Statistical significance of random-effects (lme4 or others)
Yes, you're spot on -- I oversimplified a bit. :) The deeper issue is indeed the edge of the parameter space. And the p/2 trick also breaks down for non trivial cases. As do many other asymptotic results in mixed models -- the big one is the denominator degrees of freedom. There is a big question not just in defining what the DoF are, but also whether it's reasonable to use the F distribution based on asymptotics. Phillip
On 7/9/20 2:29 pm, Emmanuel Curis wrote:
Hi, There is a point I don't understand in your answer: On Mon, Sep 07, 2020 at 07:52:21AM +0000, Alday, Phillip wrote: [...]
* The p/2 for LRT on the random effects comes from the standard LRT being a two-sided test, but because variances are bounded at zero, you actually need a one-sided test.
I thought the LRT test was always one-sided, because under the null-hypothesis that additional parameters are all uneeded, the two models have the same likelihood, hence the ratio should be 1, its log 0; the chi-square can only be positive by nature (which is consistent with the likelihood always higher for a model with more parameter), hence the test is by nature one-sided - that is, p = p(LRT > lrt_obs) and not p = p(LRT > |lrt-obs|) + p(LRT < -|lrt_obs|). Wasn't the p/2 because the asymptotic distribution of the LRT in this special case is *not* a 1-df khi-square, because the special case of sigma?=0 is at the boundary of the parameter space and not ??inside??. Instead, it is a 50-50 mixture of a 1-df khi-square and a almost surely constant 0. An asymptotic result that does not hold for more complex cases. Am I wrong? Or may be it is just a point of what is called a 1 or 2-sided test? Best regards,