[R-meta] Interpretation of continuous moderator in 3-level meta-regression

Reza Norouzian rnorouz|@n @end|ng |rom gm@||@com
Wed Sep 8 20:30:00 CEST 2021 

Daniel,

You said mod1 is coded in continuous percentage points (0.0, 0.1, 0.5,
..., 0.9, 1.0) or it's a binary factor variable {rows with either 0 or
1}? My answer may or may not be exactly what you're looking for. But
since you linked a post that discussed this, I just offer some
thoughts.

You could potentially compute the within and between study effects of mod1.

IF mod1 is in continuous percentage points:

library(dplyr)

new_df <-
df %>%
  group_by(studyid) %>%
  mutate(mod1_btw_study = mean(mod1), mod1_wthn_study = mod1 -
mod1_btw_study) %>% ungroup

And then, use:   mods = ~mod1_btw_study + mod1_wthn_study, data = new_df

Alternatively, you could just use:

mods = ~mod1_btw_study + mod1, data = new_df

In the first parameterization, you can do: "mod1_btw_study -
mod1_wthn_study" to get the contextual effect of mod1.

In the second parametrization, you directly get the contextual effect
of mod1 (via "mod1_btw_study" coefficient).

Either way, the interpretation of contextual effect would then be: the
average difference in two true row effects with the same mod1 value
that come from studies whose average mod1 values differs by 1
percentage point.


IF mod1 is a binary factor, you would do the same thing but via dummy
variables (I'm showing method 1 from above):

library('fastDummies') # May be others know of a better package

df$mod1 <- factor(df$mod1) # you can also rename 0 and 1 here if you want

new_df <- df %>%
dummy_cols(select_columns = mod1) %>%
group_by(across(all_of(studyid))) %>%
mutate(across(starts_with(paste0(mod1, "_")), list(wthn = ~ . -
mean(.), btw = ~ mean(.)))) %>% ungroup


mods = ~mod1_1_btw + mod1_1_wthn, data = new_df ## Here I'm taking
mod1_0_btw + mod1_0_wthn as reference categories

Now if you do: mod1_1_btw - mod1_1_wthn, data = new_df, you get the
contextual effect of mod1. The interpretation this time becomes:

On average, how much do two true row effects with mod1 == 1 differ if
they come from studies whose percentage of mod1 == 1 rows differs by
1%.

When we do contextual effect stuff with factor variables (requiring
dummies), they are more commonly referred to as "compositional
effects" because speaking of "studies whose percentage of mod1 == 1"
is like asking about their composition of mod1 == 1.

If you want to use the code above, please check it for typos etc.

Kind regards,
Reza




On Wed, Sep 8, 2021 at 11:01 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
> Dear Daniel,
>
> Yes, that's correct.
>
> I would be cautious if there are no 1's in mod1 for the actual data, since you would then be extrapolating, but I assume there are, so it's all good.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of daniel.f.gucciardi using gmail.com
> >Sent: Wednesday, 08 September, 2021 8:54
> >To: r-sig-meta-analysis using r-project.org
> >Subject: [R-meta] Interpretation of continuous moderator in 3-level meta-
> >regression
> >
> >Hi all,
> >
> >I was hoping to seek your advice on the interpretation of a 3-level
> >meta-regression with a continuous variable. Briefly, my effect size (yi) is
> >sedentary time in minutes and moderator (mod1) is the percentage of wear
> >time for a 24-hour period for the device used to assess sedentary behaviour.
> >I have 55 effect sizes (esid) from 36 studies (studyid). The moderator
> >varies among effect sizes.
> >
> >I have coded the moderator on a scale of 0-1; for example, if someone wore
> >the device for 50% of the 24-hour period, we coded them as 0.50. I removed
> >the intercept in the moderator analysis because a value of 0 for the
> >moderator should technically equate to 0 min for the effect size
> >(https://www.metafor-project.org/doku.php/tips:models_with_or_without_interc
> >ept).
> >
> >library(metafor)
> >
> >mods_result <- rma.mv(yi, vi,
> >                      data = df,
> >                      level = 95,
> >                      method = "REML",
> >                      tdist = TRUE,
> >                      mods = ~mod1-1,
> >                      random = ~1 | studyid/esid)
> >
> >summary(mods_result)
> >
> >Model Results:
> >
> >estimate       se     tval  df    pval     ci.lb     ci.ub
> >mod1  802.2315  19.6706  40.7833  54  <.0001  762.7943  841.6686  ***
> >
> >I read this post with interest
> >(https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-August/003125.html)
> >, which used chronological age as the moderator. For my case, should I
> >interpret the estimate of approx. 802 min as the expect value for the
> >moderator at 1 (so 100% wear time)?
> >
> >Cheers,
> >Daniel
>
> _______________________________________________
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis using r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis


On Wed, Sep 8, 2021 at 11:02 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
> Dear Daniel,
>
> Yes, that's correct.
>
> I would be cautious if there are no 1's in mod1 for the actual data, since you would then be extrapolating, but I assume there are, so it's all good.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of daniel.f.gucciardi using gmail.com
> >Sent: Wednesday, 08 September, 2021 8:54
> >To: r-sig-meta-analysis using r-project.org
> >Subject: [R-meta] Interpretation of continuous moderator in 3-level meta-
> >regression
> >
> >Hi all,
> >
> >I was hoping to seek your advice on the interpretation of a 3-level
> >meta-regression with a continuous variable. Briefly, my effect size (yi) is
> >sedentary time in minutes and moderator (mod1) is the percentage of wear
> >time for a 24-hour period for the device used to assess sedentary behaviour.
> >I have 55 effect sizes (esid) from 36 studies (studyid). The moderator
> >varies among effect sizes.
> >
> >I have coded the moderator on a scale of 0-1; for example, if someone wore
> >the device for 50% of the 24-hour period, we coded them as 0.50. I removed
> >the intercept in the moderator analysis because a value of 0 for the
> >moderator should technically equate to 0 min for the effect size
> >(https://www.metafor-project.org/doku.php/tips:models_with_or_without_interc
> >ept).
> >
> >library(metafor)
> >
> >mods_result <- rma.mv(yi, vi,
> >                      data = df,
> >                      level = 95,
> >                      method = "REML",
> >                      tdist = TRUE,
> >                      mods = ~mod1-1,
> >                      random = ~1 | studyid/esid)
> >
> >summary(mods_result)
> >
> >Model Results:
> >
> >estimate       se     tval  df    pval     ci.lb     ci.ub
> >mod1  802.2315  19.6706  40.7833  54  <.0001  762.7943  841.6686  ***
> >
> >I read this post with interest
> >(https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-August/003125.html)
> >, which used chronological age as the moderator. For my case, should I
> >interpret the estimate of approx. 802 min as the expect value for the
> >moderator at 1 (so 100% wear time)?
> >
> >Cheers,
> >Daniel
>
> _______________________________________________
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis using r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis

More information about the R-sig-meta-analysis mailing list