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 ***
---
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.
