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st: Assess interfacility variation with xtlogit sigma_u


From   Laurel.Copeland@med.va.gov
To   statalist@hsphsun2.harvard.edu
Subject   st: Assess interfacility variation with xtlogit sigma_u
Date   Wed, 27 Aug 2003 15:01:29 -0400

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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