Jan Gertheiss

Sparse modeling of categorial explanatory variables

Shrinking methods in regression analysis are usually designed for metric predictors. If independent variables are categorial some modifications are necessary. In this article two L1-penalty based methods for factor selection and clustering of categories are presented and investigated. The first approach is designed for nominal scale levels, the second one for ordinal predictors. All methods are illustrated and compared in simulation studies, and applied to real world data from the Munich rent standard. The paper is a preprint of an article published in The Annals of Applied Statistics. Please use the journal version for citation.

Longitudinal scalar-on-functions regression with application to tractography data

We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the studys primary goals is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires the development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and predictor measurements per patient; (3) Gaussian or non-Gaussian outcomes; and (4) missing values within functional predictors. We propose two versions of a new method, longitudinal functional principal components regression (PCR). These methods extend the well-known functional PCR and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The new methods are compared with existing approaches, and the most promising techniques are used for analyzing the tractography data.

Feature Extraction in Signal Regression: A Boosting Technique for Functional Data Regression

The main objectives of feature extraction in signal regression are improved accuracy of the prediction of future data and the identification of relevant parts of the signal. A feature extraction procedure is introduced that uses boosting techniques to select the relevant parts of the signal, whereby the proposed blockwise boosting procedure simultaneously selects intervals in the signal’s domain and estimates the effect on the response. The blocks that are defined explicitly use the underlying metric of the signal. It is demonstrated in simulation studies and with real-world data that the proposed approach competes well with procedures like PLS, P-Spline signal regression, and functional data regression. Supplemental materials are available online.

Regularization and model selection with categorical predictors and effect modifiers in generalized linear models

Varying-coefficient models with categorical effect modifiers are considered within the framework of generalized linear models. We distinguish between nominal and ordinal effect modifiers, and propose adequate Lasso-type regularization techniques that allow for (1) selection of relevant covariates, and (2) identification of coefficient functions that are actually varying with the level of a potentially effect modifying factor. For computation, a penalized iteratively reweighted least squares algorithm is presented. We investigate large sample properties of the penalized estimates; in simulation studies, we show that the proposed approaches perform very well for finite samples, too. In addition, the presented methods are compared with alternative procedures, and applied to real-world data.

How olfactory acuity affects the sensory assessment of boar fat: a proposal for quantification.

Due to animal welfare concerns the production of entire male pigs is one viable alternative to surgical castration. Elevated levels of boar taint may, however, impair consumer acceptance. Due to the lack of technical methods, control of boar taint is currently done using sensory quality control. While the need for control measures with respect to boar taint has been clearly stated in EU legislation, no specific requirements for selecting assessors have yet been documented. This study proposes tests for the psychophysical evaluation of olfactory acuity to key volatiles contributing to boar taint. Odor detection thresholds for androstenone and skatole are assessed as well as the subjects ability to identify odorants at various levels through easy-to-use paper smell strips. Subsequently, fat samples are rated by the assessors, and the accuracy of boar taint evaluation is studied. Considerable variation of olfactory performance is observed demonstrating the need for objective criteria to select assessors.

Rating Scales as Predictors - the Old Question of Scale Level and some Answers

Rating scales as predictors in regression models are typically treated as metrically scaled variables or, alternatively, are coded in dummy variables. The first approach implies a scale level that is not justified, the latter approach results in a large number of parameters to be estimated. Therefore, when rating scales are dummy-coded, applications are often restricted to the use of a few predictors. The penalization approach advocated here takes the scale level serious by using only the ordering of categories but is shown to work in the high dimensional case. We consider the proper modeling of rating scales as predictors and selection procedures by using penalization methods that are tailored to ordinal predictors. In addition to the selection of predictors, the clustering of categories is investigated. Existing methodology is extended to the wider class of generalized linear models. Moreover, higher order differences that allow shrinkage towards a polynomial as well as monotonicity constraints and alternative penalties are introduced. The proposed penalization approaches are illustrated by use of the Motivational States Questionnaire.

Supervised feature selection in mass spectrometry-based proteomic profiling by blockwise boosting

When feature selection in mass spectrometry is based on single m/z values, problems arise from the fact that variability is not only in vertical but also in horizontal direction, i.e. also slightly differing m/z values may correspond to the same feature. Hence, we propose to use the full spectra as input to a classifier, but to select small groups -- or blocks -- of adjacent m/z values, instead of single m/z values only. For that purpose we modify the LogitBoost to obtain a version of the so-called blockwise boosting procedure for classification. It is shown that blockwise boosting has high potential in predictive proteomics.

Regularized regression for categorical data

In the last two decades, regularization techniques, in particular penalty-based methods, have become very popular in statistical modelling. Driven by technological developments, most approaches have been designed for high-dimensional problems with metric variables, whereas categorical data has largely been neglected. In recent years, however, it has become clear that regularization is also very promising when modelling categorical data. A specific trait of categorical data is that many parameters are typically needed to model the underlying structure. This results in complex estimation problems that call for structured penalties which are tailored to the categorical nature of the data. This article gives a systematic overview of penalty-based methods for categorical data developed so far and highlights some issues where further research is needed. We deal with categorical predictors as well as models for categorical response variables. The primary interest of this article is to give insight into basic properties of and differences between methods that are important with respect to statistical modelling in practice, without going into technical details or extensive discussion of asymptotic properties.

Spatially regularized estimation for the analysis of dynamic contrast‐enhanced magnetic resonance imaging data

Competing compartment models of different complexities have been used for the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging data. We present a spatial elastic net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed a priori. A multi-compartment approach is considered, which is translated into a restricted least square model selection problem. This is done by using a set of basis functions for a given set of candidate rate constants. The form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment. Using a spatial elastic net estimator, we chose a sparse set of basis functions per voxel, and hence, rate constants of compartments. The spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently. The proposed estimation method is evaluated for simulated images and applied to an in vivo dataset.

Wert und Akzeptanz einer Alzheimer-Risikodiagnostik

BACKGROUND It is quite common that people suffering from cognitive impairment only visit a doctor when the symptoms have already reached an advanced stage. This is often due to a fear of Alzheimer’s disease or a dread of exhausting diagnostic procedures and exposure of personal details; however, an early diagnosis and therapy increases the chance of preserving the quality of life for a longer period of time. OBJECTIVES Evaluation of a risk assessment for Alzheimer’s disease by magnetic resonance imaging (MRI) with respect to the acceptance and value by participants. METHODS In this prospective preventive study 106 subjects between the age of 39 and 89 years (median age 68 years) with general risk factors were included and underwent a risk assessment for Alzheimer’s disease by standard MRI of the brain using a 1 T open MRI with subsequent hippocampal volumetry. Participants were stratified into two distinct subgroups according to the individual hippocampal atrophy status, one with elevated and the other with reduced risk. All participants were thoroughly interviewed regarding anxieties and mental well-being before and after the risk assessment. RESULTS As expected, participants with a reduced risk had a significant improvement in well-being and a reduction of fears and worries after the examination. Neither a significant deterioration of the mental situation nor an increase of fears and worries was found for participants with an elevated risk. Of the participants 90% stated that MRI-based risk stratification generated positive perspectives for the future. The assessment revealed a high acceptance by most of the participants (94%). CONCLUSION An MRI-based risk assessment is beneficial to the patient’s quality of life and as a low threshold approach may induce more individuals with concerns to take advantage of an early diagnosis of Alzheimer’s disease.