[R-meta] Time as indicator vs time as meaning

Tue, Oct 12, 2021 6:05 AM

While Stefanou contacted me off-list and also shared the data with me, I want to bring this back here.

So, now that I have seen the data, I see that the "time_wthn" and "time_btw" variables were computed based on the measurenent occasion counter (time), not the time variable itself (time_wk). That mixes different things and of course then the results are not the same. So, using your data, do the following:

dat$time_btw <- ave(dat$time_wk, dat$study, FUN=mean)
dat$time_wthn <- dat$time_wk - dat$time_btw
dat$time_wthn <- round(dat$time_wthn, 8)

and then run:

model1 <- rma.mv(yi ~ time_btw + time_wthn, vi,
                 random = list(~ time_wthn | study, ~time_wk | study),
                 struct = c("GEN","CAR"), data=dat)

model2 <- rma.mv(yi ~ time_btw + time_wthn, vi,
                 random = list(~ time_wthn | study, ~time_wthn | study),
                 struct = c("GEN","CAR"), data=dat)

model1
model2

which yields:

Variance Components:

outer factor: study      (nlvls = 49)
inner term:   ~time_wthn (nlvls = 44)                                                                                 

            estim    sqrt  fixed  rho:  intr    tm_w 
intrcpt    0.4685  0.6845     no           -  1.0000 
time_wthn  0.0229  0.1513     no          no       - 

outer factor: study   (nlvls = 49)
inner factor: time_wk (nlvls = 12)

            estim    sqrt  fixed 
gamma^2    0.0603  0.2456     no 
phi        0.0295             no 

for model1 and the same for model2. So all is as expected.

profile(model1) also indicates peaks at all the estimates. And yes, that estimate of rho drifts towards 1. Not nice when that happens, but that's where the peak of the likelihood surface is.

I also see in the data now that there are at times multiple effects at the same time point. So one could even extend the model above further, for example with:

dat$obs <- 1:nrow(dat)

model3 <- rma.mv(yi ~ time_btw + time_wthn, vi,
          random = list(~ time_wthn | study, ~time_wk | study, ~ 1 | obs),
          struct = c("GEN","CAR"), data=dat)
model3

This further improves the fit:

anova(model1, model3)

These are some suggestions - I have not looked more deeply into these data. And my comment from before stands: You probably need a proper V matrix, not just the sampling variances (vi) if these effects are measured in the same people within studies.

One final thing: The line

dat$time_wthn <- round(dat$time_wthn, 8)

is a bit weird and seems unncessary. Well, I just got screwed by floating point issues. There is a part in rma.mv() where I figure out the *unique* time point values for struct="CAR" and use unique() for that. In essence, this is what happens:

unique(c(1/2, sqrt(1/2)*sqrt(1/2)))

Argh. Rounding time_wthn a bit solves that issue here. Of course, that needs to be fixed eventually in rma.mv() itself.

Best,
Wolfgang

-----Original Message-----
From: Stefanou Revesz [mailto:stefanourevesz at gmail.com]
Sent: Sunday, 10 October, 2021 23:29
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] Time as indicator vs time as meaning

Resending Model 2:

#***********************
MODEL 2:
#***********************
rma.mv(yi ~ time_btw + time_wthn, vi,
              random =
                list(~ time_wthn | study, ~time_wthn | study), struct
= c("GEN","CAR"),data=data)

Variance Components:

outer factor: study      (nlvls = 49)
inner term:   ~time_wthn (nlvls = 9)

           estim    sqrt  fixed  rho:    intr  tm_w
intrcpt    0.4034  0.6351     no             -    no
time_wthn  0.1141  0.3377     no        1.0000     -

outer factor: study     (nlvls = 49)
inner factor: time_wthn (nlvls = 9)

           estim    sqrt  fixed
gamma^2    0.0770  0.2775     no
phi        0.0000             no

Model Results:

          estimate      se    zval    pval    ci.lb   ci.ub
intrcpt      0.1155  0.1861  0.6204  0.5350  -0.2493  0.4802
time_btw     0.3184  0.1815  1.7540  0.0794  -0.0374  0.6741    .
time_wthn    0.3247  0.0658  4.9344  <.0001   0.1957  0.4536  ***

On Sun, Oct 10, 2021 at 4:24 PM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

-----Original Message-----
From: Stefanou Revesz [mailto:stefanourevesz at gmail.com]
Sent: Sunday, 10 October, 2021 23:03
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] Time as indicator vs time as meaning

ATTACHMENT(S) REMOVED: image.png

Thanks! Reporting back the results for two models (note: "time_wk" =
"time_meaning_wks").
In model 1,  I used "time_wk" to the left of | for "CAR".
In model 2, I used "time_whtn" to the left of | for "CAR".
In both models, rho is estimated to be 1. But the likelihood profile
for rho seems ok for both models (attached).

However, in model 1, phi is estimated to be 0.1170. In model 2, phi is
estimated to be 0. In both models, the likelihood profiles for phi
seem ok.
Which phi, then, seems appropriate?

Thank you,
Stefanou

#******************************
MODEL 1:
#******************************
rma.mv(yi ~ time_btw + time_wthn, vi,
              random =
        list(~ time_wthn | study, ~time_wk | study), struct =
c("GEN","CAR"),data=data)

Variance Components:

outer factor: study    (nlvls = 49)
inner term:   ~time_wk (nlvls = 12)

         estim    sqrt  fixed  rho:    intr  tm_w
intrcpt  0.1306  0.3614     no             -    no
time_wk  0.0236  0.1536     no        1.0000     -

outer factor: study   (nlvls = 49)
inner factor: time_wk (nlvls = 12)

           estim    sqrt  fixed
gamma^2    0.0703  0.2652     no
phi        0.0544             no

Model Results:

          estimate      se    zval    pval    ci.lb   ci.ub
intrcpt      0.0049  0.1816  0.0272  0.9783  -0.3510  0.3608
time_btw     0.3399  0.2164  1.5708  0.1162  -0.0842  0.7641
time_wthn    0.2837  0.0708  4.0064  <.0001   0.1449  0.4224  ***

Something doesn't match up here. The first part of the 'random' formula says '~

time_wthn | study' but the output says that the inner term is ~time_wk.

#******************************
MODEL 2:
#******************************
rma.mv(yi ~ time_btw + time_wthn, vi,
              random =
                list(~ time_wthn | study, ~time_wthn | study), struct
= c("GEN","CAR"),data=data)
Variance Components:

outer factor: study      (nlvls = 49)
inner term:   ~time_wthn (nlvls = 9)

           estim    sqrt  fixed  rho:    intr  tm_w
intrcpt    0.4034  0.6351     no             -    no
time_wthn  0.1141  0.3377     no        1.0000     -

outer factor: study     (nlvls = 49)
inner factor: time_wthn (nlvls = 9)

           estim    sqrt  fixed
gamma^2    0.0770  0.2775     no
phi        0.0000             no

Test for Residual Heterogeneity:
QE(df = 402) = 1450.3879, p-val < .0001

Test of Moderators (coefficients 2:3):
QM(df = 2) = 24.4255, p-val < .0001

Model Results:

          estimate      se    zval    pval    ci.lb   ci.ub
intrcpt      0.1155  0.1861  0.6204  0.5350  -0.2493  0.4802
time_btw     0.3184  0.1815  1.7540  0.0794  -0.0374  0.6741    .
time_wthn    0.3247  0.0658  4.9344  <.0001   0.1957  0.4536  ***

[R-meta] Time as indicator vs time as meaning

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