I have a binary(1/0) classification task. I am trying to find $p(y = 1 | X)$ where $X$ is the vector of input variables and $y$ is the binary output label.
Suppose that for some records the output labels ($y$) are missing.
Scenario 1: Labels are Missing Completely at Random (MCAR)
While estimating the model, is there a difference between discarding records without labels vs. using Expectation Maximization to estimate missing labels?
Scenario 2: Labels are Missing at Random (MAR) conditional on $X$
While estimating the model, is there a difference between discarding records without labels vs. using Expectation Maximization to estimate missing labels?
Scenario 3: Labels are Not Missing at Random (NMAR)
In this case there is clearly a difference between discarding records without labels vs. using EM.
Which option is better? Is there an all-time winner or does it depend on missingness mechanism?
I am asking the difference in terms of model bias, and estimation efficiency.