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# Re: st: Significance Tests for Individual Random Effect Parameters/Variance Components in Hierarchical Linear Modeling

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Significance Tests for Individual Random Effect Parameters/Variance Components in Hierarchical Linear Modeling Date Fri, 8 Feb 2013 10:06:58 +0100

```On Thu, Feb 7, 2013 at 10:18 PM, Anthony Fulginiti wrote:
> I was working on a manuscript a few months ago using hierarchical linear modeling to examine group differences in self-esteem over time.  During the manuscript preparation, I was reviewing many articles and books using hierarchical linear modeling and noticed that results for individual random effect parameters/variance components were usually accompanied by a chi-square/z statistic and a specific probability value.  However, in the STATA output, the random effect parameters are listed with an estimate, standard error and 95% confidence interval but no such chi-square/z statistic or specific probability value.
>
> Is there a way for STATA to produce such a statistic/probability value (via conducting significance tests) for the individual random effect parameters?  If so, how?

The problem with these chi-square/z-statistic is that they are test
statistics of a null hypothesis that is "on the boundary of the
parameter space". The null hypothesis is that the variance equals 0,
and a variance can only be larger than or equal to 0. Weird things
happen at such boundaries, and as a concequence the sampling
distribution of the chi-square under the null-hypothesis will not
correspond with a chi-square(1) distribution and the sampling
distribution of the z statistic under the null hypothesis will not
correspond to a normal(0,1) distribution. That is a good reason for
not reporting such statistics. See for example:

Gutierrez, R., S. Carter, and D. M. Drukker. 2001. On boundary-value
likelihood-ratio tests. Stata Technical Bulletin 60: 15–18.
<http://www.stata.com/products/stb/journals/stb60.pdf>

Hope this helps,
Maarten

By the way, in the Statalist FAQ you could (and should) have read that
Stata is spelled Stata and not STATA.

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
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