[R-meta] Metareg: Significant reduction in tau-squared but no change in i-squared

[Richard Simonson]

I've conducted a meta-regression with metareg on a random-effects
meta-analysis and am attempting to describe the results. The output of the
model is at the end of my description

Based on the regression model, I'm given that our R-squared is 12%, which I
take that to mean ~23% of the heterogeneity was accounted for when
covarying the model.

I also see that there was a reduction in tau-squared from the random
effects meta-analysis to the meta-regression, but no change in I-squared.

Can someone help me understand why, with a positive non-zero r-squared,
there's a change in tau-squared but not in I-squared?

Which one is more feasible to report that we were able to account for some
of the heterogeneity?

Thanks!

Meta output:
I-squared: 87%
tau-squared: .27

Meta-reg output
tau^2 (estimated amount of residual heterogeneity):     0.2426 (SE = 0.2570)
tau (square root of estimated tau^2 value):                    0.4925
I^2 (residual heterogeneity / unaccounted variability):    86.68%
H^2 (unaccounted variability / sampling variability):       7.51
R^2 (amount of heterogeneity accounted for):               12.25%

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