[R-meta] Is it normal for Rho (=ICC) to be 1.000 in rma.mv()?

[Viechtbauer, Wolfgang (SP)]

Dear Simon,

The rho values are correlations, so this has nothing to do with variability. High values of rho indicate strong correlations.

But in the model with "UN", three of those correlations are being estimated based on 1 pair, two are based on 3 pairs, and only the 1-2 pair occurs more often. So essentially, for most of those correlations, there is very little information to estimate them. Also, the corresponding variance components might be essentially 0, in which case one wouldn't have to think about the correlations anyway.

In the model with "AR", the autocorrelation coefficient indeed drifts towards 1. This can happen. Why this happens in this case is impossible to say for me without more information.

This aside, if 'random = list(~time|study, ~1|esid)', then there is only one '~ inner | outer' term, so the second "UN" in c("UN","UN") or c("AR","UN") is irrelevant. This doesn't affect anything but might suggest a misunderstanding of what the model is actually doing.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Simon Harmel
>Sent: Monday, 03 May, 2021 1:26
>To: R meta
>Subject: [R-meta] Is it normal for Rho (=ICC) to be 1.000 in rma.mv()?
>
>Dear All,
>
>I have fit the model below. However, rho (= ICC) is estimated to be
>"1.0000". Does this mean there is extreme variability between true effects
>within each time point? (Or extreme dependence between true effects within
>each time point?)
>
>Should I try to find time-related moderators that can potentially explain
>some of this variability in the true effects? How low an rho (=ICC) is
>reasonably acceptable?
>
>ps: if we set `struct= c("UN","UN")`, we get the following (is this
>normal?):
>    rho.1   rho.2   rho.3   rho.4         1   2   3   4
>1       1  1.0000  1.0000  0.5000     -  no  no  no
>2  1.0000       1  1.0000  0.5000    31   -  no  no
>3  1.0000  1.0000       1  0.5000     3   3   -  no
>4  0.5000  0.5000  0.5000       1     1   1   1   -
>
>#-------- My current model:
>
>rma.mv(yi ~ 0 + time + x1 + x2, V = V, struct= c("AR","UN"),
>                    random = list(~time|study, ~1|esid),
>                    data = data)
>
>OUTPUT:
>Variance Components:
>
>                    estim    sqrt  nlvls  fixed  factor
>sigma^2    0.2117  0.4601    255     no    esid
>
>outer factor: study (nlvls = 49)
>inner factor: time (nlvls = 4)
>
>                estim    sqrt     fixed
>tau^2      0.2679  0.5176     no
>rho          1.0000                 no <<<--------- Isn't this odd?
>
>Test for Residual Heterogeneity:
>QE(df = 249) = 1432.5141, p-val < .0001
>
>Test of Moderators (coefficients 1:6):
>QM(df = 6) = 46.1983, p-val < .0001
>
>Model Results:
>
>          estimate         se        zval      pval        ci.lb     ci.ub
>time1    0.5928  0.1221   4.8561  <.0001   0.3535  0.8320  ***
>time2    0.5671  0.1346   4.2119  <.0001   0.3032  0.8310  ***
>time3    0.6288  0.2328   2.7013  0.0069   0.1726  1.0850   **
>time4    1.4178  0.4640   3.0556  0.0022   0.5084  2.3272   **
>x1        -0.0114  0.0068  -1.6810  0.0928  -0.0248  0.0019    .
>x2         0.0133  0.0207   0.6433  0.5200  -0.0272  0.0538