#Helper function that overrides response variable with non-NA (e.g. 1) so that the returned design.matrix for all of s1 is returned
#returns design matrix for s1 with complete.obs for auxiliary variables
design_matrix.s1_return <- function(formula, data){
data[,all.vars(formula)[1]] <- 1 #change response values non-NA to trick lm function
model.matrix(formula, data=data)}
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