thr3ads.net - R help - [R] meta analysis with repeated measure-designs? [Jun 2010]

If this information is useful, please help other people find it:
Share via:

Gerrit Hirschfeld

2010-Jun-12 10:44 UTC

[R] meta analysis with repeated measure-designs?

Dear all,

I am trying to run a meta analysis of psycholinguistic reaction-time experiments
with the meta package. The problem is that most of the studies have a
within-subject designs and use repeated measures ANOVAs to analyze their data.
So at present it seems that there are three non-optimal ways to run the
analysis.

1. Using metacont() to estimate effect sizes and standard errors. But as the
different sores are dependent this would result in biased estimators (Dunlap,
1996). Suppose I had the correlations of the measures (which I do not) would
there by an option to use them in metacont() ?

2. Use metagen() with an effect size that is based on the reported F for the
contrasts but has other disadvantages (Bakeman, 2005). The problem I am having
with this is that I could not find a formular to compute the standard error of
partial eta squared. Any Ideas?

3. Use metagen() with r computed from p-values (Rosenthal, 1994) as effect size
with the problem that sample-size affects p as much as effect size.

Is there a fourth way, or data showing that correlations can be neglected as
long as they are assumed to be similar in the studies?
Any ideas are much apprecciated. 

best regards
Gerrit

______________________________
Gerrit Hirschfeld, Dipl.-Psych.

Psychologisches Institut II
Westf?lische Wilhelms-Universit?t
Fliednerstr. 21
48149 M?nster
Germany

psycholinguistics.uni-muenster.de
GerritHirschfeld.de
Fon.: +49 (0) 251 83-31378
Fon.: +49 (0) 234 7960728
Fax.: +49 (0) 251 83-34104

Viechtbauer Wolfgang (STAT)

2010-Jun-12 13:59 UTC

head link

[R] meta analysis with repeated measure-designs?

Dear Gerrit,

the most appropriate approach for data of this type would be a proper
multivariate meta-analytic model (along the lines of Kalaian & Raudenbush,
1996). Since you do not know the correlations of the reaction time measurements
across conditions for the within-subject designs, a simple solution is to
"guestimate" those correlations and then conduct sensitivity analyses
to make sure your conclusions do not depend on those guestimates.

Best,

--
Wolfgang Viechtbauer                        http://www.wvbauer.com/
Department of Methodology and Statistics    Tel: +31 (0)43 388-2277
School for Public Health and Primary Care   Office Location:
Maastricht University, P.O. Box 616         Room B2.01 (second floor)
6200 MD Maastricht, The Netherlands         Debyeplein 1 (Randwyck)


----Original Message----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Gerrit Hirschfeld Sent: Saturday, June 12, 2010 12:45
To: r-help at r-project.org
Subject: [R] meta analysis with repeated measure-designs?
> Dear all,
>
> I am trying to run a meta analysis of psycholinguistic reaction-time
> experiments with the meta package. The problem is that most of the
> studies have a within-subject designs and use repeated measures ANOVAs to
> analyze their data. So at present it seems that there are three
> non-optimal ways to run the analysis.
>
> 1. Using metacont() to estimate effect sizes and standard errors. But as
> the different sores are dependent this would result in biased estimators
> (Dunlap, 1996). Suppose I had the correlations of the measures (which I
> do not) would there by an option to use them in metacont() ?
>
> 2. Use metagen() with an effect size that is based on the reported F for
> the contrasts but has other disadvantages (Bakeman, 2005). The problem I
> am having with this is that I could not find a formular to compute the
> standard error of partial eta squared. Any Ideas?
>
> 3. Use metagen() with r computed from p-values (Rosenthal, 1994) as
> effect size with the problem that sample-size affects p as much as effect
> size.
>
> Is there a fourth way, or data showing that correlations can be neglected
> as long as they are assumed to be similar in the studies?
> Any ideas are much apprecciated.
>
> best regards
> Gerrit
>
> ______________________________
> Gerrit Hirschfeld, Dipl.-Psych.
>
> Psychologisches Institut II
> Westf?lische Wilhelms-Universit?t
> Fliednerstr. 21
> 48149 M?nster
> Germany
>
> psycholinguistics.uni-muenster.de
> GerritHirschfeld.de
> Fon.: +49 (0) 251 83-31378
> Fon.: +49 (0) 234 7960728
> Fax.: +49 (0) 251 83-34104
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Gerrit Hirschfeld

2010-Jun-14 08:58 UTC

head link

[R] meta analysis with repeated measure-designs?

Hi, 

thanks for the references I will try the sensitivitiy-analysis in R and try out
winbugs if that does not work (little afraid of switching programmes).

I also had an idea for a reasonable estimate of the correlations. Some studies
report both results from paired t-tests and means and SDs, and thus allow to
calculate two estimates for d one based on M and SD alone the other on t. The
difference between the two estimates should be systematically related to the
correlations of measures.

I will keep you posted, if I have a solution or hit a wall.

efachristo and dank je wel!

Gerrit


On 12.06.2010, at 15:59, Viechtbauer Wolfgang (STAT) wrote:
> Dear Gerrit,
> 
> the most appropriate approach for data of this type would be a proper
multivariate meta-analytic model (along the lines of Kalaian & Raudenbush,
1996). Since you do not know the correlations of the reaction time measurements
across conditions for the within-subject designs, a simple solution is to
"guestimate" those correlations and then conduct sensitivity analyses
to make sure your conclusions do not depend on those guestimates.
> 
> Best,
> 
> --
> Wolfgang Viechtbauer                        http://www.wvbauer.com/
> Department of Methodology and Statistics    Tel: +31 (0)43 388-2277
> School for Public Health and Primary Care   Office Location:
> Maastricht University, P.O. Box 616         Room B2.01 (second floor)
> 6200 MD Maastricht, The Netherlands         Debyeplein 1 (Randwyck)
> 
> 
> ----Original Message----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at
r-project.org] On
> Behalf Of Gerrit Hirschfeld Sent: Saturday, June 12, 2010 12:45
> To: r-help at r-project.org
> Subject: [R] meta analysis with repeated measure-designs?
> 
>> Dear all,
>> 
>> I am trying to run a meta analysis of psycholinguistic reaction-time
>> experiments with the meta package. The problem is that most of the
>> studies have a within-subject designs and use repeated measures ANOVAs
to
>> analyze their data. So at present it seems that there are three
>> non-optimal ways to run the analysis.
>> 
>> 1. Using metacont() to estimate effect sizes and standard errors. But
as
>> the different sores are dependent this would result in biased
estimators
>> (Dunlap, 1996). Suppose I had the correlations of the measures (which I
>> do not) would there by an option to use them in metacont() ?
>> 
>> 2. Use metagen() with an effect size that is based on the reported F
for
>> the contrasts but has other disadvantages (Bakeman, 2005). The problem
I
>> am having with this is that I could not find a formular to compute the
>> standard error of partial eta squared. Any Ideas?
>> 
>> 3. Use metagen() with r computed from p-values (Rosenthal, 1994) as
>> effect size with the problem that sample-size affects p as much as
effect
>> size.
>> 
>> Is there a fourth way, or data showing that correlations can be
neglected
>> as long as they are assumed to be similar in the studies?
>> Any ideas are much apprecciated.
>> 
>> best regards
>> Gerrit
>> 
>> ______________________________
>> Gerrit Hirschfeld, Dipl.-Psych.
>> 
>> Psychologisches Institut II
>> Westf?lische Wilhelms-Universit?t
>> Fliednerstr. 21
>> 48149 M?nster
>> Germany
>> 
>> psycholinguistics.uni-muenster.de
>> GerritHirschfeld.de
>> Fon.: +49 (0) 251 83-31378
>> Fon.: +49 (0) 234 7960728
>> Fax.: +49 (0) 251 83-34104
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
______________________________
Gerrit Hirschfeld, Dipl.-Psych.

Psychologisches Institut II
Westf?lische Wilhelms-Universit?t
Fliednerstr. 21
48149 M?nster
Germany

psycholinguistics.uni-muenster.de
GerritHirschfeld.de
Fon.: +49 (0) 251 83-31378
Fon.: +49 (0) 234 7960728
Fax.: +49 (0) 251 83-34104

Mike Cheung

2010-Jun-16 08:47 UTC

head link

[R] meta analysis with repeated measure-designs?

Dear Gerrit,

If the correlations of the dependent effect sizes are unknown, one
approach is to conduct the meta-analysis by assuming that the effect
sizes are independent. A robust standard error is then calculated to
adjust for the dependence. You may refer to Hedges et. al., (2010) for
more information. I have coded it here for reference.

Hedges, L. V., Tipton, E., & Johnson, M. C. (2010). Robust variance
estimation in meta-regression with dependent effect size estimates.
Research Synthesis Methods, 1(1), 39-65. doi:10.1002/jrsm.5

Regards,
Mike
-- 
---------------------------------------------------------------------
 Mike W.L. Cheung               Phone: (65) 6516-3702
 Department of Psychology       Fax:   (65) 6773-1843
 National University of Singapore
 http://courses.nus.edu.sg/course/psycwlm/internet/
---------------------------------------------------------------------

library(metafor)

#### Robust SE based on Hedges et al., (2010) Eq. 6
#### rma.obj: object fitted by metafor()
#### cluster: indicator for clusters of studies
robustSE <- function(rma.obj, cluster=NULL, CI=.95) {
  # m: no. of clusters; assumed independent if not specified
  if (is.null(cluster)) {
      m=nrow(rma.obj$X)
  } else {
      m=nlevels(unique(as.factor(cluster)))
  }
  res2 <- diag(residuals(rma.obj)^2)
  X <- rma.obj$X
  b <- rma.obj$b
  W <- diag(1/(rma.obj$vi+rma.obj$tau2))     # Use vi+tau2
  meat <- t(X) %*% W %*% res2 %*% W %*% X    # W is symmetric
  bread <- solve( t(X) %*% W %*% X)
  V.R <- bread %*% meat %*% bread            # Robust sampling covariance
matrix
  p <- length(b)                             # no. of predictors
including intercept
  se.R <- sqrt( diag(V.R)*m/(m-p) )          # small sample adjustment (Eq.7)
  t.R <- b/se.R
  p.R <- 2*(1-pt(abs(t.R),df=(m-p)))
  crit <- qt( 1-CI/2, df=(m-p) )
  ci.lb <- b-crit*se.R
  ci.ub <- b+crit*se.R
  data.frame(estimate=b, se.R=se.R, t.R=t.R, p.R=p.R, ci.lb=ci.lb, ci.ub=ci.ub)
}


## Example: calculate log relative risks and corresponding sampling variances
data(dat.bcg)
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg,
data=dat.bcg)
dat <- cbind(dat.bcg, dat)

## random-effects model
fit1 <- rma(yi, vi, data=dat, method="DL")
summary(fit1)

estimate       se     zval     pval    ci.lb    ci.ub
 -0.7141   0.1787  -3.9952   <.0001  -1.0644  -0.3638      ***

## Robust SE
robustSE(fit1)
          estimate      se.R       t.R         p.R     ci.lb      ci.ub
intrcpt -0.7141172 0.1791445 -3.986265 0.001805797 -0.725588 -0.7026465

## mixed-effects model with two moderators (absolute latitude and
publication year)
fit2 <- rma(yi, vi, mods=cbind(ablat, year), data=dat, method="DL")
summary(fit2)

         estimate       se     zval    pval     ci.lb    ci.ub
intrcpt   -1.2798  25.7550  -0.0497  0.9604  -51.7586  49.1990
ablat     -0.0288   0.0090  -3.2035  0.0014   -0.0464  -0.0112  **
year       0.0008   0.0130   0.0594  0.9526   -0.0247   0.0262

### Robust SE
robustSE(fit2)
             estimate         se.R         t.R         p.R         ci.lb
intrcpt -1.2797914381 22.860353022 -0.05598301 0.956458098 -2.749670e+00
ablat   -0.0287644840  0.007212163 -3.98832970 0.002566210 -2.922821e-02
year     0.0007720798  0.011550188  0.06684565 0.948022174  2.942412e-05
               ci.ub
intrcpt  0.190086881
ablat   -0.028300755
year     0.001514735




On Mon, Jun 14, 2010 at 4:58 PM, Gerrit Hirschfeld
<Gerrit.Hirschfeld at uni-muenster.de> wrote:> Hi,
>
> thanks for the references I will try the sensitivitiy-analysis in R and try
out winbugs if that does not work (little afraid of switching programmes).
>
> I also had an idea for a reasonable estimate of the correlations. Some
studies report both results from paired t-tests and means and SDs, and thus
allow to calculate two estimates for d one based on M and SD alone the other on
t. The difference between the two estimates should be systematically related to
the correlations of measures.
>
> I will keep you posted, if I have a solution or hit a wall.
>
> efachristo and dank je wel!
>
> Gerrit
>
>
> On 12.06.2010, at 15:59, Viechtbauer Wolfgang (STAT) wrote:
>
>> Dear Gerrit,
>>
>> the most appropriate approach for data of this type would be a proper
multivariate meta-analytic model (along the lines of Kalaian & Raudenbush,
1996). Since you do not know the correlations of the reaction time measurements
across conditions for the within-subject designs, a simple solution is to
"guestimate" those correlations and then conduct sensitivity analyses
to make sure your conclusions do not depend on those guestimates.
>>
>> Best,
>>
>> --
>> Wolfgang Viechtbauer ? ? ? ? ? ? ? ? ? ? ? ?http://www.wvbauer.com/
>> Department of Methodology and Statistics ? ?Tel: +31 (0)43 388-2277
>> School for Public Health and Primary Care ? Office Location:
>> Maastricht University, P.O. Box 616 ? ? ? ? Room B2.01 (second floor)
>> 6200 MD Maastricht, The Netherlands ? ? ? ? Debyeplein 1 (Randwyck)
>>
>>
>> ----Original Message----
>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at
r-project.org] On
>> Behalf Of Gerrit Hirschfeld Sent: Saturday, June 12, 2010 12:45
>> To: r-help at r-project.org
>> Subject: [R] meta analysis with repeated measure-designs?
>>
>>> Dear all,
>>>
>>> I am trying to run a meta analysis of psycholinguistic
reaction-time
>>> experiments with the meta package. The problem is that most of the
>>> studies have a within-subject designs and use repeated measures
ANOVAs to
>>> analyze their data. So at present it seems that there are three
>>> non-optimal ways to run the analysis.
>>>
>>> 1. Using metacont() to estimate effect sizes and standard errors.
But as
>>> the different sores are dependent this would result in biased
estimators
>>> (Dunlap, 1996). Suppose I had the correlations of the measures
(which I
>>> do not) would there by an option to use them in metacont() ?
>>>
>>> 2. Use metagen() with an effect size that is based on the reported
F for
>>> the contrasts but has other disadvantages (Bakeman, 2005). The
problem I
>>> am having with this is that I could not find a formular to compute
the
>>> standard error of partial eta squared. Any Ideas?
>>>
>>> 3. Use metagen() with r computed from p-values (Rosenthal, 1994) as
>>> effect size with the problem that sample-size affects p as much as
effect
>>> size.
>>>
>>> Is there a fourth way, or data showing that correlations can be
neglected
>>> as long as they are assumed to be similar in the studies?
>>> Any ideas are much apprecciated.
>>>
>>> best regards
>>> Gerrit
>>>
>>> ______________________________
>>> Gerrit Hirschfeld, Dipl.-Psych.
>>>
>>> Psychologisches Institut II
>>> Westf?lische Wilhelms-Universit?t
>>> Fliednerstr. 21
>>> 48149 M?nster
>>> Germany
>>>
>>> psycholinguistics.uni-muenster.de
>>> GerritHirschfeld.de
>>> Fon.: +49 (0) 251 83-31378
>>> Fon.: +49 (0) 234 7960728
>>> Fax.: +49 (0) 251 83-34104
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________
> Gerrit Hirschfeld, Dipl.-Psych.
>
> Psychologisches Institut II
> Westf?lische Wilhelms-Universit?t
> Fliednerstr. 21
> 48149 M?nster
> Germany
>
> psycholinguistics.uni-muenster.de
> GerritHirschfeld.de
> Fon.: +49 (0) 251 83-31378
> Fon.: +49 (0) 234 7960728
> Fax.: +49 (0) 251 83-34104
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Mike Cheung

2010-Jun-18 09:21 UTC

head link

[R] meta analysis with repeated measure-designs?

Dear Gerrit,

Sorry. There was an error in my previous code. As a record, the
followings are the revised code.


#### Robust SE based on Hedges et al., (2010) Eq. 6 on Research
Synthesis Methods
#### rma.obj: object fitted by metafor()
#### cluster: indicator for clusters of studies
robustSE <- function(rma.obj, cluster=NULL, CI=.95) {
  # m: no. of clusters; assumed independent if not specified
  # rma.obj$not.na: complete cases
  if (is.null(cluster)) {
      m=length(rma.obj$X[rma.obj$not.na,1])
  } else {
      m=nlevels(unique(as.factor(cluster[rma.obj$not.na])))
  }
  res2 <- diag(residuals(rma.obj)^2)
  X <- rma.obj$X
  b <- rma.obj$b
  W <- diag(1/(rma.obj$vi+rma.obj$tau2))     # Use vi+tau2
  meat <- t(X) %*% W %*% res2 %*% W %*% X    # W is symmetric
  bread <- solve( t(X) %*% W %*% X)
  V.R <- bread %*% meat %*% bread            # Robust sampling covariance
matrix
  p <- length(b)                             # no. of predictors
including intercept
  se <- sqrt( diag(V.R)*m/(m-p) )            # small sample adjustment (Eq.7)
  tval <- b/se
  pval <- 2*(1-pt(abs(tval),df=(m-p)))
  crit <- qt( (1-CI)/2, df=(m-p), lower.tail=FALSE )
  ci.lb <- b-crit*se
  ci.ub <- b+crit*se
  data.frame(estimate=b, se=se, tval=tval, pval=pval, ci.lb=ci.lb, ci.ub=ci.ub)
}

library(metafor)
data(dat.bcg)

### calculate log relative risks and corresponding sampling variances
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg,
data=dat.bcg)
dat <- cbind(dat.bcg, dat)

### random-effects model
fit1 <- rma(yi, vi, data=dat, method="DL")
summary(fit1)

estimate       se     zval     pval    ci.lb    ci.ub
 -0.7141   0.1787  -3.9952   <.0001  -1.0644  -0.3638      ***

robustSE(fit1)
          estimate        se      tval        pval     ci.lb     ci.ub
intrcpt -0.7141172 0.1791445 -3.986265 0.001805797 -1.104439 -0.323795

### mixed-effects model with two moderators (absolute latitude and
publication year)
fit2 <- rma(yi, vi, mods=cbind(ablat, year), data=dat, method="DL")
summary(fit2)

         estimate       se     zval    pval     ci.lb    ci.ub
intrcpt   -1.2798  25.7550  -0.0497  0.9604  -51.7586  49.1990
ablat     -0.0288   0.0090  -3.2035  0.0014   -0.0464  -0.0112  **
year       0.0008   0.0130   0.0594  0.9526   -0.0247   0.0262

robustSE(fit2)
             estimate           se        tval        pval
ci.lb       ci.ub
intrcpt -1.2797914381 22.860353022 -0.05598301 0.956458098
-52.21583218 49.65624930
ablat   -0.0287644840  0.007212163 -3.98832970 0.002566210
-0.04483418 -0.01269478
year     0.0007720798  0.011550188  0.06684565 0.948022174
-0.02496334  0.02650750

-- 
---------------------------------------------------------------------
 Mike W.L. Cheung               Phone: (65) 6516-3702
 Department of Psychology       Fax:   (65) 6773-1843
 National University of Singapore
 http://courses.nus.edu.sg/course/psycwlm/internet/
---------------------------------------------------------------------

On Wed, Jun 16, 2010 at 4:47 PM, Mike Cheung <mikewlcheung at gmail.com>
wrote:> Dear Gerrit,
>
> If the correlations of the dependent effect sizes are unknown, one
> approach is to conduct the meta-analysis by assuming that the effect
> sizes are independent. A robust standard error is then calculated to
> adjust for the dependence. You may refer to Hedges et. al., (2010) for
> more information. I have coded it here for reference.
>
> Hedges, L. V., Tipton, E., & Johnson, M. C. (2010). Robust variance
> estimation in meta-regression with dependent effect size estimates.
> Research Synthesis Methods, 1(1), 39-65. doi:10.1002/jrsm.5
>
> Regards,
> Mike
> --
> ---------------------------------------------------------------------
> ?Mike W.L. Cheung ? ? ? ? ? ? ? Phone: (65) 6516-3702
> ?Department of Psychology ? ? ? Fax: ? (65) 6773-1843
> ?National University of Singapore
> ?http://courses.nus.edu.sg/course/psycwlm/internet/
> ---------------------------------------------------------------------
>
> library(metafor)
>
> #### Robust SE based on Hedges et al., (2010) Eq. 6
> #### rma.obj: object fitted by metafor()
> #### cluster: indicator for clusters of studies
> robustSE <- function(rma.obj, cluster=NULL, CI=.95) {
> ?# m: no. of clusters; assumed independent if not specified
> ?if (is.null(cluster)) {
> ? ? ?m=nrow(rma.obj$X)
> ?} else {
> ? ? ?m=nlevels(unique(as.factor(cluster)))
> ?}
> ?res2 <- diag(residuals(rma.obj)^2)
> ?X <- rma.obj$X
> ?b <- rma.obj$b
> ?W <- diag(1/(rma.obj$vi+rma.obj$tau2)) ? ? # Use vi+tau2
> ?meat <- t(X) %*% W %*% res2 %*% W %*% X ? ?# W is symmetric
> ?bread <- solve( t(X) %*% W %*% X)
> ?V.R <- bread %*% meat %*% bread ? ? ? ? ? ?# Robust sampling covariance
matrix
> ?p <- length(b) ? ? ? ? ? ? ? ? ? ? ? ? ? ? # no. of predictors
> including intercept
> ?se.R <- sqrt( diag(V.R)*m/(m-p) ) ? ? ? ? ?# small sample adjustment
(Eq.7)
> ?t.R <- b/se.R
> ?p.R <- 2*(1-pt(abs(t.R),df=(m-p)))
> ?crit <- qt( 1-CI/2, df=(m-p) )
> ?ci.lb <- b-crit*se.R
> ?ci.ub <- b+crit*se.R
> ?data.frame(estimate=b, se.R=se.R, t.R=t.R, p.R=p.R, ci.lb=ci.lb,
ci.ub=ci.ub)
> }
>
>
> ## Example: calculate log relative risks and corresponding sampling
variances
> data(dat.bcg)
> dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos,
di=cneg, data=dat.bcg)
> dat <- cbind(dat.bcg, dat)
>
> ## random-effects model
> fit1 <- rma(yi, vi, data=dat, method="DL")
> summary(fit1)
>
> estimate ? ? ? se ? ? zval ? ? pval ? ?ci.lb ? ?ci.ub
> ?-0.7141 ? 0.1787 ?-3.9952 ? <.0001 ?-1.0644 ?-0.3638 ? ? ?***
>
> ## Robust SE
> robustSE(fit1)
> ? ? ? ? ?estimate ? ? ?se.R ? ? ? t.R ? ? ? ? p.R ? ? ci.lb ? ? ?ci.ub
> intrcpt -0.7141172 0.1791445 -3.986265 0.001805797 -0.725588 -0.7026465
>
> ## mixed-effects model with two moderators (absolute latitude and
> publication year)
> fit2 <- rma(yi, vi, mods=cbind(ablat, year), data=dat,
method="DL")
> summary(fit2)
>
> ? ? ? ? estimate ? ? ? se ? ? zval ? ?pval ? ? ci.lb ? ?ci.ub
> intrcpt ? -1.2798 ?25.7550 ?-0.0497 ?0.9604 ?-51.7586 ?49.1990
> ablat ? ? -0.0288 ? 0.0090 ?-3.2035 ?0.0014 ? -0.0464 ?-0.0112 ?**
> year ? ? ? 0.0008 ? 0.0130 ? 0.0594 ?0.9526 ? -0.0247 ? 0.0262
>
> ### Robust SE
> robustSE(fit2)
> ? ? ? ? ? ? estimate ? ? ? ? se.R ? ? ? ? t.R ? ? ? ? p.R ? ? ? ? ci.lb
> intrcpt -1.2797914381 22.860353022 -0.05598301 0.956458098 -2.749670e+00
> ablat ? -0.0287644840 ?0.007212163 -3.98832970 0.002566210 -2.922821e-02
> year ? ? 0.0007720798 ?0.011550188 ?0.06684565 0.948022174 ?2.942412e-05
> ? ? ? ? ? ? ? ci.ub
> intrcpt ?0.190086881
> ablat ? -0.028300755
> year ? ? 0.001514735
>

R help - Jun 2010 - meta analysis with repeated measure-designs?

[R] meta analysis with repeated measure-designs?

[R] meta analysis with repeated measure-designs?

[R] meta analysis with repeated measure-designs?

[R] meta analysis with repeated measure-designs?

[R] meta analysis with repeated measure-designs?