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# Re: st: xtmixed model

 From Gordon Hughes To statalist@hsphsun2.harvard.edu Subject Re: st: xtmixed model Date Sun, 27 Feb 2011 11:18:23 +0000

The simple answer is yes. At you have realised, you have constrained the initial value of your data to a fixed value, so there is no basis for having a random coefficient on the constant term. In any case the results of the first model are telling you that.

But actually you should go further. Why estimate a constant at all? -xtmixed- has a noconstant option, so why not express your variable as % (or proportion) of initial weight lost since week 0 which will necessarily have a value of 0 for week zero and for which the constraint implied by the noconstant option makes sense.

Gordon Hughes
g.a.hughes@ed.ac.uk

------------------------------

Date: Sat, 26 Feb 2011 19:30:30 +0000
From: "Grove-White, Dai" <D.H.Grove-White@liverpool.ac.uk>
Subject: st: xtmixed model

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:
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:
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
Livestock Health & Welfare
School of Veterinary Science
Leahurst Campus
University of Liverpool
Neston
Wirral CH64 7TE

Telephone 077 87 567 431
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