[R-meta] When to remove the intercept and other questions

[Viechtbauer, Wolfgang (SP)]

Dear Rafael,

Let's take a simple example:

### load BCG vaccine data
dat <- get(data(dat.bcg))

### calculate log risk ratios and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)
dat

### mixed-effects meta-regression model with categorical moderator
res <- rma(yi, vi, mods = ~ alloc, data=dat)
res

You will find:

Test of Moderators (coefficients 2:3):
QM(df = 2) = 1.7675, p-val = 0.4132

Model Results:

                 estimate      se     zval    pval    ci.lb   ci.ub 
intrcpt           -0.5180  0.4412  -1.1740  0.2404  -1.3827  0.3468    
allocrandom       -0.4478  0.5158  -0.8682  0.3853  -1.4588  0.5632    
allocsystematic    0.0890  0.5600   0.1590  0.8737  -1.0086  1.1867    

The QM-test tests coefficients 2 and 3, which are the *differences* between the reference level (in this case 'alternate') and the other two levels ('random' and 'systematic'). So, this gives you a test whether the mean outcome is the same for the three levels.

### model with intercept removed
res <- rma(yi, vi, mods = ~ alloc - 1, data=dat)
res

You will find:

Test of Moderators (coefficients 1:3):
QM(df = 3) = 15.9842, p-val = 0.0011

Model Results:

                 estimate      se     zval    pval    ci.lb    ci.ub 
allocalternate    -0.5180  0.4412  -1.1740  0.2404  -1.3827   0.3468      
allocrandom       -0.9658  0.2672  -3.6138  0.0003  -1.4896  -0.4420  *** 
allocsystematic   -0.4289  0.3449  -1.2434  0.2137  -1.1050   0.2472      

In this case, the coefficients are the mean outcomes for each level. The QM-test tests coefficients 1, 2, and 3, so it tests whether the mean outcome is 0 for all three levels.

You might also want to work through these examples:

http://www.metafor-project.org/doku.php/tips:testing_factors_lincoms
http://www.metafor-project.org/doku.php/tips:multiple_factors_interactions

Best,
Wolfgang

-----Original Message-----
From: Rafael Rios [mailto:biorafaelrm at gmail.com] 
Sent: Saturday, 19 May, 2018 3:57
To: r-sig-meta-analysis at r-project.org; Viechtbauer, Wolfgang (SP)
Subject: When to remove the intercept and other questions

Dear Dr. Wolfgang and All,

I have some doubts that you could help me to clarify. I read e-mails in R-meta list of a conversation between Samuel Knapp and James Pustejovsky with the title "Testing of moderators in rma()". James clarified the following:

"When the model includes an intercept term, the omnibus test does *not* include the intercept. So the null hypothesis is b1 = 0 and b2 =0.

If you fit the model without the intercept, then the equivalent to the omnibus test from the model with an intercept would be that the average effect sizes are all equal, as in b1 = b2 = b3."

I want to compare the differences between effect sizes of four subgroups from a categorical moderator. According James, I should remove the intercept from the meta-analysis. I have had different results including or removing the intercept. That is why I am insecure about to use this approach. What do you think? Is it reasonable to remove the intercept in my case?

I also have some questions about how to obtain the intercept and slope from multi-level meta-analysis with two moderators, a categorical moderator and a continuous). How can I estimate the intercept and slope of each subgroup to include the straights in a graph.

Every help is welcome!

Best wishes,

Rafael Rios Moura.
scientia amabilis

PhD in Ecology and Conservation
Postdoctoral Researcher
Universidade Estadual de Campinas (UNICAMP)
Campinas, São Paulo, Brazil
________________________________________________________
ORCID: http://orcid.org/0000-0002-7911-4734
Research Gate: https://www.researchgate.net/profile/Rafael_Rios_Moura2
Currículo Lattes: http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4244908A8