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

[Simon Harmel]

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

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