[R] Mixed-effects model with lagged endogenous variables and autocorrelated residuals
Revilla,AJ (pgt)
A.J.Revilla at lse.ac.uk
Mon May 16 20:00:32 CEST 2005
Dear all,
I am dealing with a nonlinear model of the form yt = A*exp(-B*T)*Yt-1, where T represents time and Yt-1 accounts for the accumulated values of y from T=0 to t-1.
The problem of the models is that the error terms are autocorrelated, so I have to deal with a model combining autocorrelated residuals and lagged endogenous variables.
One common approach to this specific model is the two-step Hatanaka estimator. If I am right, it works as follows: first, the equation is fitted in order to get an estimate of the autocorrelation term, which is then included in the second step (the transformation is shown in Hatanaka, 1974), the new equation being estimated by OLS. An additional problem is that the OLS estimate of the autocorrelation term is not consistent in the presence of lagged endogenous variables, so the use of instrumental variables is needed for the first step.
So far, so good (more or less). The question is that I am interested in fitting a mixed-effects model (I would like to obtain subject-specific coefficients, and my panel of data is too short to fit separate regressions), so that the coefficients will be estimated either by ML or REML.
Do you have any clue of how to approach this? Is the rho estimate obtained from the nlme package consistent? Could I substitute it directly in the second step? Are there better options? Any suggestions will be MUCH appreciated.
Thank you very much,
Antonio
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