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The documentation claims to be able to handle svyglm models from the survey library, and indeed, the prediction() does calculate point estimates and standard errors. However, the library seems unable to summarise these results. Here is an example based on an example in the svyglm function documentation.
data(api)
dstrat<-svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
api.reg <- svyglm(api.stu~enroll, design=dstrat)
p1 <- predict(api.reg, type = "response", se.fit = T)
mean(p1)
p2 <- prediction(api.reg)
summary(p2)
When I run this in R 3.6.3 on a macOS Mohave 10.14.4 I get
Prediction SE z p lower upper
621.5 NA NA NA NA NA
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