[R-meta] Dependent Measure Modelling Question

[James Pustejovsky]

Grace,

To your first question, yes it is possible to use Wald_test to do "robust"
anovas for comparing factor level combinations. The interface works
similarly to anova(), but the constraints have to be provided in the form
of a matrix. Here is an example based on Wolfgang's tutorial:

library(metafor)
dat <- dat.raudenbush1985
dat$weeks <- cut(dat$weeks, breaks=c(0,1,10,100),
labels=c("none","some","high"), right=FALSE)
dat$tester <- relevel(factor(dat$tester), ref="blind")
res.i2 <- rma(yi, vi, mods = ~ weeks:tester - 1, data=dat)

# ANOVA with model-based variances
anova(res.i2, L=c(0,1,-1,0,0,0))
linearHypothesis(res.i2, c("weekssome:testerblind - weekshigh:testerblind =
0"))
anova(res.i2, L=c(0,0,0,0,1,-1))
linearHypothesis(res.i2, c("weekssome:testeraware - weekshigh:testeraware =
0"))

# Wald tests with RVE
library(clubSandwich)

# some vs. high, test = blind
Wald_test(res.i2, constraints = matrix(c(0,1,-1,0,0,0), nrow = 1),
          vcov = "CR2", cluster = dat$author)

# some vs. high, test = aware
Wald_test(res.i2, constraints = matrix(c(0,0,0,0,1,-1), nrow = 1),
          vcov = "CR2", cluster = dat$author)

To your second question about models that allow for differing levels of
heterogeneity, this tutorial from the metafor site discusses it a bit:
http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates?s[]=inner&s[]=outer

For your model, I think the syntax might be something along the lines of
the following:

StimulibyEmotion <-

  rma.mv(yi, vi, mods = ~ StimuliType:Emotion -1,

         random = list(~ 1 | studyID, ~ Emotion | outcome, ~ 1 | effectID),

         struct = "UN",

           tdist = TRUE, data=dat)


This model allows for varying levels of outcome-level heterogeneity,
depending on the emotion being assessed. The struct = "UN" argument
controls the assumption made about how the random effects for each emotion
co-vary within levels of an outcome. Just for sake of illustration, I've
assumed that the between-study heterogeneity is constant (~ 1 | studyID)
and the effect-level heterogeneity is also constant (~ 1 | effectID). I'm
not at all sure that this is the best (or even really an appropriate)
model. To get a sense of that, I think we'd need to know more about the
structure of your data, what's nested in what, and the distinction between
outcome and effectID.

Cheers,
James

On Mon, Mar 11, 2019 at 11:03 PM Grace Hayes <grace.hayes3 using myacu.edu.au>
wrote:

> Dear James,
>
> Thank you for your response to my previous query. Yes, the effect size
> estimates are statistically dependent. Therefore, as per your
> recommendation, I have read over a few tutorials that cover multivariate
> meta-analysis and robust variances estimations. Specifically, the one that
> you wrote about using club sandwich to run co-efficient tests followed by
> Wald-tests. This article was most helpful! I have a follow up question
> regards the use of the Wald-test, which I have outlined below.
>
> My three potential moderators are: task_design (two levels), Emotion (6
> levels) and StimuliType (5 levels). To test the moderating effect of each
> of these variables I ran the following:
>
> allModerator <- rma.mv( yi, vi, mods = ~ task_design + Emotion +
> StimuliType, random = ~ 1 |  studyID/outcome/effectID, tdist = TRUE, data
> = dat)
>
> coef_test(allModerator, vcov = "CR2")
>
> #NUMBER OF EMOTIONS
>
> Wald_test(allModerator, constraints = 2, vcov = "CR2")
>
> #EMOTIONTYPE
>
> Wald_test(allModerator, constraints = 3:7, vcov = "CR2")
>
> #STIMULITYPE
>
> Wald_test(allModerator, constraints = 8:11, vcov = "CR2")
>
> The constraints for each Wald test match the coefficients related to each
> moderator, so I believe these tested for the significance of each moderator
> while adjusting for the other two moderating variables. However, I was also
> interested in variance across the estimated average effect produced by each
> stimuli format for each emotion. I followed the below guide by Wolfgang
> Viechtbauer, that showed how to parameterize the model to provide the
> estimated average effect for each factor level combinations.
>
> http://www.metafor-project.org/doku.php/tips:multiple_factors_interactions
>
> My model was:
>
> StimulibyEmotion <- rma.mv(yi, vi, mods = ~ StimuliType:Emotion -1, random = ~ 1 |  studyID/outcome/effectID, tdist = TRUE, data=dat)
>
> coef_test(StimulibyEmotion, vcov = "CR2")
>
> Wolfgang then uses anovas to test factor level combination against each
> other. Can I use the Wald test to do this to my robust variance estimations?
>
> Also, would it be possible for you to please elaborate on what you meant
> by "a model that allows for different heterogeneity levels for each
> emotion", or provide a link to an article demonstrating this? As a first
> time used of R and metafor, I wasn't sure how to go about this.
>
> Many thanks,
>
> Grace
>
>
> ------------------------------
> *From:* James Pustejovsky <jepusto using gmail.com>
> *Sent:* Tuesday, 12 February 2019 1:37 PM
> *To:* Grace Hayes
> *Cc:* r-sig-meta-analysis using r-project.org
> *Subject:* Re: [R-meta] Dependent Measure Modelling Question
>
> Grace,
>
> It sounds like the data that you're describing has two factors, emotion
> type and task type, and that both are within-study factors (in other words,
> a given study might report results for multiple emotion types and/or
> multiple task types). Are the emotion types and task types also measured
> within-participant, such that a given participant in a study gets assessed
> with multiple task types, on multiple emotion types, or both? If so, then
> one challenge in analyzing this data structure is that the effect size
> estimates will be statistically dependent. There are several ways to handle
> this (multivariate meta-analysis, robust variance estimation), which we've
> discussed in many previous posts on the listserv.
>
> Other than this issue, it sounds to me like it would be possible
> to  analyze both factors---emotion type and task type---together in one big
> model. The major advantage of doing so is that the joint model would let
> you examine differences in emotion types *while controlling for task
> types*, as well as examining differences in task types *while controlling
> for emotion types*. Controlling for the other factor (and maybe other
> covariates that are associated with effect size magnitude) should provide
> clearer, more interpretable results for differences on a given factor.
> There is also evidence that using a multivariate meta-analysis model can
> potentially mitigate outcome reporting bias to some extent (see Kirkham,
> Riley, & Williamson, 2012; Hwang & Desantis, 2018).
>
> A further advantage of using one big model is that it would let you adjust
> for other potential moderators that might have similar associations for
> each emotion type and each task type. If you conduct separate analyses for
> each emotion type (for example), you would have to analyze these moderators
> separately, so you'd end up with 6 sets of moderator analyses instead of
> just one.
>
> The main challenge in the "one big meta-analysis model" approach is that
> it requires careful checking of the model's assumptions. For example, you
> would need to assess whether the between-study heterogeneity is similar
> across the six emotion types and, if not, fit a model that allows for
> different heterogeneity levels for each emotion.
>
> James
>
>
> Hwang, H., & DeSantis, S. M. (2018). Multivariate network meta‐analysis to
> mitigate the effects of outcome reporting bias. *Statistics in medicine*.
>
> Kirkham, J. J., Riley, R. D., & Williamson, P. R. (2012). A multivariate
> meta‐analysis approach for reducing the impact of outcome reporting bias in
> systematic reviews. *Statistics in medicine*, *31*(20), 2179-2195.
>
> On Mon, Feb 11, 2019 at 3:16 AM Grace Hayes <grace.hayes3 using myacu.edu.au>
> wrote:
>
> Hi all,
>
>
> I have a question regarding a meta-analysis of multiple dependent outcomes
> that I would like to conduct using metafor.
>
>
> For this meta-analysis of emotion recognition in ageing, I'm interested in
> age-effects (young adults vs. older adults) on four different emotion
> recognition tasks (Task A, Task B, Task C, Task D). Studies in this area
> typically compare older adults' performance to younger adults' performance
> on more than one of these emotion recognition task.
>
>
> For each task there are also multiple outcomes.  Each task produces an
> accuracy age-effect for each emotion type included (I.e., anger, sadness,
> fear). Up to 6 different emotions are included (Emotion 1, Emotion 2,
> Emotion 3, Emotion 4, Emotion 5, Emotion 6). I therefore have some studies
> with, for example, 6 different age-effects from 3 different emotions tasks;
> a total of 18 dependent outcomes.
>
>
> Ideally I would like to investigate age-effects for each of the six
> emotion types seperately (with Tasks A, B, C and D combined), and
> age-effects for each task type seperately (with Emotions 1-6 combined). I
> would then like to compare the effects for each emotion type (Emotions 1-6
> separately) produced by each task  (Measure A, B, C, D separately).
>
>
> My question is, can I have a model that analyses emotion type and task
> type all together? Is this possible and statistically appropriate? Will it
> tell me the age-effects produced for each emotion by each task, or will it
> only tell me if task type and emotion type are significant moderators?
>
>
> I am also interested to know if I can add additional moderators such as
> number of emotions included in the task and year of publication?
>
>
> One concern that has been brought to my attention is overfitting from too
> many factors. Another is that output would be difficult too interpret, and
> thus it has been recommended that I perhaps run separately analyses for
> each task.
>
>
> Any advice would be much appreciated.
>
>
> Sincerely,
>
> Grace Hayes
>
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>
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