likelihood-ratio test of rho=0 chibar2(01)

[zaineb belkhiria]

hello everyone
I hope you could help me. i am using the random effects logit model. To choose between the simple logit model and the random effects logit model i used the test displayed at the bottom of the estimation table "likelihood-ratio test of rho=0 chibar2(01)= "
I didn't find any reference about this test, i.e. its name. Is the name of this test Breusch-Pagan Lagrange multiplier (LM) ? or is it a different test from Breusch-Pagan Lagrange multiplier (LM) ?
Thank you for taking the time to help me.

[Maarten Buis]

It is a version of a likelihood ratio test. It is a bit more complicated because the null hypothesis is on the edge of the parameter space (a variance cannot be less than 0, so a null hypothesis that a variance equals 0 is at the edge of the possible values that a variance could take), that is why Stata calls the statistic chibar2 instead of chi2. The sampling distribution of that statistic under the null hypothesis does not follow a chi-squared distribution, as is usual with likelihood ratio tests, but a mixture of I believe a chi squared and a single spike at 0. Anyhow you can see more here: https://www.statalist.org/forums/for...rm-for-chibar2

[zaineb belkhiria]

Thank you very much Sir.