[R-meta] One-Sided Note

[Viechtbauer Wolfgang (SP)]

Hi Dan,

You do not seem to be signed up for the list (at least not under that address). Usually, posts my non-members are held as pending until one of the admins take action, but sometimes they might get rejected outright. Anyway, if you want to post, please sign up. I am cc-ing the list, since this is where you wanted this to go in the first place.

Admittedly, this is a bit of a headscratcher, but let me see if I can get this right. For a fixed effect, we want to test:

H0: beta = 0 vs H1: beta != 0

So, we compare the likelihood under H0 versus the maximized likelihood under the alternative. The MLE of beta may be negative or positive and will lead to an improvement in the likelihood (unless the MLE happens to be exactly 0). The LRT chi-square value reflects the amount of improvement in the likelihood and is in that sense one-sided (0 = no improvement at all, corresponding to an MLE of 0 versus > 0 = some improvement, corresponding to an MLE != 0). If the improvement is large enough, that is, the LRT chi-square value is larger than 3.84, we reject H0 (so, for determining the p-value of the LRT, we only look in the upper tail of the chi-square distribution). But in terms of beta, we are conducting a two-sided test. The same applies to the Wald-type chi-square test that you got with anova(res2,btt=2).

For a variance component, we want to test:

H0: sigma^2 = 0 vs H1: sigma^2 > 0.

Again, we compare the likelihood under H0 versus the maximized likelihood under the alternative. Again, the p-value of the LRT is determined based on the upper tail of the chi-square distribution. But here, the MLE of sigma^2 can only be >= 0. So, in terms of sigma^2, we are conducting a one-sided test. That is why I wrote that p-values for LRTs of variance components provided by anova() are not two-sided.

Best,
Wolfgang

-- 
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and    
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD    
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com    

-----Original Message-----
From: ieshan at gmail.com [mailto:ieshan at gmail.com] On Behalf Of Dan Brooks
Sent: Thursday, August 17, 2017 21:57
To: Viechtbauer Wolfgang (SP)
Subject: One-Sided Note

Hi Wolfgang:

For some reason the mailing list is rejecting this message.

In a note to the R Meta mailing list just now, you said:
Also, p-values for LRTs of variance components provided by anova() are not two-sided.

In a recent meta-analysis, I used:

> anova(res,res2)

after fitting the model with and without a moderator (mods =~factor(variable_with_two_levels)) with method="ML". These results are generally quite similar to the results from testing the individual factor in model res2 with anova(res2,btt=2). The first analysis gives p=.0103, the second gives p=.0068.

I realize your comment was about a specific point in this other paper, but am I to take it that the results provided by these tests are one-sided rather than two-sided? 
Best-
Dan