TABLE 1.

Distinctions among major covariance structures

Covariance structure	Description
Independent (In)	Assumes there are no correlations among age classes for the dependent variable.
Compound symmetry (Cs)	Assumes that measurements at each age are correlated to all other measurements to the same degree, e.g., there is only one correlation value for all pairs of age classes.
First-order autoregressive (Ar1)	Assumes that correlations are high for neighboring age classes and fall off as time between age classes increases.
	Correlations decrease as a specific, linear function of time between age classes until correlations reach zero.
	Assumes equal variances among ages.
	h option allows unequal variances (Ar1h).
First-order autoregressive with random effects (Ar1R)	Assumes that correlations will decrease by some linear function determined by the amount of time between the two ages being correlated. Incorporates the possibility that because repeated measures were taken on the same individuals over time, no two measurements are completely independent, regardless of the separation between them, and therefore correlations never reach zero.
	Assumes equal variances among ages.
	h option allows unequal variances (Ar1Rh).
Toeplitz (Toep)	Assumes decreasing correlation with time between ages.
	Does not require that these correlations decrease by a definable function.
	h option allows unequal variances (Toeph).
Unstructured (Un)	Assumes that each age class may have a unique correlation with any other age class.
	Allows for unequal variances, covariances among age classes.
	Running PROC MIXED using the unstructured covariance model allows viewing the raw covariance and correlation values for each pair of age classes, without assuming an underlying pattern of correlations.