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| From | Maarten Buis <maartenlbuis@gmail.com> |
| 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 --------------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/