st: xtmixed model

["Grove-White, Dai" <D.H.Grove-White@liverpool.ac.uk>]

Dear list
I am relatively new to multi level modelling so please excuse the query if silly!  I am running a mixed effects linear model on a weight loss study.  Due to the large range of horses and small number (n=12 horses and weight range is 200 - 600kg) I am modelling the weight loss as a proportion of the weight at the start of the study transformed as arcsin(square_root wt_proportion)
the model is 
. xtmixed  transprop_wt week c.week#c.week ||id: week, var
Performing EM optimization: 
Performing gradient-based optimization: 
Iteration 0:   log restricted-likelihood =  366.38495  
Iteration 1:   log restricted-likelihood =  366.38495  
Computing standard errors:
Mixed-effects REML regression                   Number of obs      =       192
Group variable: id                              Number of groups   =        12
                                                Obs per group: min =        16
                                                               avg =      16.0
                                                               max =        16

                                                Wald chi2(2)       =    273.25
Log restricted-likelihood =  366.38495          Prob > chi2        =    0.0000
------------------------------------------------------------------------------
transprop_wt |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        week |  -.0307454   .0020573   -14.94   0.000    -.0347776   -.0267131
             |
      c.week#|
      c.week |    .001064   .0001071     9.94   0.000     .0008541    .0012739
             |
       _cons |    1.58295   .0137351   115.25   0.000     1.556029     1.60987
------------------------------------------------------------------------------
------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent              |
                   var(week) |   8.70e-06   4.62e-06      3.07e-06    .0000246
                  var(_cons) |   .0016897   .0007985      .0006692    .0042662
-----------------------------+------------------------------------------------
               var(Residual) |   .0007861   .0000862      .0006341    .0009746
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(2) =   184.98   Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. 
where week is week of study - I have put in week squared since it improves model fit as judged by LR test.  When I plot out fitted values the starting value ie for week 1 is different for different horses.  This does not seem logical since the proportional weight of all horses at the start should be the same (= 1.0) by definition as should the transformed prop_weight.  In fact it seems that maybe I should not have a random intercept at all ie just have a random slope model.  Is that correct and if so what would the code be for a model with random slope only. Would it be

 xtmixed  transprop_wt week c.week#c.week ||week:, var
Performing EM optimization: 
Performing gradient-based optimization: 
Iteration 0:   log restricted-likelihood =  273.52452  
Iteration 1:   log restricted-likelihood =  273.89258  
Iteration 2:   log restricted-likelihood =  273.89262  
Iteration 3:   log restricted-likelihood =  273.89262  
Computing standard errors:
Mixed-effects REML regression                   Number of obs      =       192
Group variable: week                            Number of groups   =        16
                                                Obs per group: min =        12
                                                               avg =      12.0
                                                               max =        12

                                                Wald chi2(2)       =    258.25
Log restricted-likelihood =  273.89262          Prob > chi2        =    0.0000
------------------------------------------------------------------------------
transprop_wt |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        week |  -.0307454   .0035542    -8.65   0.000    -.0377115   -.0237792
             |
      c.week#|
      c.week |    .001064   .0002032     5.24   0.000     .0006656    .0014624
             |
       _cons |    1.58295   .0131277   120.58   0.000      1.55722    1.608679
------------------------------------------------------------------------------
------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
week: Identity               |
                  var(_cons) |   8.86e-26   8.60e-25      4.84e-34    1.62e-17
-----------------------------+------------------------------------------------
               var(Residual) |   .0028315   .0002913      .0023145    .0034641
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) =  3.4e-13 Prob >= chibar2 = 1.0000


Many thanks

Dai 

Dai Grove-White BVSc MSc DBR PhD DipECBHM FRCVS
Head of Division
Livestock Health & Welfare
School of Veterinary Science
Leahurst Campus
University of Liverpool
Chester High Road
Neston
Wirral CH64 7TE

Telephone 077 87 567 431
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/