[R-meta] Model with intercept gives 0 heterogeneity but without intercept is ok

[Luke Martinez]

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 using maastrichtuniversity.nl> wrote:

> >-----Original Message-----
> >From: Luke Martinez [mailto:martinezlukerm using 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
>

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