A researcher here would like to assess interfacility variation in the
receipt of benzodiazepines by depressed patients. Another colleague
suggested using xtlogit, remarking that
"sigma_u gives you the facility level standard deviation in the log
odds of benzo use
w. a standard error and 95% confidence interval on the facility
level standard deviation."
I obtained the data from the first researcher and ran the analysis
suggested.
How do we interpret the results? The sigma_u obtained is 0.34 (SE=.014), as
shown below.
Is this a lot? a little? What does the standard deviation in the log odds of
something represent, how big might it be (range), what else needs to be
considered with it in order for its value to have meaning, etc.?
There are 128,029 patients at 134 facilities.
Thank you very much,
Laurel
. use c:\adherence\forlaurel
. desc
Contains data from c:\adherence\forlaurel.dta
obs: 128,029
vars: 3
size: 2,048,464 (99.0% of memory free)
----------------------------------------------------------------------------
--
storage display value
variable name type format label variable label
----------------------------------------------------------------------------
--
facility float %9.0g first 3 digits of
stn_num
anybenzo float %9.0g 1 = Used
Benzodiazepine
ID float %9.0g Patient ID
----------------------------------------------------------------------------
--
Sorted by:
. xtlogit anybenzo, i(facility)
Fitting comparison model:
Iteration 0: log likelihood = -79880.821
Fitting full model:
tau = 0.0 log likelihood = -64723.911
tau = 0.1 log likelihood = -63736.488
tau = 0.2 log likelihood = -63760.93
Iteration 0: log likelihood = -63736.488
Iteration 1: log likelihood = -63736.218
Iteration 2: log likelihood = -63736.197
Iteration 3: log likelihood = -63736.195
Random-effects logistic regression Number of obs =
121643
Group variable (i): facility Number of groups =
134
Random effects u_i ~ Gaussian Obs per group: min =
9
avg =
907.8
max =
3206
Wald chi2(0) =
0.00
Log likelihood = -63736.195 Prob > chi2 =
.
----------------------------------------------------------------------------
--
anybenzo | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
_cons | -.5480285 .0246479 -22.23 0.000 -.5963374
-.4997196
-------------+--------------------------------------------------------------
--
/lnsig2u | -2.151144 .0837696 -2.31533
-1.986959
-------------+--------------------------------------------------------------
--
sigma_u | .3411026 .014287 .3142191
.3702861
rho | .0341584 .0027637 .029137
.0400095
----------------------------------------------------------------------------
--
Likelihood-ratio test of rho=0: chibar2(01) = 3.2e+04 Prob >=
chibar2 = 0.000
Note: 34 completely determined panels
Laurel A Copeland, PhD
VA Ann Arbor Health System
(734) 769-7100 x6206
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