[R] generalized least squares with empirical error covariance matrix

Andrew Schuh aschuh at atmos.colostate.edu
Wed May 9 22:09:34 CEST 2007

I have a bayesian hierarchical normal regression model, in which the 
regression coefficients are nested, which I've wrapped into one 
regression framework, y = X %*% beta + e .  I would like to run data 
through the model in a filter style (kalman filterish), updating 
regression coefficients at each step new data can be gathered.  After 
the first filter step, I will need to be able to feed the a non-diagonal 
posterior covariance in for the prior of the next step.  "gls" and "glm" 
seem to be set up to handle structured error covariances, where mine is 
more empirical, driven completely by the data.  Explicitly solving w/ 
"solve" is really sensitive to small values in the covariance matrix and 
I've only been able to get reliable results at the first step by using 
weighted regression w/ lm().  Am I missing an obvious function for 
linear regression w/ a correlated  prior on the errors for the updating 
steps?  Thanks in advance for any advice.

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