fix level 1 variance

[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

[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
------------------------------------------------------------------------------

[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)
--------------------------------------------------------------------------------

[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