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

[Luke Martinez]

Dear Colleagues.

I fitted two exact same models except that for one I included the intercept
(Model 1) in the model, for the other, I didn't (Model 2).

I wonder why for Model 1 the estimate of between-study heterogeneity is "0"
but for Model 2 that estimate is not "0"?

Thank you very much,
Luke

set.seed(132)
data <- expand.grid(study = 1:60, outcome = rep(1:2,2))
data$X <- rnorm(nrow(data))
e <- rnorm(nrow(data))
data$yi <- .8+.6*data$X + e
data$vi <- runif(nrow(data))

Model1 <- rma.mv(yi ~ 1 + X, vi, random = ~ 1 | study/outcome, data = dat)

                       estim    sqrt  nlvls  fixed         factor
sigma^2.1  0.0000  0.0001     60     no          study
sigma^2.2  0.4707  0.6861    120     no  study/outcome


Model2 <- rma.mv(yi ~ 0 + X, vi, random = ~ 1 | study/outcome, data = dat)

                    estim    sqrt  nlvls  fixed         factor
sigma^2.1  0.5634  0.7506     60     no          study
sigma^2.2  0.4878  0.6984    120     no  study/outcome

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