Satisfying a Simplex Structure is Simpler than it should be

Markedly different types of growth (learning) curves may generate indistinguishable covariance structures. We illustrate with an example of a 5 × 5 covariance matrix representing longitudinal measurements at five occasions. This example appears to conform closely to a simplex correlation pattern, and a simplex covariance structure provides an excellent fit (using LISREL V) to this covariance matrix. However, the (known) structure of this example differs greatly from the simplex model. In addition to indicating that an excellent fit of a simplex structure can be misleading, this example provides an opportunity to question common uses of covariance structure models for the study of growth.