## 8.1 Calculating meta-regressions in R

Meta-regressions can be conducted in R using the metareg function in meta. To show the similarity between subgroup analysis and meta-regression with categorical predictors, I will first conduct a meta-regression with my variable Control as a predictor again.

metareg(m.hksj,Control)
##
## Mixed-Effects Model (k = 18; tau^2 estimator: SJ)
##
## tau^2 (estimated amount of residual heterogeneity):     0.1343 (SE = 0.0536)
## tau (square root of estimated tau^2 value):             0.3665
## I^2 (residual heterogeneity / unaccounted variability): 73.92%
## H^2 (unaccounted variability / sampling variability):   3.84
## R^2 (amount of heterogeneity accounted for):            0.00%
##
## Test for Residual Heterogeneity:
## QE(df = 15) = 40.0161, p-val = 0.0005
##
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 15) = 0.9467, p-val = 0.4100
##
## Model Results:
##
##                         estimate      se    tval    pval    ci.lb   ci.ub
## intrcpt                   0.4252  0.2250  1.8899  0.0782  -0.0543  0.9048
## Controlno intervention    0.1003  0.2678  0.3744  0.7134  -0.4706  0.6711
## ControlWLC                0.3380  0.2765  1.2224  0.2404  -0.2514  0.9274
##
## intrcpt                 .
## Controlno intervention
## ControlWLC
##
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We see in the output that the metareg function uses the values of Control (i.e, the three different types of control groups) as a moderator. It takes “information only” as a dummy-coded reference group, and “no intervention” and “WLC” as dummy-coded predictors. Under Test of Moderators, we can see that control groups are not significantly associated with effect size differences $$F_{2,15}=0.947$$, $$p=0.41$$. Our regression model does not explain any of the variability in our effect size data ($$R^2=0\%$$).

Below Model Results, we can also see the $$\beta$$-values (estimate) of both predictors, and their significance level pval. As we can see, both predictors are not significant.

Continuous variables

Let us assume I want to check if the publication year of a study is associated with effect size differences. I have stored the variable pub_year, containing the publication year of every study in my dataset, and conducted the meta-analysis with it. I stored my meta-analysis output in the m.pubyear output.

Now, I can use this predictor in a meta-regression.

output.metareg<-metareg(m.pubyear,pub_year)
output.metareg
##
## Mixed-Effects Model (k = 18; tau^2 estimator: DL)
##
## tau^2 (estimated amount of residual heterogeneity):     0.0831 (SE = 0.0488)
## tau (square root of estimated tau^2 value):             0.2883
## I^2 (residual heterogeneity / unaccounted variability): 64.69%
## H^2 (unaccounted variability / sampling variability):   2.83
## R^2 (amount of heterogeneity accounted for):            0.00%
##
## Test for Residual Heterogeneity:
## QE(df = 16) = 45.3076, p-val = 0.0001
##
## Test of Moderators (coefficient 2):
## QM(df = 1) = 0.0054, p-val = 0.9412
##
## Model Results:
##
##           estimate       se     zval    pval     ci.lb    ci.ub
## intrcpt    -1.4580  27.6151  -0.0528  0.9579  -55.5825  52.6666
## pub_year    0.0010   0.0137   0.0737  0.9412   -0.0259   0.0280
##
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As you can see from the output, pub_year was now included as a predictor, but it is not significantly associated with the effect size ($$p=0.9412$$).