[R-sig-ME] [R] coef se in lme
dave fournier
otter at otter-rsch.com
Fri Oct 19 07:32:30 CEST 2007
The AD Model Builder method I posted earlier takes into account the
uncertainty in the mean and both std deviations in Harold's simple model.
Y_ij - mu + u_i +eps_ij
To illustrate this
I built a little model and simulated a data set with 1<=i<=10, 1<=j<=5
observations. Below are the parameter estiamtes tigether with their
estimated std devs. The true values were mu=3.0 sigma_u=2.0 and sigma=3.0
> 1 mu 2.4091e+00 7.4307e-01
> 2 log_sigma_u 6.3908e-01 3.4913e-01
> 3 log_sigma 1.1354e+00 1.1180e-01
> 4 u -3.1695e-01 6.4561e-01
> 5 u 2.0441e-01 6.4496e-01
> 6 u 5.1996e-01 6.4748e-01
> 7 u 4.3754e-01 6.4661e-01
> 8 u 4.8381e-01 6.4708e-01
> 9 u 1.2214e+00 6.6075e-01
> 10 u -1.7631e+00 6.7793e-01
> 11 u 3.3987e-01 6.4578e-01
> 12 u -1.7663e-01 6.4485e-01
> 13 u -9.5030e-01 6.5439e-01
then I fixed log_sigma_u and log_sigma at their
estimated values and obtained.
> # fixed sd's
> index name value std dev
> 1 mu 2.4093e+00 7.4307e-01
> 2 u -3.1736e-01 6.4407e-01
> 3 u 2.0456e-01 6.4407e-01
> 4 u 5.2045e-01 6.4407e-01
> 5 u 4.3794e-01 6.4407e-01
> 6 u 4.8426e-01 6.4407e-01
> 7 u 1.2226e+00 6.4407e-01
> 8 u -1.7650e+00 6.4407e-01
> 9 u 3.4016e-01 6.4407e-01
> 10 u -1.7689e-01 6.4407e-01
> 11 u -9.5138e-01 6.4407e-01
and finally I almost fixed mu
(can't fix it completley because then there would be
no "fixed" effects and the model thinks there is
nothing to do.) and obtained
> # all fixed
> index name value std dev
> 1 mu 2.4093e+00 2.2361e-03
> 2 u -3.1736e-01 5.9145e-01
> 3 u 2.0456e-01 5.9145e-01
> 4 u 5.2045e-01 5.9145e-01
> 5 u 4.3794e-01 5.9145e-01
> 6 u 4.8426e-01 5.9145e-01
> 7 u 1.2226e+00 5.9145e-01
> 8 u -1.7650e+00 5.9145e-01
> 9 u 3.4016e-01 5.9145e-01
> 10 u -1.7689e-01 5.9145e-01
> 11 u -9.5138e-01 5.9145e-01
So for example u(1) the first random effect has estimated std devs
6.4561e-01, 6.4407e-01, and 5.9145e-01
under the three models. It appears that most of the "extra" uncertainty
in u(1) comes from the uncertainty in mu.
--
David A. Fournier
P.O. Box 2040,
Sidney, B.C. V8l 3S3
Canada
Phone/FAX 250-655-3364
http://otter-rsch.com
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