I have a dataset with 12 predictor variables and a binary response variable. There's 5960 observations. One of the predictor variables has 1,260 missing values so I'm using k-nearest neighbours to impute them. The distance metric is Euclidean and k = 1 is the default of the algorithm.
Question: Should I include the response variable in the k-nearest neighbours algorithm?
My thoughts were that this may introduce some sort of overfitting.