[R-meta] Model with intercept gives 0 heterogeneity but without intercept is ok
-----Original Message----- From: Luke Martinez [mailto:martinezlukerm at gmail.com] Sent: Monday, 30 August, 2021 20:46 To: Viechtbauer, Wolfgang (SP) Cc: R meta Subject: Re: [R-meta] Model with intercept gives 0 heterogeneity but without intercept is ok Dear?Wolfgang, Thank you. 1- To make sure I understand this correctly, you're saying that because I killed the intercept, then the intercept for one or more continuous?moderators equals 0 for all studies, thus, there is no intercept to vary across the levels of study, hence no between-study variance component can be estimated (sigma^2.1 == 0), correct?
This doesn't sound right. Removing the intercept in this model says that the average effect must be 0 when X = 0. One can still estimates the variance components whether there is an intercept or not. They have different interpretations though, since the variances are estimated as deviations from a line that has an intercept of 0 or not.
2- Under this circumstance (killing intercept with continuous?moderators only), the intercepts (or averages) for "study/outcome" combinations can still vary across study-outcome combinations, and thus, in isolation from "sigma^2.1",? the other "sigma^2.2" can be [correctly] estimated, correct?
Again, both variance components can be estimated. It just happens to be the case that sigma^2.1 is estimated to be essentially 0 in Model1.
3- I have seen models?where the intercept is killed in the fixed part, but present in the random part. Based on what you said, in such models at least 1 categorical moderator must be present so the between-study variance component can be estimated (e.g., below), correct?
Again, all variance components can be estimated whether the fixed part includes an intercept or not.
data$gender <- sample(c("M","F"),nrow(data),replace = TRUE)
rma.mv(yi ~ 0 + X + gender, vi, random = ~ 1 | study/outcome)
? ? ? ? ? ? ? ? ? ? ?estim ? ?sqrt ?nlvls ?fixed ? ? ? ? factor
sigma^2.1 ?0.0000 ?0.0001 ? ? 60 ? ? no ? ? ? ? ?study? <---? ?Still "0" ?
sigma^2.2 ?0.5932 ?0.7702 ? ?120 ? ? no ?study/outcome
In this case, the model is identical whether you use '0 + X + gender' or 'X + gender', just the parameterization of the fixed part is different. Please see the link I posted.
Thank you very much, Luke On Mon, Aug 30, 2021 at 11:26 AM Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer at maastrichtuniversity.nl> wrote: Dear Luke, If X is a continuous moderator, removing the intercept forces the line to go through the origin. That is very rarely a sensible thing to do. See also: https://www.metafor-project.org/doku.php/tips:models_with_or_without_intercept Best, Wolfgang
-----Original Message----- From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Luke Martinez Sent: Monday, 30 August, 2021 18:02 To: R meta Subject: [R-meta] Model with intercept gives 0 heterogeneity but without
intercept
is ok Dear Colleagues. I fitted two exact same models except that for one I included the intercept (Model 1) in the model, for the other, I didn't (Model 2). I wonder why for Model 1 the estimate of between-study heterogeneity is "0" but for Model 2 that estimate is not "0"? Thank you very much, Luke set.seed(132) data <- expand.grid(study = 1:60, outcome = rep(1:2,2)) data$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