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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Wald test in Random Coefficient Model |

Date |
Fri, 25 Feb 2011 09:05:54 +0000 (GMT) |

--- On Thu, 24/2/11, Joerg Luedicke wrote: > you could do to check if the variation of the effect across > country is sort of considerable is to do a likelihood ratio > test in which you compare the model fit with and without the > random coefficient (-help lrtest-). The bahavior of this test is not quite what we would expect. The problem is that the null hypothesis is on the boundary of the parameter space, i.e. the null hypothesis is that the country level variance equals 0, and a variance can only be >= 0. There is a discussion of that in (Gutierrez et al. 2001). In the simulation below you can see that the distribution of the p-values for the likelihood ratio test of a true null- hypothesis for this variance really deviate from the uniform distribution. Remember, that a test should reject a true null- hypothesis 5% of the samples when we choose a significance level of 5%, 10% of the samples when we choose a significance level of 10%, etc. This means that a good performing test should yield p-values that follow a uniform distribution. *-------------------- begin example -------------------- program drop _all program define sim, rclass drop _all set obs 50 gen country = _n expand 10 gen x = rnormal() gen y = runiform() < invlogit(0 + x) xtset country logit y x est store a xtlogit y x est store b lrtest a b, force return scalar p = r(p) end simulate p=r(p), reps(1000) : sim quantile p, aspect(1) *------------------ end example ------------------ (For more on examples I sent to the Statalist see: http://www.maartenbuis.nl/example_faq ) Hope this helps, Maarten Gutierrez, R., S. Carter, and D. M. Drukker. 2001. On boundary-value likelihood-ratio tests. Stata Technical Bulletin, 60: 15–18. <http://stata-press.com/journals/stbcontents/stb60.pdf> -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Wald test in Random Coefficient Model***From:*Joerg Luedicke <joerg.luedicke@gmail.com>

**References**:**Re: st: Wald test in Random Coefficient Model***From:*Joerg Luedicke <joerg.luedicke@gmail.com>

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