[R-meta] Dependent Measure Modelling Question

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 at gmail.com>
*Sent:* Tuesday, 12 February 2019 1:37 PM
*To:* Grace Hayes
*Cc:* r-sig-meta-analysis at 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 at 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

        [[alternative HTML version deleted]]

Thanks again James,

In terms of the structure of my data; emotion outcomes ('Emotion'), are
nested in tasks ('StimuliType'), which are nested in studies ('StudyID).

The variable 'outcome' is one that I created that is a combination of the
'Emotion' and 'StimuliType' factors (i.e., DynamicAnger, StaticAnger,
StaticDisgust), whereas the variable 'effectID' contains an unique identifier
for each effect.

I created these variables and defined the random effects as, random = ~ 1
|  studyID/outcome/effectID, to account for the fact that some studies
produced effects with the same factor combination (i.e., the same emotion
from two tasks of the same stimuli type). Therefore, effects with the same
factor combination ('outcome') but different studyID were independent, but
effects with the same factor combination ('outcome') and the same studyID
were dependent.

Perhaps then, to apply the inner|outer formula to my data I would need to
instead use Emotion|effectID?

Cheers,
Grace


*Grace Hayes*

Psychologist | Doctor of Philosophy (PhD) Candidate

Cognition and Emotion Research Centre

School of Behavioural and Health Sciences, Faculty of Health Sciences

Australian Catholic University





Level 3, Mary Glowrey Building,

115 Victoria Parade, Fitzroy, VIC 3065
*T:* +61 3 9230 8131
*E**:* grace.hayes3 at myacu.edu.au
*W:* http://ccaer.acu.edu.au/




------------------------------
*From:* James Pustejovsky <jepusto at gmail.com>
*Sent:* Thursday, 14 March 2019 2:21 AM
*To:* Grace Hayes
*Cc:* r-sig-meta-analysis at r-project.org
*Subject:* Re: [R-meta] Dependent Measure Modelling Question

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 at 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 at gmail.com>
*Sent:* Tuesday, 12 February 2019 1:37 PM
*To:* Grace Hayes
*Cc:* r-sig-meta-analysis at 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 at 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

        [[alternative HTML version deleted]]

Hi James,

Yes that is correct, I have some studies with multiple ES estimates for
the same combination of task and emotion.

Grace


*Grace Hayes*

Psychologist | Doctor of Philosophy (PhD) Candidate

Cognition and Emotion Research Centre

School of Behavioural and Health Sciences, Faculty of Health Sciences

Australian Catholic University





Level 3, Mary Glowrey Building,

115 Victoria Parade, Fitzroy, VIC 3065
*T:* +61 3 9230 8131
*E**:* grace.hayes3 at myacu.edu.au
*W:* http://ccaer.acu.edu.au/




------------------------------
*From:* James Pustejovsky <jepusto at gmail.com>
*Sent:* Friday, 22 March 2019 1:37 PM
*To:* Grace Hayes
*Cc:* r-sig-meta-analysis at r-project.org
*Subject:* Re: [R-meta] Dependent Measure Modelling Question

Grace,

Sorry for the delay getting back to you. Your response is helpful in
clarifying the structure of your data, but I'm still not sure I follow why
you need the unique effectID in the model. Are there some studies where you
have multiple ES estimates for the same combination of emotion and task
(e.g., two measures of dynamic anger)?

James

On Wed, Mar 13, 2019 at 10:37 PM Grace Hayes <grace.hayes3 at myacu.edu.au>
wrote:

Thanks again James,

In terms of the structure of my data; emotion outcomes ('Emotion'), are
nested in tasks ('StimuliType'), which are nested in studies ('StudyID).

The variable 'outcome' is one that I created that is a combination of the
'Emotion' and 'StimuliType' factors (i.e., DynamicAnger, StaticAnger,
StaticDisgust), whereas the variable 'effectID' contains an unique identifier
for each effect.

I created these variables and defined the random effects as, random = ~ 1
|  studyID/outcome/effectID, to account for the fact that some studies
produced effects with the same factor combination (i.e., the same emotion
from two tasks of the same stimuli type). Therefore, effects with the same
factor combination ('outcome') but different studyID were independent, but
effects with the same factor combination ('outcome') and the same studyID
were dependent.

Perhaps then, to apply the inner|outer formula to my data I would need to
instead use Emotion|effectID?

Cheers,
Grace


*Grace Hayes*

Psychologist | Doctor of Philosophy (PhD) Candidate

Cognition and Emotion Research Centre

School of Behavioural and Health Sciences, Faculty of Health Sciences

Australian Catholic University





Level 3, Mary Glowrey Building,

115 Victoria Parade, Fitzroy, VIC 3065
*T:* +61 3 9230 8131
*E**:* grace.hayes3 at myacu.edu.au
*W:* http://ccaer.acu.edu.au/




------------------------------
*From:* James Pustejovsky <jepusto at gmail.com>
*Sent:* Thursday, 14 March 2019 2:21 AM
*To:* Grace Hayes
*Cc:* r-sig-meta-analysis at r-project.org
*Subject:* Re: [R-meta] Dependent Measure Modelling Question

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 at 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 at gmail.com>
*Sent:* Tuesday, 12 February 2019 1:37 PM
*To:* Grace Hayes
*Cc:* r-sig-meta-analysis at 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 at 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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