Learn how to employ moderators - categorical, continuous, or both - in your meta-analysis using Metafor in R. Explore special cases with categorical moderators, handling multiple independent variables, and utilizing fudge adjustment for mixed models.
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Moderators in Metafor One of the nice things about Metafor is the ease of handling moderators, those third variables that condition the relations contained in the effect sizes The mods command is used to introduce moderators into the model Continuous variables are the default and need no special identification Categorical variables are identified by the factor label. There are two ways to use the mods command: mods = cbind(mod1, mod2, mod3) mods = ~mod1+mod2+mod3
Special Cases of Categorical Moderators Two different models may be computed with categorical variables, and their interpretation is different, so it is important to know which is which The command -1 (minus one) after a variable designated as categorical by the factor command will suppress the intercept. The test of the coefficients will be an omnibus test of the null that all the levels of the moderator are simultaneously zero. This is analogous in ordinary regression to checking overall R-square before checking any individual coefficient If the -1 command is omitted, one category will be set to the intercept (coded zero), and the subsequent categories will estimate the DIFFERENCE between the reference (intercept) mean and the mean of that level of the category. This is the test of the significance of the difference in effect due to the moderator (what most people want when they want to test a moderator).
Multiple Independent Variables You may include multiple independent variables of both kinds (continuous and categorical) It is also possible to test for nonlinear terms, such as interactions and quadratic effects. Given the small number of studies (effect sizes) and the large number of possible moderators in most meta-analyses, you want to consider Type I and Type II errors before you start
Fudge Adjustment If you run a mixed model (there is a residual random effects variance component, essentially a random-effects model with one or more moderators), you can ask for omnibus and individual tests of coefficients based on the F and t distributions rather than the chi-square distribution. This compensates for the uncertainty about the actual value of tau-squared. This is analogous to the Higgins PI discussed earlier. The adjustment is called the Knapp and Harting adjustment; you direct Metafor to apply this by knha = TRUE (usually a more conservative test).
R code: McLeod Data correlations between parenting and childhood depression 1: no moderator simple overall analysis 2: same as 1 but clinical diagnosis of the child (Dx) moderator is added 3: same as 2, but Knapp and Harting adjustment 4: same as 2, but suppressing the intercept 5: same as 2, but adding the continuous moderator Age
