# Re: st: Negative LR test statistic ?

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Negative LR test statistic ? Date Tue, 22 Dec 2009 08:56:17 +0000 (GMT)

```--- On Tue, 22/12/09, Ekrem Kalkan wrote:
> Still, I think there should be a different
> reason rather than degrees of freedom.

You can illustrate that this is a sample size
related problem using the simulation below.
Here I am testing a true null hypothesis after
logistic regression with a likelihood ratio test
on a dataset with 25, 50, 75, 100 observations.

In the simulation that uses only 25 observations
102 out of 1000 samples produced a negative Chi^2
statistic, this reduced to only 6 in the
simulation with sample size 50, and 0 to the
simulations with 75 and 100 observations.

*---------------- begin example ---------------------
program drop _all
program define sim, rclass
drop _all
set obs `1'
gen x1 = rnormal()
gen x2 = rnormal()
gen x3 = rnormal()
gen y = runiform() < invlogit(-2 + x1)
logit y x1 x2 x3
est store a
logit y x1
est store b
lrtest a b
return scalar chi2 = r(chi2)
end

set seed 12345
simulate chi2 = r(chi2), reps(1000) nodots : sim 25
count if chi2 < 0

simulate chi2 = r(chi2), reps(1000) nodots : sim 50
count if chi2 < 0

simulate chi2 = r(chi2), reps(1000) nodots : sim 75
count if chi2 < 0

simulate chi2 = r(chi2), reps(1000) nodots : sim 100
count if chi2 < 0
*--------------------- end example -------------------
( For more on how to use examples I sent to statalist see:
http://www.maartenbuis.nl/stata/exampleFAQ.html )

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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```