Second, the model by attributing all the variance other than that from the latent variable to error, precludes the possibility of analytically modelling other sources of systematic variation. This is difficult to achieve and may be overly restrictive in some circumstances. As an alternative it is possible to use a more general model which allows items to be factorially complex. In one version of this model P 1 and P 2 represent a trait and a method factor and affect all items in the test. In practice tests ought to be investigated to determine which model best represents them.
Representation is determined by properties of the test and the purposes of the researcher.
In most instances where tests are designed to measure traits they conform to some variant of model four or five. In order to overcome this researchers need to use more sophisticated techniques to determine reliability. Ironically the test-retest method proves to be the best design for estimating reliability for models four and five. Unfortunately to estimate reliability for these models a more complex method than simply correlating aggregates at time one and time two is needed. The appropriate analytic techniques require a detailed knowledge of covariance structure analysis.