Multiple Imputation Inferences for Count Data

Multiple imputation is frequently used for inference with missing data. In cases when the population quantity of interest is desired to be an integer, the original methods for inference need to be modified, as the point estimates based on the average are generally not integers.In this thesis, I propose a modification to the original combining rules, which provides the point estimate as the median of quantities from imputed datasets. Thus, the point estimate of the population quantity of interest is integer-valued when the number of imputed datasets is odd. I derive an estimator of the variance of this modified estimator, as well as a method for obtaining confidence intervals. I compare this method to other ad-hoc methods, such as rounding the original point estimate. Simulations show that these two methods provide similar results, although the novel method has slightly larger mean absolute error. The coverage rate of both methods are close to the nominal coverage of 95%. The correct derivation of variance is important, and simulations show that if one uses the median as point estimate without correcting the variance, the coverage rate is systematically lower.