arXiv subjects

Moritz Berger

Publications and source records attributed to Moritz Berger.

At least 19 recordsLinked to original sources

arXiv2026

A tool to determine the degrees of freedom in tree-structured varying coefficient models

The tree-structured varying coefficient (TSVC) model is a flexible approach for generalized regression, where the linear effects of the covariates are allowed to vary with the values of effect modifiers. Relevant effect modifiers and interactions are identified using recursive partitioning. In TSVC models, analogously to other semi- and nonparametric regression approaches, one needs to account for the cost of data-driven model building when deriving the model degrees of freedom (DoF). To address this issue, we develop an easy-to-apply formula to approximate the DoF of a TSVC model. This formula is employed for model selection based on the Bayesian information criterion (BIC) and compared to the naive solution, setting the DoF to the number of free model parameters, in a simulation study. To illustrate the proposed DoF method, TSVC models using BIC-based selection were fitted to data from the Survey of Health, Ageing, and Retirement in Europe. Results indicated that calculation of the DoF using the proposed formula resulted in more accurate selection results with improved predictive ability.

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arXiv2026

A Simulation Study to Compare Inferential Properties when Modelling Ordinal Outcomes: The Case for the (Plain but Robust) Proportional Odds Model

Ordinal measurements are common outcomes in studies within psychology, as well as in the social and behavioral sciences. Choosing an appropriate regression model for analysing such data poses a difficult task. This paper aims to facilitate modeling decisions for quantitative researchers by presenting the results of an extensive simulation study on the inferential properties of common ordinal regression models: the proportional odds model, the category-specific odds model, the location-shift model, the location-scale model, and the linear model, which incorrectly treats ordinal outcomes as metric. The simulations were conducted under different data generating processes based on each of the ordinal models and varying parameter configurations within each model class. We examined the bias of parameter estimates as well as type I error rates ($\alpha$-errors) and the power of statistical parameter testing procedures corresponding to the respective models. Our findings reveal several highlights. For parameter estimates, we observed that cumulative ordinal regression models exhibited large biases in cases of large parameter values and high skewness of the outcome distribution in the true data generation process. Regarding statistical hypothesis testing, the proportional odds model and the linear model showed the most reliable results. Due to its better fit and interpretability for ordinal outcomes, we recommend the use of the proportional odds model unless there are relevant contraindications.

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arXiv2025

Flexible tree-structured regression for clustered data with an application to quality of life in older adults

Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of units, which requires taking the dependence of observations into account. This is, for example, the case in cross-national studies, as presented here, where country-specific effects should not be neglected. To address this issue, we present a flexible tree-structured approach that achieves a sparse modeling of unit-specific effects and identifies subgroups (based on individual-level covariates) that differ with regard to the outcome. The methodological advances were motivated by the analysis of quality of life in older adults using data from the survey of Health, Ageing and Retirement in Europe. Application of the proposed model yields promising results and illustrated the accessibility of the approach. A comparison to alternative methods with regard to variable selection and goodness-of-fit was performed in several simulation experiments.

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arXiv2024

Confidence intervals for tree-structured varying coefficients

The tree-structured varying coefficient model (TSVC) is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using recursive partitioning techniques. To quantify uncertainty in TSVC models, we propose a procedure to construct confidence intervals of the estimated partition-specific coefficients. This task constitutes a selective inference problem as the coefficients of a TSVC model result from data-driven model building. To account for this issue, we introduce a parametric bootstrap approach, which is tailored to the complex structure of TSVC. Finite sample properties, particularly coverage proportions, of the proposed confidence intervals are evaluated in a simulation study. For illustration, we consider applications to data from COVID-19 patients and from patients suffering from acute odontogenic infection. The proposed approach may also be adapted for constructing confidence intervals for other tree-based methods.

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arXiv2023

Modeling the Ratio of Correlated Biomarkers Using Copula Regression

Modeling the ratio of two dependent components as a function of covariates is a frequently pursued objective in observational research. Despite the high relevance of this topic in medical studies, where biomarker ratios are often used as surrogate endpoints for specific diseases, existing models are based on oversimplified assumptions, assuming e.g.\@ independence or strictly positive associations between the components. In this paper, we close this gap in the literature and propose a regression model where the marginal distributions of the two components are linked by Frank copula. A key feature of our model is that it allows for both positive and negative correlations between the components, with one of the model parameters being directly interpretable in terms of Kendall's rank correlation coefficient. We study our method theoretically, evaluate finite sample properties in a simulation study and demonstrate its efficacy in an application to diagnosis of Alzheimer's disease via ratios of amyloid-beta and total tau protein biomarkers.

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arXiv2023

Detection of nonlinearity, discontinuity and interactions in generalized regression models

In generalized regression models the effect of continuous covariates is commonly assumed to be linear. This assumption, however, may be too restrictive in applications and may lead to biased effect estimates and decreased predictive ability. While a multitude of alternatives for the flexible modeling of continuous covariates have been proposed, methods that provide guidance for choosing a suitable functional form are still limited. To address this issue, we propose a detection algorithm that evaluates several approaches for modeling continuous covariates and guides practitioners to choose the most appropriate alternative. The algorithm utilizes a unified framework for tree-structured modeling which makes the results easily interpretable. We assessed the performance of the algorithm by conducting a simulation study. To illustrate the proposed algorithm, we analyzed data of patients suffering from chronic kidney disease.

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arXiv2022

How Do Drivers Self-Regulate their Secondary Task Engagements? The Effect of Driving Automation on Touchscreen Interactions and Glance Behavior

With ever-improving driver assistance systems and large touchscreens becoming the main in-vehicle interface, drivers are more tempted than ever to engage in distracting non-driving-related tasks. However, little research exists on how driving automation affects drivers' self-regulation when interacting with center stack touchscreens. To investigate this, we employ multilevel models on a real-world driving dataset consisting of 10,139 sequences. Our results show significant differences in drivers' interaction and glance behavior in response to varying levels of driving automation, vehicle speed, and road curvature. During partially automated driving, drivers are not only more likely to engage in secondary touchscreen tasks, but their mean glance duration toward the touchscreen also increases by 12% (Level 1) and 20% (Level 2) compared to manual driving. We further show that the effect of driving automation on drivers' self-regulation is larger than that of vehicle speed and road curvature. The derived knowledge can facilitate the safety evaluation of infotainment systems and the development of context-aware driver monitoring systems.

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arXiv2020

Non Proportional Odds Models are Widely Dispensable -- Sparser Modeling based on Parametric and Additive Location-Shift Approaches

The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modeling. While proportional odds models are often too simple, non proportional odds models are typically unnecessary complicated and seem widely dispensable. The class of location-shift models is also extended to allow for smooth effects. The additive location-shift model contains two functions for each explanatory variable, one for the location and one for dispersion. It is much sparser than hard-to-handle additive models with category-specific covariate functions but more flexible than common vector generalized additive models.

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arXiv2020

Transition Models for Count Data: a Flexible Alternative to Fixed Distribution Models

A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared by utilizing several real data applications.

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arXiv2020

Views on Quality Requirements in Academia and Practice: Commonalities, Differences, and Context-Dependent Grey Areas

Context: Quality requirements (QRs) are a topic of constant discussions both in industry and academia. Debates entwine around the definition of quality requirements, the way how to handle them, or their importance for project success. While many academic endeavors contribute to the body of knowledge about QRs, practitioners may have different views. In fact, we still lack a consistent body of knowledge on QRs since much of the discussion around this topic is still dominated by observations that are strongly context-dependent. This holds for both academic and practitioners' views. Our assumption is that, in consequence, those views may differ. Objective: We report on a study to better understand the extent to which available research statements on quality requirements, as found in exemplary peer-reviewed and frequently cited publications, are reflected in the perception of practitioners. Our goal is to analyze differences, commonalities, and context-dependent grey areas in the views of academics and practitioners to allow a discussion on potential misconceptions (on either sides) and opportunities for future research. Method: We conducted a survey with 109 practitioners to assess whether they agree with research statements about QRs reflected in the literature. Based on a statistical model, we evaluate the impact of a set of context factors to the perception of research statements. Results: Our results show that a majority of the statements is well respected by practitioners; however, not all of them. When examining the different groups and backgrounds of respondents, we noticed interesting deviations of perceptions within different groups that may lead to new research questions. Conclusions: Our results help identifying prevalent context-dependent differences about how academics and practitioners view QRs and pinpointing statements where further research might be useful.

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arXiv2020

Assessing the Calibration of Subdistribution Hazard Models in Discrete Time

The generalization performance of a risk prediction model can be evaluated by its calibration, which measures the agreement between predicted and observed outcomes on external validation data. Here, methods for assessing the calibration of discrete time-to-event models in the presence of competing risks are proposed. The methods are designed for the class of discrete subdistribution hazard models, which directly relate the cumulative incidence function of one event of interest to a set of covariates. Simulation studies show that the methods are strong tools for calibration assessment even in scenarios with a high censoring rate and/or a large number of discrete time points. The proposed approaches are illustrated by an analysis of nosocomial pneumonia.

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arXiv2019

Tree-Structured Scale Effects in Binary and Ordinal Regression

In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity. In particular since it has been demonstrated that misleading effects can occur if one ignores the presence of a scaling component it is important to account for potential scaling effects in the regression model, which is not possible in available recursive partitioning methods. The proposed recursive partitioning method yields two trees, one for the location and one for the scaling. They show in a simple interpretable way how variables interact to determine the binary or ordinal response. The developed algorithm controls for the global significance level and automatically selects the variables that have an impact on the response. The modelling approach is illustrated by several real-world applications.

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arXiv2019

A Random Forest Approach for Modeling Bounded Outcomes

Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the unit interval, however, classical random forest approaches may severely suffer as they do not account for the heteroscedasticity in the data. A random forest approach is proposed for relating beta distributed outcomes to explanatory variables. The approach explicitly makes use of the likelihood function of the beta distribution for the selection of splits during the tree-building procedure. In each iteration of the tree-building algorithm one chooses the combination of explanatory variable and splitting rule that maximizes the log-likelihood function of the beta distribution with the parameter estimates derived from the nodes of the currently built tree. Several simulation studies demonstrate the properties of the method and compare its performance to classical random forest approaches as well as to parametric regression models.

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arXiv2017

Tree-Structured Modelling of Varying Coefficients

The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a set of explanatory variables and it is unknown which variables are modified by which covariates. A recursive partitioning strategy is proposed that is able to deal with the complex selection problem. The tree-structured modelling yields for each covariate, which is modified by other variables, a tree that visualizes the modified effects. The performance of the method is investigated in simulations and two applications illustrate its usefulness.

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arXiv2017

Semiparametric Regression for Discrete Time-to-Event Data

Time-to-event models are a popular tool to analyse data where the outcome variable is the time to the occurrence of a specific event of interest. Here we focus on the analysis of time-to-event outcomes that are either intrisically discrete or grouped versions of continuous event times. In the literature, there exists a variety of regression methods for such data. This tutorial provides an introduction to how these models can be applied using open source statistical software. In particular, we consider semiparametric extensions comprising the use of smooth nonlinear functions and tree-based methods. All methods are illustrated by data on the duration of unemployment of U.S. citizens.

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arXiv2016

Item-Focussed Trees for the Detection of Differential Item Functioning in Partial Credit Models

Various methods to detect differential item functioning (DIF) in item response models are available. However, most of the methods assume that the responses are binary, for ordered response categories available methods are scarce. In the present paper DIF in the widely used partial credit model is investigated. An item-focussed tree is proposed that allows to detect DIF-items, which might affect the performance of the partial credit model. The method uses tree methodology yielding a tree for each item that is detected as DIF-item. The resulting trees show which variables induce DIF and in which way. The visualization as trees makes the results easily accessible. The method is compared to an alternative approach, simulations demonstrate the performance of the method and an application illustrates how it works for real data.

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arXiv2015

Tree-Structured Clustering in Fixed Effects Models

Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of effects that have to be estimated. A recursive partitioning (or tree based) method is proposed that identifies clusters of units that share the same effect. The approach reduces the number of parameters to be estimated and is useful in particular if one is interested in identifying clusters with the same effect on a response variable. It is shown that the method performs well and outperforms competitors like the finite mixture model in particular if the heterogeneity component is correlated with explanatory variables. In two applications the usefulness of the approach to identify clusters that share the same effect is illustrated.

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arXiv2015

Detection of Uniform and Non-Uniform Differential Item Functioning by Item Focussed Trees

Detection of differential item functioning by use of the logistic modelling approach has a long tradition. One big advantage of the approach is that it can be used to investigate non-uniform DIF as well as uniform DIF. The classical approach allows to detect DIF by distinguishing between multiple groups. We propose an alternative method that is a combination of recursive partitioning methods (or trees) and logistic regression methodology to detect uniform and non-uniform DIF in a nonparametric way. The output of the method are trees that visualize in a simple way the structure of DIF in an item showing which variables are interacting in which way when generating DIF. In addition we consider a logistic regression method in which DIF can by induced by a vector of covariates, which may include categorical but also continuous covariates. The methods are investigated in simulation studies and illustrated by two applications.

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