RE: Fixed elements within a block covariance matrix

From: Jakob Ribbing - Jakob.Ribbing@farmbio.uu.se Subject: RE: [NMusers] Fixed elements within a block covariance matrix Date: 1/14/2004 4:12 AM Dear all, If one views correlation between two etas as a result of a mutual covariate not currently included in the covariate model, one can easily come up with examples where only one of three off diagonals truly is 0. In the example with correlation between individual CL, V and Ka, a measure of body size could very well act as a covariate on both CL and V, just as geno- or phenotype of a drug transporter may act on both CL and Ka. By this mechanism, as long as there is no correlation between body size and genotype/phenotype of the transporter, individual etas may be correlated for CL and V, as well as for CL and Ka, without any correlation between individual V and Ka. Notice that this example holds even if two different measures of body size (WT, WT^0.75, LBW, BSA, et c) are appropriate for CL and V, respectively. It is also possible that the off-diagonal non-zero correlations are all positive. A positive correlation between CL and Ka may not be plausible from a perspective of physiology or evolution in this example but if it was (or if the example was Q, V and Ka), we could very well have all non-zero correlations between etas being positive. In this example, the off-diagonal etas would not have been necessary, had we only included a proper covariate model. However, my point is not that off-diagonal etas are a result of bad covariate modelling. The true covariate model is far more complex than this example, consisting of covariates which are unknown and cannot be measured. Jakob Ribbing _______________________________________________________