estimating AR1 parameters of level one error

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-
project.org] On Behalf Of Steve Candy
Sent: Friday, May 22, 2015 02:55
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] estimating AR1 parameters of level one error

Thanks Wolfgang

Yes I agree its possible and I have fitted such a model using random
subject-splines. I found numerical instability but this may not be the
case with other applications. So my statement "not sensible" is not
justifiable. I should have said "can be problematic". The marginal
covariance is much more complex and harder to describe graphically  than
the random intercepts plus AR(1) error model which I have used
extensively and combined with the log-transform of the response to allow
for "splaying-out" of curves in time or adding extra variance parameters
to model that or other types of variance heterogeneity. I have found this
type of model more stable in practice.

Thanks for correcting me.

Regards

Steve

It is certainly possible to have a model with random intercepts and

slopes
(for time) and also AR(1) correlated residuals over time within
individuals.
The random slopes model differences in the trend between individuals,
while

the AR(1) structure models how the residuals are fluctuating around the

person-specific slopes within individuals. Of course, you need to have a
sufficient number of follow-up measurements within individuals to
distinguish >those two elements. But this is certainly possible. And in
fact, ignoring serial correlation in the residuals when it is present
could
lead to inflated Type I error rates for the mean trend effect.

Best,
Wolfgang