# [R-meta] Back transformation of double arscine transformed estimates in metafor

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Sat Oct 5 14:16:11 CEST 2019

```Dear Daniel,

If level 5 is the reference level, then that is what the intercept represents, so the 0.0183 cannot represent level 5. You would have to provide the output of 'b' for me to tell you better what is being estimated here, but 0.0183 is the estimated proportion for whatever level the last coefficient represents in the model.

If you want all estimated proportions for all 6 levels, then you can get this with a single command:

predict(b, newmods=rbind(0, diag(5)), transf=transf.ilogit)

The first will be for the reference level, the rest for each other level.

Best,
Wolfgang

-----Original Message-----
From: Daniel Mønsted Shabanzadeh [mailto:dmshaban using gmail.com]
Sent: Saturday, 05 October, 2019 12:31
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] Back transformation of double arscine transformed estimates in metafor

Dear Wolfgang

I have now run the models, but still seem to have some conversion problems when trying to obtain proportions from the regression model. The variable age_cor is categorical with 6 levels (level 5 is ref.).

b<-rma.glmm(xi=compl_treat, ni=total, mods = ~age_cor, measure = "PLO", data=a)
c<-predict(b, newmods=c(0,0,0,0,1), transf=transf.ilogit)
print(c)

pred  ci.lb  ci.ub  cr.lb  cr.ub
0.0183 0.0064 0.0516 0.0011 0.2460

As far as I interpretate this results, it means that if age_cor is fixed at 0 in level 1-4 and level 5 is fixed at 1, the proportion is 0.0183. Is it not possible to obtain proportions from all levels in the variabel when one level is the reference? Like the case in studies with relative risks exploring multiple level categorical variables with one reference level.

Regards,
Daniel