Statistical Methods and Models for Interdependent Categorical, particularly Ordinal Data

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There are various statistical methods available for analyzing and modeling high-dimensional, interdependent variables, such as graphical models or principal component analysis. Those methods, however, usually require continuous or metrically scaled data. Corresponding methods for high-dimensional categorical, particularly ordinal data are rather limited, although those kind of data is frequently found in various applications. Therefore, the goal of the project is to fill this gap in statistical methodology by developing appropriate methods, such as regularized graphical models and principal component analysis for ordinal variables. Besides scale level – nominal vs. ordinal – we will distinguish between variables that are ordered among each other, e.g. over time, and variables without a specific structure that implies some specific association pattern. For modeling the first type of data, we will also borrow and extend methods from functional data analysis, leading, e.g., to “optimal scaling for categorical functional data” or “graphical models for discrete functional data”. On the one hand, the methods to be developed will be motivated by and tailored to real world data problems, such as sensory quality control. On the other hand, the methods proposed shall, in general, not be restricted to a specific field of application, but be applicable as broadly as possible. All data analyses will be done in close cooperation with the corresponding collaborators.