Residual Covariance (R) Matrix

Figure 1. Residual covariance (R) matrix for unstructured covariance model
Residual covariance (R) matrix for unstructured covariance model

The diagonal elements of the two matrices are very similar. Moreover, as in the autoregressive structure, the covariance of two consecutive weeks is negative. The difference in the R matrices is that in the unstructured matrix, the covariances do not weaken as the weeks grow further apart. In fact, the covariation between weeks 1 and 3 (and 2 and 4) is nearly equal to their variances!

The reason for this is that some customers in the study shop on a biweekly basis, thus in weeks when they do not do the majority of their shopping, their purchases are at or near zero. Since these values are outlying compared to normal weekly purchases, they exert an undue influence on the model. In further analysis using Week as a repeated effect, you will need to decide whether to remove these customers from the data file or think of a way to incorporate their information without skewing the model.

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