[R-meta] between-study variance
James Pustejovsky
jepu@to @end|ng |rom gm@||@com
Thu Jan 19 17:29:06 CET 2023
Wolfgang's points are spot-on. I would add, the second point about
accounting for the correlation between effect size estimates is worth
digging into a bit. The assumption you make about correlation here (or lack
of correlation) can definitely influence the variance component estimates,
shifting variance from the between-study level to the within-study level or
vice versa. I looked at this a little bit in the supplementary materials (
https://osf.io/nyv4u) of my paper with Tipton on expanding working models
for RVE meta-analysis (
https://www.jepusto.com/publication/rve-meta-analysis-expanding-the-range/).
See Section S4.3 especially.
James
On Thu, Jan 19, 2023 at 9:51 AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> Dear Karen,
>
> In principle, variance components can be equal to 0. That is not
> automatically an indication that there is something wrong.
>
> A few observations:
>
> 1) You are including "factor(Cell)-1" as a moderator, which apparently is
> a factor with 10 levels (hence, the QM-statistic has 10 dfs). If this
> moderator varies (mostly) at the study level, then with 27 studies it could
> be the case that this moderator 'sucks up' the study level heterogeneity.
> What happens when you leave out this moderator?
>
> 2) I see that the input to V is called 'invn'. This appears to be a vector
> with the inverse sample sizes (e.g., 1/0.000509684 = 1962). This is not
> quite right for computing the sampling variance of correlation
> coefficients. More importantly, this does not capture the covariance
> between multiple correlation coefficients coming from the same sample. See
> help(rcalc) for a function that will construct the var-cov matrix for
> dependent correlation coefficients.
>
> As for simplified dataset: The copy of dput() you put below got cut off.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of Karen Alexander
> >Sent: Thursday, 19 January, 2023 16:33
> >To: r-sig-meta-analysis using r-project.org
> >Subject: Re: [R-meta] between-study variance
> >
> >Hello,
> >
> >I am a PhD candidate at the University of Nebraska-Lincoln in the
> Quantitative,
> >Qualitative, and Psychometric program and am running a meta-analysis with
> complex
> >data using the framework from Wilson, et al., (2016) (Fitting
> meta-analytic
> >structural equation models with complex datasets) https://doi-
> >org.libproxy.unl.edu/10.1002/jrsm.1199
> >
> >Specifically, when running the following code to get the unadjusted pooled
> >correlation matrix without the intercept
> >
> >step1 <- rma.mv(yi = r, V = invn,
> > data = data1,
> > random = list(~ 1|studyID, ~ 1|ESID),
> > method = "ML", mods = ~ factor(Cell)-1)
> >summary(step1)
> >
> >I get the following output which indicates that the between-study
> variance is 0.
> >
> >
> >Multivariate Meta-Analysis Model (k = 376; method: ML)
> >
> > logLik Deviance AIC BIC AICc
> > 87.6057 1749.7597 -151.2114 -104.0563 -150.3519
> >
> >Variance Components:
> >
> > estim sqrt nlvls fixed factor
> >sigma^2.1 0.0000 0.0000 28 no studyID
> >sigma^2.2 0.0339 0.1841 376 no ESID
> >
> >Test for Residual Heterogeneity:
> >QE(df = 366) = 12265.8732, p-val < .0001
> >
> >Test of Moderators (coefficients 1:10):
> >QM(df = 10) = 110.8337, p-val < .0001
> >
> >Model Results:
> >
> >---
> >Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> >
> >1) I find that hard to believe. So, I made a subset of my data and ran
> the model
> >with the subset, and while all other values changed, the between-study
> variance
> >was still 0.
> >
> >2) So, now I am questioning either my code and/or my dataset.
> >
> >Because of the complexity of the data, the dataset is rather wieldy. I
> have a
> >simplified version below, but it may need to be sent as an attachment,
> which I am
> >happy to do as well.
> >
> >structure(list(studyID = c(10000L, 10000L, 10000L, 10000L, 10000L,
> >10000L, 10000L, 10000L, 10000L, 10000L, 10000L, 10000L, 10000L,
> >10000L, 10000L, 10000L, 10000L, 10000L, 10000L, 13000L, 13000L,
> >13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L,
> >13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L,
> >13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L,
> >14000L, 14000L, 14000L, 14000L, 14000L, 14000L, 15000L, 15000L,
> >15000L, 15000L, 15000L, 15000L, 15000L, 15000L, 15000L, 15000L,
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> >18000L, 19000L, 20000L, 20000L, 20000L, 20000L, 20000L, 20000L,
> >20000L, 20000L, 20000L, 21000L, 21000L, 21000L, 21000L, 21000L,
> >21000L, 21000L, 21000L, 21000L, 21000L, 21000L, 23000L, 23000L,
> >23000L, 23000L, 23000L, 23000L, 24000L, 24000L, 24000L, 24000L,
> >24000L, 24000L, 24000L, 24000L, 24000L, 24000L, 24000L, 24000L,
> >24000L, 24000L, 24000L, 24000L, 26000L, 26000L, 26000L, 26000L,
> >26000L, 26000L, 26000L, 26000L, 28000L, 28000L, 29000L, 29000L,
> >29000L, 29000L, 29000L, 30000L, 30000L, 30000L, 30000L, 30000L,
> >30000L, 30000L, 30000L, 30000L, 32000L, 32000L, 32000L, 32000L,
> >32000L, 32000L, 32000L, 32000L, 32000L, 32000L, 32000L, 32000L,
> >32000L, 32000L, 32000L, 32000L, 33000L, 33000L, 33000L, 33000L,
> >33000L, 33000L, 33000L, 33000L, 33000L, 33000L, 33000L, 33000L,
> >35000L, 35000L, 36000L, 36000L), ESID = c(10001L, 10002L, 10003L,
> >10004L, 10005L, 10006L, 10007L, 10008L, 10009L, 10010L, 10011L,
> >10012L, 10013L, 10014L, 10015L, 10016L, 10017L, 10018L, 10019L,
> >13001L, 13002L, 13003L, 13004L, 13005L, 13006L, 13007L, 13008L,
> >13009L, 13010L, 13011L, 13012L, 13013L, 13014L, 13015L, 13016L,
> >13017L, 13018L, 13019L, 13020L, 13021L, 13022L, 13023L, 13024L,
> >13025L, 13026L, 14001L, 14002L, 14003L, 14004L, 14005L, 14006L,
> >15001L, 15002L, 15003L, 15004L, 15005L, 15006L, 15007L, 15008L,
> >15009L, 15010L, 15011L, 15012L, 15013L, 15014L, 15015L, 15016L,
> >16001L, 17001L, 17002L, 17003L, 17004L, 17005L, 17006L, 17007L,
> >17008L, 18001L, 18002L, 19001L, 20001L, 20002L, 20003L, 20004L,
> >20005L, 20006L, 20007L, 20008L, 20009L, 21001L, 21002L, 21003L,
> >21004L, 21005L, 21006L, 21007L, 21008L, 21009L, 21010L, 21011L,
> >23001L, 23002L, 23003L, 23004L, 23005L, 23006L, 24001L, 24002L,
> >24003L, 24004L, 24005L, 24006L, 24007L, 24008L, 24009L, 24010L,
> >24011L, 24012L, 24013L, 24014L, 24015L, 24016L, 26001L, 26002L,
> >26003L, 26004L, 26005L, 26006L, 26007L, 26008L, 28001L, 28002L,
> >29001L, 29002L, 29003L, 29004L, 29005L, 30001L, 30002L, 30003L,
> >30004L, 30005L, 30006L, 30007L, 30008L, 30009L, 32001L, 32002L,
> >32003L, 32004L, 32005L, 32006L, 32007L, 32008L, 32009L, 32010L,
> >32011L, 32012L, 32013L, 32014L, 32015L, 32016L, 33001L, 33002L,
> >33003L, 33004L, 33005L, 33006L, 33007L, 33008L, 33009L, 33010L,
> >33011L, 33012L, 35001L, 35002L, 36001L, 36002L), Cell = c(4L,
> >4L, 7L, 7L, 4L, 4L, 7L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
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> >"r25", "r25", "r25", "r25", "r25", "r25", "r25", "r25", "r25",
> >"r25", "r25", "r25", "r25", "r25", "r25", "r25", "r25", "r25",
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> >"r25", "r15", "r25", "r15", "r25", "r15", "r25", "r25", "r25",
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> >"r12", "r12", "r25", "r25", "r15", "r25", "r25", "r25", "r25",
> >"r15", "r12", "r12", "r25", "r25", "r25", "r25", "r25", "r25",
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> >"r34", "r25", "r25", "r25", "r25", "r25", "r25", "r25", "r25",
> >"r25", "r25", "r25", "r25", "r35", "r25", "r25", "r25"), Cell1 = c(0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> >1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
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> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
> >), Cell2 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L), Cell3 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
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> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), Cell4 = c(1L, 1L, 0L, 0L,
> >1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
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> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 1L, 0L,
> >0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L,
> >0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L,
> >0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L,
> >0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), Cell5 = c(0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
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> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
> >), Cell6 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
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> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
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> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L), Cell7 = c(0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L,
> >1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> >1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L,
> >0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> >1L, 0L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 1L,
> >1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L,
> >1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
> >1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L), Cell8 = c(0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), Cell9 = c(0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L
> >), Cell10 = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
> >0L, 0L, 0L, 0L, 0L), r = c(0.01, 0.27, 0.19, 0.19, 0.29, 0.24,
> >0.19, 0.25, 0.22, 0.24, 0.31, 0.24, 0.3, -0.17, -0.25, -0.31,
> >0.09, 0.01, -0.01, 0.03, 0.05, 0.09, 0.07, 0.02, 0, 0.07, 0.04,
> >0.02, 0.04, 0.04, 0.04, 0.01, 0.15, 0.16, 0.15, 0.15, 0.17, 0,
> >0.02, -0.02, 0.01, 0.05, 0.08, 0.06, 0.06, 0.1, 0.02, 0.07, 0.07,
> >0, 0.06, -0.03, -0.06, 0.17, 0.27, 0.06, 0.08, 0.1, 0.08, 0.26,
> >0.02, 0.49, 0.41, 0.25, 0.21, 0.31, 0.36, 0.354, 0.1, 0.15, 0.46,
> >0.22, 0.01, 0.23, 0.09, -0.27, -0.048, 0.2, 0.15, 0.04, 0, -0.4,
> >0.02, 0.03, 0.08, 0.18, 0.26, 0.24, 0.02, -0.17, -0.04, -0.13,
> >-0.07, -0.15, 0.11, 0.13, 0.16, 0.42, 0.57, 0.093, 0.633, 0.264,
> >0.302, 0.055, 0.252, 0.01, 0.08, -0.01, -0.03, 0.08, 0.06, 0.1,
> >0.01, 0.08, 0.14, 0.44, 0.18, 0.02, 0.08, 0.44, 0.54, 0.09, -0.07,
> >0.09, 0.49, 0.11, 0.04, 0.01, 0.06, -0.52727, 0.0686, -0.01,
> >-0.09, -0.01, 0.5, 0.78, -0.04, -0.07, 0.47, -0.04, -0.03, 0.55,
> >-0.06, -0.04, 0.53, 0.09, 0.03, -0.07, 0.14, 0.11, 0.08, -0.03,
> >0.12, -0.25, 0.07, 0.09, -0.18, -0.1, 0.16, -0.09, 0.04, 0.06,
> >-0.003, 0.055, 0.025, -0.039, -0.076, 0.01, -0.055, -0.002, -0.111,
> >-0.102, -0.132, -0.05, 0.04, 0.07, 0.06), invn = c(0.000509684,
> >0.000509684, 0.000509684, 0.000509684, 0.000509684, 0.000509684,
> >0.000509684, 0.000509684, 0.000509684, 0.000509684, 0.000509684,
> >0.000509684, 0.000509684, 0.000509684, 0.000509684, 0.000509684,
> >0.000509684, 0.000509684, 0.000509684, 0.000615764, 0.000661813,
> >0.000666223, 0.000710732, 0.000615764, 0.000661813, 0.000666223,
> >0.000710732, 0.000661813, 0.000666223, 0.000710732, 0.000666223,
> >0.000710732, 0.000710732, 0.000615764, 0.000661813, 0.000666223,
> >0.000710732, 0.000615764, 0.000661813, 0.000666223, 0.000710732,
> >0.000615764, 0.000661813, 0.000666223, 0.000710732, 0.000931966,
> >0.000931966, 0.000931966, 0.000931966, 0.000931966, 0.000931966,
> >0.000693481, 0.000693481, 0.000693481, 0.000693481, 0.000693481,
> >0.000693481, 0.000693481, 0.000693481, 0.000693481, 0.000693481,
> >0.000693481, 0.000693481, 0.000693481, 0.000693481, 0.000693481,
> >0.000693481, 0.001061571, 0.001824818, 0.001824818, 0.001824818,
> >0.001824818, 0.001824818, 0.001824818, 0.001824818, 0.001824818,
> >0.017241379, 0.017241379, 0.005, 0.000714796, 0.000714796, 0.000714796,
> >0.000714796, 0.000714796, 0.000714796, 0.000714796, 0.000714796,
> >0.000714796, 0.005524862, 0.005524862, 0.005524862, 0.005524862,
> >0.005524862, 0.005524862, 0.005524862, 0.005524862, 0.005524862,
> >0.005524862, 0.005524862, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05,
> >0.000305623, 0.000305623, 0.000305623, 0.000305623, 0.000305623,
> >0.000305623, 0.000305623, 0.000305623, 0.000305623, 0.000305623,
> >0.000305623, 0.000305623, 0.000305623, 0.000305623, 0.000305623,
> >0.000305623, 0.005681818, 0.005681818, 0.005681818, 0.005681818,
> >0.005681818, 0.005681818, 0.005681818, 0.005681818, 0.041666667,
> >0.041666667, 0.006535948, 0.006535948, 0.006535948, 0.006535948,
> >0.006535948, 0.003816794, 0.003816794, 0.003816794, 0.003816794,
> >0.003816794, 0.003816794, 0.003816794, 0.003816794, 0.003816794,
> >0.003546099, 0.003546099, 0.003546099, 0.003546099, 0.003584229,
> >0.003584229, 0.003584229, 0.003584229, 0.003225806, 0.003225806,
> >0.003225806, 0.003225806, 0.003225806, 0.003225806, 0.003225806,
> >0.003225806, 0.005405405, 0.005405405, 0.005405405, 0.005405405,
> >0.007751938, 0.007751938, 0.007751938, 0.007751938, 0.005780347,
> >0.005780347, 0.005780347, 0.005780347, 0.001305483, 0.001305483,
> >0.004484305, 0.008130081)), class = "data.frame
> >
> >Any assistance that you can provide would be greatly appreciated. And, if
> in the
> >end there really is no between-study variance, how interesting!
> >Thank you in advance for your help!
> >
> >Karen M. Alexander Glueckert, M. Ed.
> >Ph. D. Candidate
> >
> >University of Nebraska-Lincoln
>
> _______________________________________________
> R-sig-meta-analysis mailing list @ R-sig-meta-analysis using r-project.org
> To manage your subscription to this mailing list, go to:
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis
>
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