Visualization is widely used to explore data, examine variation, reveal trends, and diagnose models. Furthermore, interactive plots can re-focus the view to features of interest, drill down into a fine resolution, query or lookup elements, look at data from various directions, and connect plots with model analysis. However, for specific data types and specific exploratory purposes, the general interactions like brushing, panning, zooming, and querying can be insufficient. The lack of a grammar for interactive graphics makes differences between the user interactions on data and on the view of data difficult to delineate. This thesis partially addresses these issues and fills gaps in methodology from three application areas: missing values, temporal/longitudinal data, and areal data.

Interactive graphics plays different roles in three areas. In missing data analysis, many imputation methods have been developed but little has been done for exploring the missing value structure to determine the missingness pattern, or to evaluate the imputations. This research addresses this gap, focusing on an interactive tool to explore missings, check the missingness assumptions, and compare imputation methods. For temporal and longitudinal data, using static plots is inadequate for exploring the trends, seasonality or unusual individuals, especially when the data set is large. This research develops special interactions and discusses the elements and pipeline in the interactivity construction. It is implemented in the R package, cranvastime, with details on how to use for a number of datasets. For the areal data, cartograms are widely used but there is no universally good algorithm for cartogram construction or evaluation. This research proposes an evaluation criterion and utilizes an interactive interface to optimize the visualization between the original shape-reserved map and area-reserved cartogram.