Gertheiss, Jan

Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done concerning ordinal-on-ordinal regression. Motivated by survey datasets on food products consisting of Likert-type items, we propose a strategy for smoothing and selection of ordinally scaled predictors in the cumulative logit model. First, the original group lasso is modified by use of difference penalties on neighbouring dummy coefficients, thus taking into account the predictors' ordinal structure. Second, a fused lasso type penalty is presented for fusion of predictor categories and factor selection. The performance of both approaches is evaluated in simulation studies, while our primary case study is a survey on the willingness to pay for luxury food products.

Categorical data are quite common in applied statistics, and various regularized fitting procedures have been proposed for appropriate handling of such variables in regression. This chapter gives an overview of some of those techniques. Special emphasis is put on model selection with ordinal explanatory variables if the number of categories and/or the number of predictors is relatively large. In this context, regularized fitting is compared to more classical procedures like forward selection. Structuring of ordinal predictors is considered within the framework of generalized additive models (GAMs), and tools provided within this framework are employed for statistical inference.

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non‐linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non‐linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non‐linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non‐linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non‐linear transformation of the category labels and better performance on validation data than unpenalized non‐linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.

Individuals are frequently confronted with privacy-related decisions under uncertainty especially in online contexts. The resulting privacy concerns are a decisive factor for individuals to (not) use online services. In order to support individuals to make more informed decisions, we assess the current state of practice of certain online services. This analysis is focused on ride-sharing and includes popular services in Germany, Austria, and Switzerland and we investigate how they handle user data. The results show that services include a wide-ranging set of personal data and lack standardization. Furthermore, they offer limited privacy-related features. Based on this analysis, we developed a Transparency Enhancing Technology in the form of a browser extension that informs users about data practices of the services at the time of data disclosure. In addition to this, we conducted a scenario-based online experiment with a representative sample to evaluate the usability of our tool and its effect on users’ concerns and behavior. Results show significant improvements in awareness and decision reflection with limited decrease in disclosure rates of personal data.

We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is applied on a linear combination of distance measures each calculated on single covariates, with weights being estimated from the training data. The dependent variable can be categorical (binary or multi-class) or continuous, thus we consider both classification and regression problems. The methodology presented is illustrated and evaluated on artificial and real world data. Particularly it is observed that prediction accuracy can be increased, and irrelevant, noise variables can be identified/removed by ‘downgrading’ the corresponding distance measures in a completely data-driven way.