[R-meta] weight in rmv metafor

Norman DAURELLE norm@n@d@ure||e @end|ng |rom @grop@r|@tech@|r
Mon Jun 15 10:09:35 CEST 2020

Dear all, Dr Viechtbauer, Dr Del Ponte,I read what you suggested, and went through the archives of the mailing list, and even though some threads were dealing with similar questions, I didn't really find the answers I was looking for there.I have multiple questions : 1) How exactly is calculated the weight of each estimate in the function rma.mv() ?2) (this question might be answered too when answering the first one but...) Why does that function (rma.mv) attribute more weight to estimates coming from studies that have multiple estimates relatively to ones that come from studies that only have one estimate ?3) I tried to produce a reproducible example of my code, would it be possible to tell me if I got things right ?my dataset is this table (I didn't know if I could attach anything) :
> dat
              author year estimate std_error   p_value          r number_of_obs
1    Ballinger et al 1988 -19.3450    5.8220 4.638e-03 -0.6511331            17
2  Matthieu & Norman 2020  -2.7398    0.8103 7.424e-04 -0.0920000          1352
3           Khangura 2011  -1.9610    1.3470 1.536e-01 -0.2298655            40
4            Kutcher 1990 -21.1350    3.9330 1.420e-05 -0.7321321            27
5              Steed 2007 -13.9700    3.2500 7.355e-04 -0.7542836            16
6              Steed 2007 -31.9440    4.7650 2.765e-04 -0.9301781             9
7              Steed 2007  -4.2780    3.0940 1.883e-01 -0.3466844            16
8      Sprague et al 2010 -21.9880    5.3010 7.562e-04 -0.7198487            18
9     Upadhaya et al 2019 -43.6170    3.3440 1.133e-06 -0.9772861            10
10    Khangura et al 2005  -5.3500        NA 5.000e-02 -0.4200000            29
11    Khangura et al 2005 -10.5600        NA 1.000e-03 -0.5700000            29
12    Khangura et al 2005  -9.9700        NA 1.300e-02 -0.4600000            29
13    Khangura et al 2005  -5.4500        NA 1.100e-02 -0.4700000            29
14    Khangura et al 2005 -22.7500        NA 2.800e-02 -0.4200000            29
15    Khangura et al 2005 -16.8300        NA 2.200e-02 -0.4300000            29
16    Khangura et al 2005  -9.2100        NA 3.900e-02 -0.3900000            29
V1 <- c("Ballinger et al", "Matthieu & Norman", "Khangura", "Kutcher", "Steed", "Steed", "Steed", "Sprague et al",
        "Upadhaya et al", "Khangura et al", "Khangura et al", "Khangura et al", "Khangura et al", "Khangura et al",
        "Khangura et al", "Khangura et al" )
V2 <- c(1988, 2020, 2011, 1990, 2007, 2007, 2007, 2010, 2019, 2005, 2005, 2005, 2005, 2005, 2005, 2005)
V3 <- c(-19.3450, -2.7398, -1.9610, -21.1350, -13.9700, -31.9440, -4.2780, -21.9880, -43.6170, -5.3500,
        -10.5600, -9.9700, -5.4500, -22.7500, -16.8300, -9.2100)
V4 <- c(5.8220, 0.8103, 1.3470, 3.9330, 3.2500, 4.7650, 3.0940, 5.3010, 3.3440, NA, NA, NA, NA, NA, NA, NA)
V5 <- c(4.638e-03, 7.424e-04, 1.536e-01, 1.420e-05, 7.355e-04, 2.765e-04, 1.883e-01, 7.562e-04, 1.133e-06,
        5.000e-02, 1.000e-03, 1.300e-02, 1.100e-02, 2.800e-02, 2.200e-02, 3.900e-02)
V6 <- c(-0.6511331, -0.0920000, -0.2298655, -0.7321321, -0.7542836, -0.9301781, -0.3466844, -0.7198487,
        -0.9772861, -0.4200000, -0.5700000, -0.4600000, -0.4700000, -0.4200000, -0.4300000, -0.3900000)
V7 <- c(17, 1352, 40, 27, 16, 9, 16, 18, 10, 29, 29, 29, 29, 29, 29, 29)dat <- cbind(V1, V2, V3, V4, V5, V6, V7)dat <- as.data.frame(dat)dat$V1 <- as.character(dat$V1)
dat$V2 <- as.integer(as.character(dat$V2))
dat$V3 <- as.numeric(as.character(dat$V3))
dat$V4 <- as.numeric(as.character(dat$V4))
dat$V5 <- as.numeric(as.character(dat$V5))
dat$V6 <- as.numeric(as.character(dat$V6))
dat$V7 <- as.numeric(as.character(dat$V7))str(dat)dat <- dat %>% rename(author = "V1",
                      year = "V2",
                      estimate = "V3",
                      std_error = "V4",
                      p_value = "V5",
                      r = "V6",
                      number_of_obs = "V7")
for (i in 1:nrow(dat)){
  if (is.na(dat$std_error[i]) == TRUE ){
    dat$std_error[i] <- abs(dat$estimate[i]) / qt(dat$p_value[i]/2,
                                                            df=dat$number_of_obs-2, lower.tail=FALSE)
res <- rma.mv(yi = dat$estimate, V = (dat$std_error)**2, random = ~ 1 | author, data=dat)coef_test(res, vcov="CR2")forest(res, addcred = TRUE, showweights = TRUE, header = TRUE,
       order = "obs", col = "blue", slab = dat$author)
ranktest(res)The for loop that I use (and in which I use a formula that Dr Viechtbauer gave me in a previous answer) to calculate the standard errors for estimates that I didn't calculate myself gives me an error message, but still gives me values.
The error message is : 

Warning messages:
1: In data$std_error[i] <- abs(data$estimate[i])/qt(data$p_value[i]/2,  :
  number of items to replace is not a multiple of replacement length

and it is repeated on 7 lines.I am not entirely sure, but I think this comes from the fact that values are set to NAs before the loop is run and are replaced by values, so replacing an item of length 0 with an item of length 1 I believe.
I hope this example can be run simply with a copy / paste, I think it should.
Did I do things correctly ? If not what should I modify ?Thank you !Norman

----- Mail d'origine -----
De: Viechtbauer, Wolfgang (SP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
�: Norman DAURELLE <norman.daurelle using agroparistech.fr>
Cc: r-sig-meta-analysis <r-sig-meta-analysis using r-project.org>
Envoy�: Thu, 11 Jun 2020 15:33:02 +0200 (CEST)
Objet: RE: [R-meta] weight in rmv metafor

Dear Norman,

To give a simple example: When (some of the) studies contribute multiple estimates, the dataset has a multilevel structure (with estimates nested within studies). A common way to deal with this is to fit a multilevel model with random effects for studies and estimates within studies. Like this:


However, multiple estimates from the same study are actually often computed based on the same sample of subjects. In that case, the sampling errors are also correlated. The multilevel model does not capture this. For this, one would ideally want to fit a model that also allows for correlated sampling errors. Like this:


However, computing the covariances between the sampling errors within a study is difficult and requires information that is often not available.

We can ignore those correlations and use the multilevel model as a working model that is an approximation to the model that also accounts for correlated sampling errors. After fitting the multilevel model with rma.mv(), one can then use cluster robust inference methods to 'fix things up'.

Quite a bit of this has been discussed at length in previous posts on this mailing list. You might want to search the archives for some of these posts.


>-----Original Message-----
>From: Norman DAURELLE [mailto:norman.daurelle using agroparistech.fr]
>Sent: Thursday, 11 June, 2020 15:05
>To: Viechtbauer, Wolfgang (SP)
>Cc: r-sig-meta-analysis
>Subject: Re: [R-meta] weight in rmv metafor
>Thank you.
>I am not sure I understand exactly what you mean by " if the working model
>is only an approximation and doesn't cover all dependencies ".
>Could you please explain it ?
>For now I used the rma() function to synthesize the available literature
>existing on the blackleg - oil seed rape disease-yield relationship, using
>slopes as effect-sizes.
>the models that gave me the slopes I used in the meta-analysis are all Y = a
>+ bX, simple linear regressions with Y being the yield and X being the
>diseqse severity.
>So my slopes, b, are all negative, and I have obtained a "summary" effect
>size through the rma() function.
>But I indeed have two studies that for now contribute to most of the effect-
>sizes that are included in my meta-analysis.
>So why exactly is it necessary to use the rma.mv() function ?
>What exactly does the "multivariate" qualificative refer to ?
>Thank you,
>De: "Wolfgang Viechtbauer" <wolfgang.viechtbauer using maastrichtuniversity.nl>
>�: "Norman DAURELLE" <norman.daurelle using agroparistech.fr>, "r-sig-meta-
>analysis" <r-sig-meta-analysis using r-project.org>
>Envoy�: Jeudi 11 Juin 2020 22:34:55
>Objet: RE: [R-meta] weight in rmv metafor
>Dear Norman,
>If you only used rma(), then this is not correct. rma.mv() with an
>appropriately specified model (plus clubSandwich::coef_test() if the working
>model is only an approximation and doesn't cover all dependencies) would be
>more appropriate.
>>-----Original Message-----
>>From: Norman DAURELLE [mailto:norman.daurelle using agroparistech.fr]
>>Sent: Thursday, 11 June, 2020 14:13
>>To: r-sig-meta-analysis
>>Cc: Viechtbauer, Wolfgang (SP)
>>Subject: Re: [R-meta] weight in rmv metafor
>>Hi all,
>>I read this discussion and one question came to my mind : I also had some
>>studies that contributed multiple effect sizes in the meta-analysis that I
>>recently ran thanks to Dr Viechtbauer's advice.
>>For now I only used the rma function, but should I have used rma.mv because
>>of these stuides that had multiple effect sizes ?
>>Thank you !
>>De: "James Pustejovsky" <jepusto using gmail.com>
>>�: "Wolfgang Viechtbauer" <wolfgang.viechtbauer using maastrichtuniversity.nl>
>>Cc: "r-sig-meta-analysis" <r-sig-meta-analysis using r-project.org>, "Huang Wu"
>><huang.wu using wmich.edu>
>>Envoy�: Mercredi 10 Juin 2020 05:08:09
>>Objet: Re: [R-meta] weight in rmv metafor
>>Hi Huang,
>>I've written up some notes that add a bit of further intuition to the
>>discussion that Wolfgang provided. The main case that I focus on is a model
>>that is just a meta-analysis (i.e., no predictors) and that includes random
>>effects to capture both between-study and within-study heterogeneity. I
>>also say a little bit about meta-regression models with only study-level
>>On Sun, Jun 7, 2020 at 4:11 PM Viechtbauer, Wolfgang (SP) <
>>wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>> Of course the weights "impact the estimated fixed effects". But whether
>>> studies with multiple effect sizes tend to receive more weight depends on
>>> various factors, including the variances of the random effects and the
>>> sampling error (co)variances.
>>> A more detailed discussion around the way weighting works in rma.mv
>>> models can be found here:
>>> http://www.metafor-project.org/doku.php/tips:weights_in_rma.mv_models
>>> Note that weights(res, type="rowsum") currently only works in the 'devel'
>>> version of metafor, so follow
>>> https://wviechtb.github.io/metafor/#installation if you want to reproduce
>>> this part as well.
>>> I hope this clarifies things.
>>> Best,
>>> Wolfgang

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