Meta regression: adding covariates is decreasing amount of heterogeneity explained - how?

#1
Could someone please explain to me the concept behind why adding additional covariates to explore if they are moderators of the effect is actually making R^2 ( amount of between-study heterogeneity explained, decrease? My ill-advised brain is telling me that even if they are not significant moderators, the extra information contained in the variable should add something to the picture, and remove some of the heterogeneity?
 
#4
When I add one extra covariate, Tau^2 and I^2 both increase (suggesting increasing heterogeneity?) but adjusted R^2 decreases (i thought also suggesting this)? Have I misunderstood something?
 

katxt

Active Member
#5
The adjusted R^2 allows for the number of predictors in a way that reduces R^2 as the predictors goes up. At the same time raw R^2 is increasing, so it is a race between the two effects. if the new predictor is important the increase dominates. If it isn't then the reduction effect wins. So with insignificant predictors the raw R^2 goes up slightly but the value is adjusted down even more.
 
#6
The adjusted R^2 allows for the number of predictors in a way that reduces R^2 as the predictors goes up. At the same time raw R^2 is increasing, so it is a race between the two effects. if the new predictor is important the increase dominates. If it isn't then the reduction effect wins. So with insignificant predictors the raw R^2 goes up slightly but the value is adjusted down even more.
Ah OK, that makes sense thank you! ...but now I'm still wondering why tau^2 and I^2 increased!
 

katxt

Active Member
#7
wondering why tau^2 and I^2 increased!
These are not indices that I use myself. Perhaps some other reader may help. My guess is that they don't have an adjusted version and so increase as more explanatory variables are included, just as raw R^2 does.