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

#### tcpsych7

##### New Member
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?

#### katxt

##### Well-Known Member
effect is actually making R^2 ( amount of between-study heterogeneity explained), decrease?
Are you sure it does? Or do you mean the adjusted R^2?

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#### tcpsych7

##### New Member
Are you sure it does? Or do you mean the adjusted R^2?
I do mean the adjusted R^2, but was under the impression this was the amount of between-study heterogeneity explained

#### tcpsych7

##### New Member
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

##### Well-Known Member
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.

#### tcpsych7

##### New Member
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

##### Well-Known Member
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.

#### tcpsych7

##### New Member
These are not indices that I use myself. Perhaps some other reader may help. /QUOTE]
No worries, many thanks for your explanation on R^2 !