Multiple imputation with deletion of response variables and model selection?

Question

I am using the MICE package in R to impute my dataset to deal with missing values. I have missing values in both the response and the predictor variables. I am interested in following Paul T. Von Hippel's (2007) suggestion to impute the data including the response variables but not using the imputed response variables in the glm. I have figured out how to do that in MICE but I would like to also use the data in package mami to run model selection. I can't run the data in mami as it seems to refuse to run if there are any missing data which there are since we are missing data in the response variables. I get the error:

 Error in mami(imp, model = "gaussian", outcome = 
  c("j_immerged2"), method = "MA.criterion",  : 
  There is still missing data but you specified the data is 
  imputed.

Is there any way around this problem? Is there a different package I can use to run model selection on imputed data with missing data?

P.S. I did run a large number of imputations and impute both the response and predictor variables and for analysis at first. However, reviewers were not particularly fond of the choice to impute the response variables, hence why I am trying to analyze the data as stated above.

citation from above: Von Hippel, P. T. 2007. Regression with missing Ys: an improved strategy for analyzing multiply imputed data. Sociological Methodology, 37: 83-117.

Answer 1

Ok, I think (hope) this is correct.

First I created a copy of the response column and told MICE not to use it in the imputation (so essentially there is one column with the response that is imputed and used in the imputation process and one exact copy not used).

Second, I ran the imputation and then created a long format version of all your datasets:

imp3<-mice::complete(imp,"long",include=T)

Third, I removed all rows with an NA in the non-imputed response variable column:

library(tidyverse)
imp4<-imp3 %/% drop_na("response")

Fourth, I converted it back to mids object:

impA <- as.mids(imp4)

I was then able to run my glm with the imputed dataset and run model selection in MAMI because there were no longer any missing values.