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Subject:

Structured Precision Matrix

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Date:

Tue, 27 Apr 2010 16:15:05 +0200

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 ```Dear BUGS users, I need to fit a bivariate longitudinal model where the covariance structure allows for spatial autocorrelation within and between the 2 responses. I use a spatial structure because the model is bivariate: the first coordinate refers to time distances between measurements within the same response while the second coordinate refers to a "distance" between 2 measurements from different responses. I plan to use either an spatial exponential structure or a rational quadratic. However the autocorrelation parameter (range) should be different between the 2 responses, as should be the variances. So I have to create my own covariance matrix and cannot use spatial.exp or other structures. The Pig weight example illustrate a way to define a structured (AR1) precision matrix (see http://www.mrc-bsu.cam.ac.uk/bugs/winbugs/examples/pigweights.txt). The example propose an intuitive way to define the covariance matrix and then inverse it to get the precision matrix. As mentionned this solution is really slow. The example also propose a way to directly structure the precision matrix to avoid WinBUGS having to inverse the covariance, which works much more rapidly. I'm trying to implement this solution in my application by using Mathematica to analytically inverse the covariance matrix and define the precision matrix as a function of variances and autocorrelation parameters. However I can't find a tractable expression for the precision matrix as my error covariance matrix is 13x13. Is there any other way to define a structured covariance/precision matrix in WinBUGS? I can fit the model using NLME library in R so I guess that WinBUGS should be able to do it as well. Basically the covariance matrix is fairly simple. The problem is to inverse it just because WinBUGS works with precision rather than covariance matrices. Basically why is this so??? Thanks for any input. Aziz Chaouch ------------------------------------------------------------------- This list is for discussion of modelling issues and the BUGS software. For help with crashes and error messages, first mail [log in to unmask] To mail the BUGS list, mail to [log in to unmask] Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html Please do not mail attachments to the list. To leave the BUGS list, send LEAVE BUGS to [log in to unmask] If this fails, mail [log in to unmask], NOT the whole list ```