Hi there, I have been using the nlme::gls package created in R to fit a pretty simple model (linear with AR error) y(t) = beta*x(t) + e(t)? ??? ??? ??? where e(t) ~ rho*e(t-1) + Z(t) ?? ??? and Z(t)~ N(0,sig^2) I call the R routine glsObj <- nlme::gls(y ~ x -1, data=data, correlation = nlme::corAR1(form= ~x), method="ML") All seems fine. In addition, I have also coded the likelihood myself and maximized it for beta, rho and sigma. I get the exact same estimates of beta and rho, (as nlme::gls) but the estimate of sigma is not the same and i can not figure out why. The maximum likelihood estimator for sigma under this model is sig^2 = (( 1-rho^2)u(1)^2 + sum((u(t)- rho*u(t-1))^2)/n where the sum is t=2,...,n and u(t) = y(t) - X(t)*beta I have read the mixed-effects models in S and S-Plus book (nlme::gls code is based directly on this) and this problem is specified on page 204 eq (5.5). I have also calculated sigma based on (5.7) -after the transformation documented (5.2) -and i do not get the same value as either the package or my implementation. Any advice would be most welcomed. Is there a bug in the estimation of sigma in this package? Thanks Andy -- Andy Beet Ecosystem Dynamics & Assessment Branch Northeast Fisheries Science Center NOAA Fisheries Service 166 Water Street Woods Hole, MA 02543 tel: 508-495-2073 [[alternative HTML version deleted]]