Multiple imputation for continuous non-normal missing data.

Missing data problems impose great challenges to both statisticians and data practitioners. Multiple imputation (1987), a popular method for dealing with missing data problems, fills in missing items with several sets of plausible values drawn from an imputation model. This approach is especially useful when public-use (shared) databases are analyzed by many ultimate users (researchers) with varying degrees of statistical expertise and computing power, and with different scientific questions and objectives. For continuous variables with missing data, most existing imputation approaches are based on normal assumption of the data. However, variables in real data sets often deviate from normality. The two major goals of this dissertation are to develop imputation approaches that account for non-normality arising from continuous data, and to assess the performance of the normal imputation approaches under non-normal data. Tukey's gh distribution (Tukey 1977) is a flexible family that can be used to model a wide variety of continuous distributions. We achieve the first goal of this dissertation by proposing a class of gh imputation approaches using the gh distribution and its extensions. In Chapter 2, we consider modeling and imputing univariate incomplete data using the gh distribution. In Chapter 3, we propose an imputation approach in which the error distribution of the regression model is modeled through the gh distribution. In Chapter 4, we propose an imputation approach for multivariate missing data based on a multivariate extension of the gh distribution. For all proposed gh imputation approaches, we conduct simulation studies to assess their performance under various non-normal distributions. To achieve the second goal of this dissertation, we also evaluate the performance of the normal imputation approaches in these simulation studies. We find that if the mean structure is correctly specified, the normal imputation methods perform well in estimating the marginal means and regression coefficients regardless of the normal assumption. The gh imputation approaches have comparable performance. For estimating the shape of the marginal distributions, such as the proportions that are less than certain quantiles, the normal imputation approaches can perform poorly if the distribution deviates from normality, while the gh imputation approaches perform consistently well. For illustration, we apply the proposed methods to data from an adolescent driving study.PhDBiological SciencesBiostatisticsPure SciencesStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/125381/2/3192656.pd