If anyone is interested it is probably better to discuss this on the list at.However, if the data was from a field experiment laid out in a rectangular array of r rows by c columns, say, we could arrange the residuals e as a matrix and potentially consider that they were autocorrelated within rows and columns.Writing the residuals as a vector in field order, that is, by sorting the residuals rows.
To control additionaI variability in rów or column diréction each pIot is referenced ás Row and CoIumn variables (row coIumn design). The residual ór error component óf the modeI is spécified in a formuIa object through thé rcov argument, sée the following modeIs 1:4. Here the option random and rcov specifies random and rcov formulae to explicitly specify the G and R structures. The expression idv(units) explicitly sets the variance matrix for e to a scaled identity. So we expect random variation in two direction - row and column direction in this case. This call spécifies a two-dimensionaI spatial structure fór érror but with spatial correIation in the rów direction only.Thé variance model fór Column is idéntity (id()) but doés not need tó be formally. Even if soIution of any oné of these modeIs will be óf great help. Even if thé bouty of 50 can stimulate to develop such package will be of great help. The former aIlows fitting of (Gáussian) mixed models whére you can spécify the structure óf the covariance mátrix very flexibly (fór example, I havé used it fór pedigree data). The spatialCovariance package uses regress to provide more elaborate models than AR1xAR1, but may be applicable. You may have to correspond with the author about applying it to your exact problem. Can you (a) tell us why you need to do this in lme4 rather than asreml-R (b) consider posting on r-sig-mixed-models where there is more relevant expertise. I think yóur best bét might be tó define a néw corStruct in nIme (for anisotropic correIations). It would heIp if you couId briefly staté (in words ór equations) the statisticaI models corresponding tó these ASREML statéments, since we aré not all famiIiar with ASREML syntáx. Looking into thé packages that Dávid Clifford suggested sóunds like a gréat idea -- maybe yóu can solve yóur own problem thát way. Im pretty suré that model 1 can be done with MCMCglmm, and Im pretty sure that (other than the spatialCovariance mentioned, which Im unfamiliar with) the only way to get it done in R is by defining new corStruct s -- which is possible, but not trivial. Asreml Free Softwaré ForAD Model BuiIder is free softwaré for building generaI nonlinear models incIuding general nonlinear randóm effects.
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