[R-meta] Clarification on ranef.rma.mv()

Luke Martinez m@rt|nez|ukerm @end|ng |rom gm@||@com
Tue Sep 14 02:11:52 CEST 2021


Hi Wolfgang,

You'll see the meaningful results when you run the following:

lapply(rePCA_lme(fm2), summary)

The first column in the output (below) is the amount of total
between-subjects variation explained by the random intercepts. The
second column is the amount of total between-subjects variation
cumulatively explained by the random intercepts AND random slopes.

The idea is to find out whether some overfitting of random-effects
structure has taken place or not. For example, in this case, it seems
that random slopes are only responsible for a tiny amount of total
between-subjects variation as 99.41% of such variation is explained by
the random intercepts alone. So, maybe the model's random structure
can be simplified as:

lme(distance ~ age, random = ~1 | Subject , data = Orthodont)

This is a useful feature possibly for metafor as well, so I wonder how
to add some names and "prcomplist" class to do the same thing to
rma.mv just like I extended that from lmer to lme?

I don't think the fact that yi values have their own variance would
interfere with the central concept here.

Thanks,
Luke

$Subject
Importance of components:
                                         [,1]    [,2]
Standard deviation     1.7794 0.13681
Proportion of Variance 0.9941 0.00588
Cumulative Proportion  0.9941 1.00000

On Mon, Sep 13, 2021 at 1:17 PM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
> Going back to the earlier example:
>
> library(nlme)
> fm2 <- lme(distance ~ age, random = ~ age | Subject, data = Orthodont)
> rePCA_lme(fm2)
>
> This is essentially:
>
> svd(chol(as.matrix(getVarCov(fm2))))$d / sigma(fm2)
> svd(chol(as.matrix(getVarCov(fm2))))$u
>
> Doing the same with rma.mv():
>
> library(metafor)
> Orthodont$id <- 1:nrow(Orthodont)
> fm3 <- rma.mv(distance ~ age, 0, random = list(~ age | Subject, ~ 1 | id), struct="GEN", data = Orthodont)
> svd(chol(fm3$G))$d / sqrt(fm3$sigma2)
> svd(chol(fm3$G))$u
>
> No idea how to interpret this and whether the idea underlying this generalizes to the case where each yi value has its own variance (instead of estimating a single residual variance).
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: Luke Martinez [mailto:martinezlukerm using gmail.com]
> >Sent: Monday, 13 September, 2021 19:49
> >To: Viechtbauer, Wolfgang (SP)
> >Cc: R meta
> >Subject: Re: [R-meta] Clarification on ranef.rma.mv()
> >
> >Hi Wolfgang,
> >
> >My goal was to follow lme4:::rePCA.merMod assuming that there is an
> >underlying reason that lme4 developers chose not to directly apply PCA
> >to the G matrix.
> >
> >But if you think for rma.mv() models applying the PCA directly to the
> >G matrix gives the same result, I will very much appreciate a quick
> >demonstration?
> >
> >Thank you again,
> >Luke
> >
> >On Mon, Sep 13, 2021 at 11:42 AM Viechtbauer, Wolfgang (SP)
> ><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >>
> >> I am not familiar with lme4::rePCA, but if you want to do PCA on the var-cov
> >matrix of the random effects, why not just apply PCA directly to G?
> >>
> >> Best,
> >> Wolfgang
> >>
> >> >-----Original Message-----
> >> >From: Luke Martinez [mailto:martinezlukerm using gmail.com]
> >> >Sent: Monday, 13 September, 2021 18:25
> >> >To: Viechtbauer, Wolfgang (SP)
> >> >Cc: R meta
> >> >Subject: Re: [R-meta] Clarification on ranef.rma.mv()
> >> >
> >> >Sure, I recently wrote a function similar to ?lme4::rePCA for lme
> >> >models. I keep benefiting from using it. So, I was wondering if I
> >> >could extend that to rma.mv() models?
> >> >
> >> >Here is how it works for lme models:
> >> >
> >> >#-- Some helper functions:
> >> >
> >> >Tlist_lme <- function(fit) rev(pdMatrix(fit$modelStruct$reStruct,
> >> >factor = TRUE))
> >> >theta_lme <- function(fit) sapply(Tlist_lme(fit), function(i)
> >> >i[lower.tri(i, diag = TRUE)])
> >> >
> >> >lowerbd <- function(x){
> >> >dd <- diag(0, nrow=nrow(x))
> >> >dd[lower.tri(dd)] <- -Inf
> >> >dd[lower.tri(dd, diag=TRUE)]
> >> >}
> >> >
> >> >lwr_lme <- function(fit) sapply(Tlist_lme(fit), lowerbd)
> >> >
> >> >#-- main function:
> >> >
> >> >rePCA_lme <- function(x){
> >> >
> >> >  chfs <- Tlist_lme(x)
> >> >  nms <- names(chfs)
> >> >  unms <- unique(nms)
> >> >  names(unms) <- unms
> >> >
> >> >  svals <- function(m) { # this is applied each of the RE matrices
> >> >    vv <- svd(m, nv = 0L)
> >> >    names(vv) <- c("sdev", "rotation")
> >> >    vv$center <- FALSE
> >> >    vv$scale <- FALSE
> >> >    class(vv) <- "prcomp"
> >> >    vv
> >> >  }
> >> >
> >> >  structure(lapply(unms, function(m)
> >> >    svals(Matrix::bdiag(chfs[which(nms ==
> >> >                                     m)]))), class = "prcomplist")
> >> >}
> >> >
> >> >#-- Testing:
> >> >
> >> >fm2 <- lme(distance ~ age,random=~age | Subject , data = Orthodont)
> >> >
> >> >rePCA_lme(fm2)
> >> >
> >> >On Mon, Sep 13, 2021 at 11:10 AM Viechtbauer, Wolfgang (SP)
> >> ><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >> >>
> >> >> This gives the scaled (by the residual variance) Cholesky decomposition of
> >the
> >> >var-cov matrix of the random effects.
> >> >>
> >> >> We can see this if we compare:
> >> >>
> >> >> t(Tlist_lme(fm1)$Subject) %*% Tlist_lme(fm1)$Subject * sigma(fm1)^2
> >> >>
> >> >> with:
> >> >>
> >> >> VarCorr(fm1)
> >> >>
> >> >> rma.mv() also uses a Cholesky decomposition to ensure that the var-cov matrix
> >of
> >> >the random effects is (semi)positive definite. However, it does not scale
> >things
> >> >by the residual variance, since those variances are heteroscedastic.
> >> >>
> >> >> I don't know why you would want to obtain just Tlist_lme(fm1), but if you are
> >> >actually after the var-cov matrix itself, it is stored as "G" in the model
> >object.
> >> >To use your earlier example:
> >> >>
> >> >> library(metafor)
> >> >> dat <- dat.berkey1998
> >> >> res.mv <- rma.mv(yi~ outcome - 1, vi, data = dat, random = ~ outcome | trial,
> >> >struct = "UN")
> >> >> res.mv$G
> >> >>
> >> >> If you really want the Cholesky decomposition, then just do:
> >> >>
> >> >> C <- chol(res.mv$G)
> >> >> C
> >> >>
> >> >> and, as expected, t(C) %*% C is the same as res.mv$G.
> >> >>
> >> >> Best,
> >> >> Wolfgang
> >> >>
> >> >> >-----Original Message-----
> >> >> >From: Luke Martinez [mailto:martinezlukerm using gmail.com]
> >> >> >Sent: Monday, 13 September, 2021 17:27
> >> >> >To: Viechtbauer, Wolfgang (SP)
> >> >> >Cc: R meta
> >> >> >Subject: Re: [R-meta] Clarification on ranef.rma.mv()
> >> >> >
> >> >> >Dear Wolfgang,
> >> >> >
> >> >> >Thank you very much. For correlated random-effect structures in
> >> >> >rma.mv(), is it possible to extract the equivalent of the following
> >> >> >lme() information:
> >> >> >
> >> >> >Tlist_lme <- function(fit) rev(pdMatrix(fit$modelStruct$reStruct,
> >> >> >factor = TRUE))
> >> >> >
> >> >> >#----- Testing:
> >> >> >library(nlme)
> >> >> >fm1 <- lme(distance ~ age, data = Orthodont)
> >> >> >
> >> >> >Tlist_lme(fm1)
> >> >> >
> >> >> >On Mon, Sep 13, 2021 at 2:38 AM Viechtbauer, Wolfgang (SP)
> >> >> ><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >> >> >>
> >> >> >> Dear Luke,
> >> >> >>
> >> >> >> Sure:
> >> >> >>
> >> >> >> library(metafor)
> >> >> >>
> >> >> >> dat <- dat.berkey1998
> >> >> >> res.mv <- rma.mv(yi~ outcome - 1, vi, data = dat, random = ~ outcome |
> >trial,
> >> >> >struct = "UN")
> >> >> >> res.mv$rho
> >> >> >>
> >> >> >> ran.mv <- ranef.rma.mv(res.mv)
> >> >> >> cor(matrix(ran.mv[[1]]$intrcpt, ncol=2, byrow=FALSE))[1,2]
> >> >> >>
> >> >> >> The two correlations are not the same for the reasons explained at the
> >link
> >> >you
> >> >> >provided.
> >> >> >>
> >> >> >> If the dataset is not so nicely balanced, one can do something similar,
> >but
> >> >the
> >> >> >restructuring of the output from ranef() into a wide format gets a bit more
> >> >> >tedious.
> >> >> >>
> >> >> >> For example:
> >> >> >>
> >> >> >> dat <- dat[-4,]
> >> >> >> res.mv <- rma.mv(yi~ outcome - 1, vi, data = dat, random = ~ outcome |
> >trial,
> >> >> >struct = "UN")
> >> >> >> res.mv$rho
> >> >> >>
> >> >> >> ran.mv <- ranef.rma.mv(res.mv)
> >> >> >> ran.mv
> >> >> >>
> >> >> >> ran.mv <- ran.mv[[1]][1]
> >> >> >> ran.mv$study <- sapply(strsplit(rownames(ran.mv), "|", fixed=TRUE), tail,
> >1)
> >> >> >> ran.mv$arm   <- sapply(strsplit(rownames(ran.mv), "|", fixed=TRUE), head,
> >1)
> >> >> >> ran.mv
> >> >> >>
> >> >> >> wide <- reshape(ran.mv, direction="wide", idvar="study",
> >v.names="intrcpt",
> >> >> >timevar="arm")
> >> >> >> rownames(wide) <- NULL
> >> >> >> wide
> >> >> >> cor(wide[2:3], use="pairwise.complete.obs")[1,2]
> >> >> >>
> >> >> >> There might be a more elegant way to do this, but this gets the job done.
> >> >> >>
> >> >> >> Best,
> >> >> >> Wolfgang
> >> >> >>
> >> >> >> >-----Original Message-----
> >> >> >> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-
> >project.org]
> >> >On
> >> >> >> >Behalf Of Luke Martinez
> >> >> >> >Sent: Monday, 13 September, 2021 8:38
> >> >> >> >To: R meta
> >> >> >> >Subject: [R-meta] Clarification on ranef.rma.mv()
> >> >> >> >
> >> >> >> >Dear Wolfgang and List Members,
> >> >> >> >
> >> >> >> >In ordinary multilevel models (lmer), one can use ranef() of a model
> >> >> >> >to get the correlations from the conditional modes of the random
> >> >> >> >effects (https://stats.stackexchange.com/q/153253/124093) which may
> >> >> >> >reveal how much random-effects for slopes and intercepts are roughly
> >> >> >> >correlated.
> >> >> >> >
> >> >> >> >Similarly, for a struct = "UN" model, I was wondering if
> >> >> >> >"ranef.rma.mv(fitted_model)" could reveal how much random-effects for
> >> >> >> >outcome levels are roughly correlated?
> >> >> >> >
> >> >> >> >For example, for the "res.mv" model below where the REML rho estimate
> >> >> >> >is "0.775", can ranef.rma.mv(res.mv) values give a rough estimate of
> >> >> >> >this correlation conditional on the observed data?
> >> >> >> >
> >> >> >> >dat <- dat.berkey1998
> >> >> >> >res.mv <- rma.mv(yi~ outcome - 1, vi, data = dat, random = ~ outcome |
> >> >> >> >trial, struct = "UN")
> >> >> >> >
> >> >> >> >ran.mv <- ranef.rma.mv(res.mv)
> >> >> >> >
> >> >> >> >Thank you very much for your help,
> >> >> >> >Luke



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