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# st: Exercise 7.10 in Multilevel and Longitudinal Modeling Using Stata (first edition)

 From Gillian.Frost@hsl.gov.uk To statalist@hsphsun2.harvard.edu Subject st: Exercise 7.10 in Multilevel and Longitudinal Modeling Using Stata (first edition) Date Tue, 9 Mar 2010 09:45:02 +0000

```Hello all,

Looking further into my original query to Statalist (below), I have come
across an exercise in the Stata book "Multilevel and Longitudinal Modeling
Using Stata" by Rabe-Hesketh & Skrondal, which I think can help.  However,
I am struggling with the exercise (exercise 7.10 Peak-expiratory-flow data
I) and have been unable to find the solutions to see where I am going
wrong.

Part 2 of the exercise asks you to verify that the two level model (with
the variances of the two random coefficients constrained equal and if the
covariance is positive) is equivalent to the three level model, but I have
been unable to do this.  Please see the code and output below from the
models I have used.  As you can see, the models do not appear to be
equivalent.  However, I do not understand where I have made an error.

I would hugely appreciate any help with this, as this is proving to be a
huge stumbling block for me.

Many thanks,

Gillian

*****************       Start Stata code
**      Section 7.2 multilevel modelling book
use http://www.stata-press.com/data/mlmus/pefr, clear
reshape long wp wm, i(id) j(occassion)

gen i = _n
reshape long w, i(i) j(meth) string
sort id meth occassion
list id meth occassion w in 1/8, clean noobs

encode meth, gen(method)
recode method 2=0

* section 7.4.4 - three level model
xtmixed w || id: || method:, mle

* exercise 7.10
* two level model
tab method, gen(m)
xtmixed w || id: m1 m2, mle cov(exch)

******************      Output

**      Three level model
Performing EM optimization:

Iteration 0:   log likelihood = -345.29139
Iteration 1:   log likelihood = -345.29005
Iteration 2:   log likelihood = -345.29005

Computing standard errors:

Mixed-effects ML regression                     Number of obs      =  68

-----------------------------------------------------------
|   No. of       Observations per Group
Group Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
id |       17          4        4.0          4
method |       34          2        2.0          2
-----------------------------------------------------------

Wald chi2(0)       =   .
Log likelihood = -345.29005                     Prob > chi2        =   .

------------------------------------------------------------------------------
w |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
_cons |   450.8971   26.63839    16.93   0.000     398.6868
503.1074
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf.
Interval]
-----------------------------+------------------------------------------------
id: Identity                 |
sd(_cons) |   108.6037   19.05411      77.00246
153.1739
-----------------------------+------------------------------------------------
method: Identity             |
sd(_cons) |   19.47623   4.829488      11.97937
31.66474
-----------------------------+------------------------------------------------
sd(Residual) |   17.75859   2.153545      14.00184
22.52329
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(2) =   143.81   Prob > chi2 =
0.0000

Note: LR test is conservative and provided only for reference.

** Two level model
note: m2 dropped because of collinearity

Performing EM optimization:

Iteration 0:   log likelihood = -355.14961
Iteration 1:   log likelihood = -355.14961

Computing standard errors:

Mixed-effects ML regression                     Number of obs      =  68
Group variable: id                              Number of groups   =  17

Obs per group: min =   4
avg = 4.0
max =   4

Wald chi2(0)       =   .
Log likelihood = -355.14961                     Prob > chi2        =   .

------------------------------------------------------------------------------
w |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------------
_cons |   454.0498   19.42288    23.38   0.000     415.9817 492.118
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf.
Interval]
-----------------------------+------------------------------------------------
id: Exchangeable             |
sd(m1 _cons) |   79.12354   9.858542      61.97959
101.0096
corr(m1,_cons) |   .0489807   .2547191     -.4230663 .500116
-----------------------------+------------------------------------------------
sd(Residual) |   17.67097   2.122189      13.96483
22.36069
------------------------------------------------------------------------------
LR test vs. linear regression:       chi2(2) =   124.10   Prob > chi2 =
0.0000

Note: LR test is conservative and provided only for reference.

----- Forwarded by Gillian Frost/STAFF/HSL on 09/03/2010 09:25 -----

Gillian.Frost@hsl.gov.uk
Sent by: owner-statalist@hsphsun2.harvard.edu
08/03/2010 12:00
statalist@hsphsun2.harvard.edu

To
statalist@hsphsun2.harvard.edu
cc

Subject
st: -xtmixed- and differences in test-retest reliability

Hello all,

I was wondering if anyone would be able to help me with a problem I have.
I know that there must be some way to do this, but I cannot for the life
of me figure out how to do it.

A brief explanation of data:
Altogether there are about 40 subjects.  Each subject underwent a test to
assess their hearing on three different days, three times each day.  The
goal is to assess the reliability of the test (its reproducibility), as
well as any between day or within day variation in test results.

I know that I can use xtmixed to estimate a variance-components model, the

results of which can be used to estimate the test-retest reliability, the
between days (within subject) intraclass correlation coefficient (ICC),
and the within day ICC.  I would use the following model:
xtmixed result || subject: || day:

Now here is where I am getting confused.  What if I also wanted to know if

the test-retest reliability differed depending on some other factor?  For
example, what if (for some reason) the test was more reliable for males
than females?  Or more reliable for older age groups than younger ones?
How would I test for this?  I suppose I could use separate models for
males and females, but how could I then test whether the ICCs were
statistically significantly different?

Any help with this matter would be greatly appreciated.  Please just ask
if anything needs clarifying.

Many thanks,

Gillian

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