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fix level 1 variance
Posted: Wed Jul 03, 2013 10:34 am
by emily123
Hi,
I wish to fit a random coefficient model with unstructured covariance, where I can fix the level 1 random effects parameter, sigma e, to a specific value using prior knowledge obtained from a different dataset.
I can fit the same model using xtmixed and runmlwin for both IGLS and MCMC. I don't believe I can fix any parameters in Stata, but was wondering if it is possible using runmlwin?
Any advice would be much appreciated, thanks!
best wishes, Emily
Re: fix level 1 variance
Posted: Wed Jul 03, 2013 10:37 am
by GeorgeLeckie
Hi Emily,
It is very easy to specify constraints with runmlwin. Below is an example where we constrain the level-1 residual error variance to be 0.5
Best wishes
George
Code: Select all
use http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial, clear
runmlwin normexam cons standlrt, level2(school: cons) level1(student: cons) nopause
constraint define 1 [RP1]var(cons) = 0.5
runmlwin normexam cons standlrt, level2(school: cons) level1(student: cons) nopause constraints(1)
Code: Select all
. use http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial, clear
. runmlwin normexam cons standlrt, level2(school: cons) level1(student: cons) nopause
MLwiN 2.27 multilevel model Number of obs = 4059
Normal response model
Estimation algorithm: IGLS
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 65 2 62.4 198
-----------------------------------------------------------
Run time (seconds) = 1.71
Number of iterations = 4
Log likelihood = -4678.6211
Deviance = 9357.2422
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | .0023908 .0400224 0.06 0.952 -.0760516 .0808332
standlrt | .5633712 .0124654 45.19 0.000 .5389394 .5878029
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: school |
var(cons) | .0921275 .0181475 .0565591 .127696
-----------------------------+------------------------------------------------
Level 1: student |
var(cons) | .565731 .0126585 .5409208 .5905412
------------------------------------------------------------------------------
. constraint define 1 [RP1]var(cons) = 0.5
. runmlwin normexam cons standlrt, level2(school: cons) level1(student: cons) nopause constraints(1)
( 1) [RP1]var(cons) = .5
MLwiN 2.27 multilevel model Number of obs = 4059
Normal response model
Estimation algorithm: IGLS
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 65 2 62.4 198
-----------------------------------------------------------
Run time (seconds) = 1.51
Number of iterations = 4
Log likelihood = -4694.4922
Deviance = 9388.9844
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | .0018578 .0401241 0.05 0.963 -.0767839 .0804995
standlrt | .562891 .0117265 48.00 0.000 .5399075 .5858745
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: school |
var(cons) | .0939082 .0182508 .0581373 .1296792
-----------------------------+------------------------------------------------
Level 1: student |
var(cons) | .5 0 .5 .5
------------------------------------------------------------------------------
Re: fix level 1 variance
Posted: Wed Jul 03, 2013 10:46 am
by GeorgeLeckie
Hi Emily,
You also said " I don't believe I can fix any parameters in Stata". You can in Stata 13 using the -me- suite of commands.
Code: Select all
use http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial, clear
constraint define 1 _b[var(e.normexam):_cons] = 0.5
meglm normexam standlrt || school:, constraints(1)
and you will get the following output
Code: Select all
. use http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial, clear
. constraint define 1 _b[var(e.normexam):_cons] = 0.5
. meglm normexam standlrt || school:, constraints(1)
Fitting fixed-effects model:
Iteration 0: log likelihood = -4880.2547
Iteration 1: log likelihood = -4880.2547
Refining starting values:
Grid node 0: log likelihood = -4698.6738
Fitting full model:
Iteration 0: log likelihood = -4698.6738
Iteration 1: log likelihood = -4694.5823
Iteration 2: log likelihood = -4694.4925
Iteration 3: log likelihood = -4694.4924
Mixed-effects GLM Number of obs = 4059
Family: Gaussian
Link: identity
Group variable: school Number of groups = 65
Obs per group: min = 2
avg = 62.4
max = 198
Integration method: mvaghermite Integration points = 7
Wald chi2(1) = 2297.55
Log likelihood = -4694.4924 Prob > chi2 = 0.0000
( 1) [var(e.normexam)]_cons = .5
--------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
standlrt | .562891 .0117434 47.93 0.000 .5398744 .5859075
_cons | .0018577 .040131 0.05 0.963 -.0767976 .080513
---------------+----------------------------------------------------------------
school |
var(_cons)| .093909 .0186238 .0636647 .138521
---------------+----------------------------------------------------------------
var(e.normexam)| .5 (constrained)
--------------------------------------------------------------------------------
Re: fix level 1 variance
Posted: Wed Jul 03, 2013 10:58 am
by emily123
Thanks so much for your quick reply - very helpful, and very simple! Sorry I missed this in all the documentation/do files.
best wishes, Emily