Multiple Imputation Multiple Imputation Missing data method developed

Multiple Imputation

Multiple Imputation Missing data method developed by Donald Rubin n Simulate multiple samples of “complete” data, and compute estimates and standard errors from the complete data. n Rubin distinguished multiple imputation from n – Different models – Same model n We will focus on same-model multiple imputation

Missing Data mechanism n Missing data mechanisms – MCAR (Missing completely at random)— missing data are a random subsample of complete data – MAR (Missing at random)—missing data mechanism may depend on independent variables, but not the response

Missing Data mechanism n Ignorable nonresponse – MCAR – Parameter for missing process different from data parameters n Example for discussion – Growth curve models for largemouth bass

Computer Example n 5 Teachers, 3 methods, Y=relative improvement Method Teacher 1 Teacher 2 Teacher 3 Teacher 4 Teacher 5 A 10, 7 6 11 6 6 B 4 . 8. 5 4, 5 3 C 9 13 16 8 6

Multiple Imputation simulation Repeated draws i=1, …, M from the posterior predictive distribution of the missing data. n The complete data sets have the same set of fully observed responses. n In practice, there are numerous ways to generate complete data. n Introductory methods rely on monotone missingness, and classic results for conditional distributions of jointly multivariate normal random variables. n

Multiple Imputation simulation n In a multivariate normal setting (some values of Y missing), we generate our draws from Y|X:

Multiple Imputation Estimation n Combining results from imputation for parameters of interest is surprisingly straightforward. E. g. , let q represent the PMM’s for Method. We can compute

Multiple Imputation Estimation n Our estimate and its standard error can be computed as:

Multiple Imputation Estimation n Combining estimates in SAS is non- standard. n Our example with LSMeans is atypical, and more straightforward than most.