st: RE: Random slope model in xtmixed

["Bontempo, Daniel E" <deb193@ku.edu>]

I think this is due to not modeling the covariance of level and slope. The covariance changes depending on where the year (slope) is centered. The estimation appears to be coming up with different values of the other random effects in an attempt to compensate for the un-modeled covariance, which is different in each case. I believe that difference in random effects then drive the differences in fixed effects, as well as account for the overall LL differences.

You can quickly see if I am on the right track by specifying "cov(unstructured)" and running the models again.


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nicola Man
Sent: Tuesday, April 03, 2012 11:09 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Random slope model in xtmixed

Hi,

I have a question about fitting random slopes in mixed models that I can't make sense of.  The random slope variable is year which ranges from 2004 to 2009.  As an illustrative example, I fitted two models which are exactly the same except:

Model 1) year, y2009, is recalculated so that 2009 gets a value of 0 to 2004 which gets a value of -5 (i.e. y2009=2009-Year)

Model 2) year, y2007, is recalculated so that 2009 gets a value of 2 to 2004 which gets a value of -3 (i.e. y2007=2007-Year)

Below is the abbreviated output:
. xtmixed lgt_P_ART4_nm2 y2009 ib1.HIVprevG_UNGASS || CtryN: y2009 , var nolog

Mixed-effects ML regression                     Number of obs      =       683
Group variable: CtryN                           Number of groups   =       128

                                                Obs per group: min =         1
                                                               avg =       5.3
                                                               max =         6

                                                Wald chi2(1)       =    269.38
Log likelihood = -920.36467                     Prob > chi2        =    0.0000

--------------------------------------------------------------------------------
lgt_P_ART4_nm2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
         y2009 |   .4921368   .0299851    16.41   0.000     .4333672    .5509065
         _cons |   .4236186   .1367187     3.10   0.002     .1556548    .6915824
--------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
CtryN: Independent           |
                  var(y2009) |   .0856863   .0143532      .0617061    .1189858
                  var(_cons) |   2.165006   .3010598      1.648517    2.843314
-----------------------------+------------------------------------------------
               var(Residual) |   .3364985   .0234767      .2934923    .3858065
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(2) =   670.34   Prob > chi2 = 0.0000

. xtmixed lgt_P_ART4_nm2 y2007 || CtryN: y2007 , var nolog

Mixed-effects ML regression                     Number of obs      =       683
Group variable: CtryN                           Number of groups   =       128

                                                Obs per group: min =         1
                                                               avg =       5.3
                                                               max =         6


                                                Wald chi2(1)       =    247.17
Log likelihood = -914.25608                     Prob > chi2        =    0.0000

--------------------------------------------------------------------------------
lgt_P_ART4_nm2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
         y2007 |   .4993922   .0317645    15.72   0.000     .4371349    .5616495
         _cons |  -.5720239   .1271442    -4.50   0.000    -.8212219   -.3228259
--------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
CtryN: Independent           |
                  var(y2007) |    .099806   .0169902      .0714916    .1393344
                  var(_cons) |   1.960566   .2713017      1.494834    2.571403
-----------------------------+------------------------------------------------
               var(Residual) |   .3294286   .0225424       .288081    .3767106
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(2) =   682.56   Prob > chi2 = 0.0000

I get completely different estimates including that for the LL for the model as a whole. Does anyone have an idea as to why that might be the case?

Regards,
Nicola
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