[R-meta] Model with intercept gives 0 heterogeneity but without intercept is ok
Thank you. That would mean that in all four cases below, I can interpret sigma^2.1 as: the variation in true effect sizes at the study level (i.e., averaged within each study across all studies), above and beyond the explanatory power of gender, sector, and X (if such variables across studies). Thanks, again, Luke (A): rma.mv(yi ~ 0 + gender + sector + X , vi, random = ~ 1 | study/outcome, data = data) (B): rma.mv(yi ~ 0 + sector + gender + X , vi, random = ~ 1 | study/outcome, data = data) (C): rma.mv(yi ~ gender + sector + X , vi, random = ~ 1 | study/outcome, data = data) (D): rma.mv(yi ~ sector + gender + X , vi, random = ~ 1 | study/outcome, data = data) On Mon, Aug 30, 2021 at 4:54 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
-----Original Message----- From: Luke Martinez [mailto:martinezlukerm at gmail.com] Sent: Monday, 30 August, 2021 23:17 To: Viechtbauer, Wolfgang (SP) Cc: R meta Subject: Re: [R-meta] Model with intercept gives 0 heterogeneity but
without
intercept is ok Thank you, Wolfgang. I visited the link you kindly shared. But that link
only
discusses the effect of removing the intercept on the fixed parts, not
random
parts. Also, in that link the fixed parts only include either a categorical or
only a
continuous moderator, but not both types of moderators together. For
example, if
we have two categorical moderators and one continuous moderator, as in:
data$gender <- sample(c("M","F"),nrow(data),replace = TRUE)
data$sector <- sample(c("Pr","Pv", "NGO"),nrow(data),replace = TRUE)
Then, removing the intercept is the matter of which categorical moderator
appears
last in the formula! For example, in: (A): rma.mv(yi ~ 0 + gender + sector + X , vi, random = ~ 1 |
study/outcome,
data = data) R removes the intercept for "sector" because it appears last. But, in: (B): rma.mv(yi ~ 0 + sector + gender + X , vi, random = ~ 1 |
study/outcome,
data = data) R removes the intercept for "gender" because it appears last. My question is that do these behaviors in the fixed-part, essentially,
change the
meaning/nature (e.g., what average is varying across study levels) of the
random
parts?
In the models above: No. All of the models are above are essentially the same, the fixed effects are just parameterized differently. They have the same log likelihood, the same fitted values, the same residuals, etc. etc.
Apparently, the random part is not related to the fixed-part in rma.mv(),
and
that's why both (A) and (B), with or without the intercepts (i.e., 4 specification) all give the exact same estimates of their two variance
components? This is true if the different parameterizations of the fixed effects are ultimately identical (as is the case above).
Thank you, Luke