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Expectation-Maximization high missing rates and multiple variables

I know MICE can be used for imputation of multiple variables simultaneously. The expectation maximization approach (EM) can be used to impute missing data. Typically, one should only be using imputation on variables with missing rates of < 10%; is there an imputation approach that allows robust imputation when missing rates are much higher? Is the EM approach suitable? The scenario considered is where there are ~50 variables being considered with potential collinearity.

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