PC program for analyzing one-sample longitudinal data sets which satisfy the two-stage polynomial growth curve model

The two-stage polynomial growth curve model is described and a GAUSS program to perform the associated computations is documented and made available to interested readers. The two-stage model is similar to that considered by us earlier (Schneiderman and Kowalski: American Journal of Physical Anthropology 67:323-333, 1985; American Journal of Human Biology 1:31-42, 1989), i.e., it is appropriate for the analysis of one-sample longitudinal data collected at either equal or unequal time intervals. Here, however, the covariance matrix, Σ, instead of being considered arbitrary, is now assumed to have the special structure Σ = W A W' + σ² I. We show the conditions under which this special structure may be expected to arise and how it may be exploited to produce sharper results in certain situations. The method and the program are illustrated and the results are contrasted to those obtained when Σ is arbitrary. It is suggested that the two-stage model is more efficient when the same degree polynomial is adequate to model the data in the two situations, but that, should a higher degree be necessary for the two-stage model, confidence intervals and/or bands may be wider than those corresponding to Σ arbitrary.