. In the model of a single observed variable we assume that the true score of the variable changes as a Markovian process. We show that stability and reliability of a test can not be estimated separately in the ordinary test-retest model which assumes equal stability for subjects, but that they can be estimated separately with our model. In the model of a latent variable (factor) we assume various stabilities for the latent variable and the non-zero covariances of specific factors in a test and a retest. These models are applied to actual data, and stabilities and reliabilities of tests are estimated quantitatively.