# How to correctly interpret coefficient of a multiple meta-regression in metafor?

When fitting a multiple meta-regression in metafor, the output shows multiple coefficients, for each predictor.

To make an example, similar to what is done here: https://www.metafor-project.org/doku.php/tips:meta_regression_with_log_rr

dat <- escalc(measure="OR", ai=cpos, bi=cneg, ci=tpos, di=tneg, data=dat.bcg)
res <- rma(yi, vi, mods = ~ alloc+ablat, data=dat)


where ablat is a continuous moderator, and alloc a categorical moderator.

The output shows:

Mixed-Effects Model (k = 13; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0.1402 (SE = 0.1109)
tau (square root of estimated tau^2 value):             0.3744
I^2 (residual heterogeneity / unaccounted variability): 68.79%
H^2 (unaccounted variability / sampling variability):   3.20
R^2 (amount of heterogeneity accounted for):            58.50%

Test for Residual Heterogeneity:
QE(df = 9) = 24.3281, p-val = 0.0038

Test of Moderators (coefficients 2:4):
QM(df = 3) = 12.4943, p-val = 0.0059

Model Results:

estimate      se     zval    pval    ci.lb   ci.ub
intrcpt           -0.2609  0.4017  -0.6495  0.5160  -1.0483  0.5265
allocrandom        0.1801  0.3482   0.5170  0.6051  -0.5025  0.8626
allocsystematic   -0.1461  0.3766  -0.3881  0.6979  -0.8842  0.5919
ablat              0.0294  0.0091   3.2222  0.0013   0.0115  0.0473  **

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Now, we know that exponentiation of the coefficients for allocrandom and allocsystemic will gave us the "ratio of Odds Ratio", compared to the "alternate" location; similar, we know that the exponentiation of the coefficient for ablat will gave us the average odds ratio for one-unit increase in absolute latitude (Let's skip for a moment the proble of the exponentiation as a non-linear transformation, for simplicity).

Now, the question is related to the formal interpretation of these coefficients in a multiple meta-regression model like the one reported above.

It is right to say that, according to this multiple meta-regression model, the change in average odds ratio for one-unit increase in absolute latitude is 1.03 (which is equal to the exponentiation of the coefficient 0.0294), independently from the type of allocation? Or do I miss something?

On the log scale, the model essentially implies that there are three parallel lines for the relationship between ablat and the log odds ratios, that is, the lines all have the same slope (i.e., 0.0294), but different intercepts, depending on the alloc level. People will use different terminology to describe this in words. Some might say that 0.0294 is the slope "controlling for alloc". Some might say that it is the slope when "holding alloc constant". I guess one could also say it is the slope "independently of alloc". So, in that sense, the answer to your question is yes, you can phrase the findings as you did.