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Re: st: xtmixed model
From
Gordon Hughes <G.A.Hughes@ed.ac.uk>
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:
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
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