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I tried to fit a non-linear meta-regression model with a restricted cubic spline using the package "metafor" in R, as reported in here: https://www.metafor-project.org/doku.php/tips:non_linear_meta_regression.

However, I have some doubts in interpreting coefficients in the output. This is the example output:

Mixed-Effects Model (k = 80; tau^2 estimator: REML)
 
tau^2 (estimated amount of residual heterogeneity):     0.0262 (SE = 0.0085)
tau (square root of estimated tau^2 value):             0.1619
I^2 (residual heterogeneity / unaccounted variability): 57.08%
H^2 (unaccounted variability / sampling variability):   2.33
R^2 (amount of heterogeneity accounted for):            91.24%
 
Test for Residual Heterogeneity:
QE(df = 76) = 165.4692, p-val < .0001
 
Test of Moderators (coefficients 2:4):
QM(df = 3) = 374.5340, p-val < .0001
 
Model Results:
 
                estimate      se     zval    pval    ci.lb    ci.ub
intrcpt           0.0070  0.0902   0.0773  0.9384  -0.1698   0.1838
rcs(xi, 4)xi     -0.0242  0.0315  -0.7693  0.4417  -0.0859   0.0375
rcs(xi, 4)xi'     0.4506  0.0870   5.1777  <.0001   0.2801   0.6212  ***
rcs(xi, 4)xi''   -1.4035  0.2537  -5.5326  <.0001  -1.9007  -0.9063  ***
 
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The output shows three differenet coefficients which reflect different part of the spline curve. However, what is the reference group (i.e., how can I find the "limit values" of that portion of the spline)? How can trasnform "xi", "xi'" and "xi''" in range of the predictor?

Thank you in advance.

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