Multiple comparisons using multiple imputation under a two-way mixed effects interaction model

Missing data is commonplace with both surveys and experiments. For this dissertation, we consider imputation methods founded in Survey Sampling, and assess their performance with experimental data. With a two-way interaction model, missing data renders Multiple Comparisons Procedures invalid; we seek a resolution to this problem through development of a Multiple Imputation Procedure. By completing an incomplete data set, we obtain a balanced data set for which multiple comparisons of treatment effects may be performed.;We develop an imputation procedure, Repeated Measures Normal Imputation (RMNI), for use with any hierarchical linear model. The advantage of RMNI is that the procedure preserves the underlying variance-covariance matrix structure of the model. The two-way interaction model has a spherical variance-covariance matrix, and the property of sphericity is required for the existence of a valid Multiple Comparisons Procedure. With RMNI, we are assured that the imputed values do not violate assumptions regarding the structure of the variance-covariance matrix of the data. With multiple imputations, we are assured that the imputed values are not treated as real observed data. Through RMNI, we are able to demonstrate the construction of a multiply-imputed confidence interval for each treatment contrast using a standard Tukey procedure, with confidence that the width of the interval is adjusted for uncertainty due to missing data.