[R-meta] between-study variance
Viechtbauer, Wolfgang (NP)
wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Thu Jan 19 16:49:59 CET 2023
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,
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>13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L,
>13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L, 13000L,
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>13017L, 13018L, 13019L, 13020L, 13021L, 13022L, 13023L, 13024L,
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>32003L, 32004L, 32005L, 32006L, 32007L, 32008L, 32009L, 32010L,
>32011L, 32012L, 32013L, 32014L, 32015L, 32016L, 33001L, 33002L,
>33003L, 33004L, 33005L, 33006L, 33007L, 33008L, 33009L, 33010L,
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>), Cell6 = c(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, 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
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