Prof. Dr. Rainer Schwabe
Prof. Dr. Rainer Schwabe
Institute for Mathematical Stochastics (IMST)
Current projects
Optimal Design for Thurstonian IRT Models
Duration: 01.10.2024 bis 30.09.2027
The main aim of the present project is the development of optimal designs for Thurstonian IRT modes in the case of metric, binary, or ordinal responses which provide a sufficiently good estimation of the trait scores. In addition, binary paired comparisons will be considered which are derived from ranking more than two alternatives. In the present situation, optimal designs are characterized by combinations of those values of item parameters, factor loadings and intercepts which optimize prior determined criteria, as correlation between estimated and true trait scores. In order to apply these models in the selection of personnel, only positive factor loadings are admitted. This condition is supported by simulation studies and requires the development of novel types of optimal designs. Beyond properties of optimal designs developed in the literature so far, three more requirements have to be particularly taken into account: (a) the specific form of the non-linearity, (b) the restriction of the design region, and © the constraint that alternatives have to load on mutually distinct factors, respectively. To implement the findings of the project in practical applications, a user-friendly program in R is to be developed using a shiny app.
Optimal Design for General Linear Mixed Models
Duration: 01.01.2024 bis 30.06.2025
In many applications, in particular in clinical studies, more than one observation can be made at each unit or individual. Observations will then be no longer statistically independent within units. A common approach to cope with the dependence is to use mixed models which contain unit specific random effects apart from the fixed effects describing the impact of the explanatory variables on the response. The aim of the present project is to determine a characterization of optimal designs for estimating the fixed effects under general model assumptions which cover both models with random coefficients as well as longitudinal data with random time effects.
Optimal Design for Reference Curves in Medical Diagnostics
Duration: 01.07.2024 bis 30.06.2025
In medical diagnostics, reference curves play an important role for the detection of pathological deviations which give an indication for a disease or a damage. Such reference curves are determined on the basis of measurements made at healthy test persons. When reference curves are created, both the variability within individual test persons as well as the variability between distinct test persons are to be taken into account in order to obtain valid reference regions. To achieve this, suitable hierarchical models can be employed which describe the essential characteristics of the response variable used for the diagnostics in dependence on one or more covariates. The aim of the present project is to design calibration experiments in such a way that most precise reference regions are obtained for deviations without pathological findings with respect to the sensitivity of the resulting diagnostic test.
Design of Interlaboratory Experiments for Determining the Limit of Detection in PCR Testing
Duration: 01.09.2021 bis 31.03.2025
PCR testing is a highly sensitive technique to detect nucleic acids. It has gained wide acceptance in routine testing in the last years, but more efforts are needed to evaluate its performance. One crucial point is the limit of detection which serves as a measure of the sensitivity of the testing method. This limit of detection can be determined in interlaboratory experiments. However, the results will commonly vary between laboratories. The laboratories in a study may be considered as representatives of the entity of laboratories which will work with the testing method. The variation between the laboratories can, hence, be modeled by random effects. The aim of the present project is to develop optimal or, at least, efficient designs for estimating the underlying model parameters, for quantifying the influence of the laboratories, and for determining the limit of detection as precisely as possible.
Optimal Design for Spherical Design Regions (II)
Duration: 01.10.2019 bis 31.12.2024
The validity of statistical models is often restricted to a local region for the explanatory variables. This region is typically assumed to be rectangular in many applications which means that the explanatory variables may vary independently of each other. In some situations, however, spherical regions are more meaningful which are described by a bounded Euclidean or Mahalanobis distance to a central point for the experimental settings.
The aim of the design of an experiment is to determine optimal or at least efficient settings for the explanatory variables in order to optimize the quality of the statistical analysis. In the case of classical models of linear regression characterizations of optimal designs are well established for spherical regions which use concepts of invariance and symmetry.
The purpose of the present project is to develop optimal designs on spherical regions for generalized linear models resp. nonlinear models which are nowadays frequently used in practical applications. First results obtained for Poisson count data show substantial deviations of the corresponding optimal designs from those for classical linear models.
Optimal Sampling Design for Big Data (II)
Duration: 01.04.2024 bis 05.12.2024
Modern information technology allows for collecting hugh amounts of data both in terms of units (size) as well as in terms of variables (multivariate observations) which are frequently called "Big Data”. However, the pure availability of Big Data does not necessary lead to further insight into causal structures within the data. Instead the sheer amount of data may cause severe problems for a statistical analysis. Moreover, in many situations parts (certain variables) of the data are cheap to obtain while other variables of interest may be expensive. Therefore prediction of the expensive variables would be desirable. This can be achieved by standard statistical methods when for a suitable subsample also the expensive variables are available. To reduce costs and/or improve the accuracy of the prediction there is a need for optimal sampling schemes. Concepts of optimal design theory originally related to technical experiments may be deployed in a non-standard way to generate efficient sampling strategies. Basic concepts like relaxation to continuous distributions of the data and symmetry properties may lead to substantial reduction in complexity and, hence, to feasible solutions. To make this general ideas more precise and to put them on a sound foundation to make them applicable to real data constitutes the aim of the present project.
Completed projects
Optimal Sampling Design for Big Data
Duration: 01.04.2020 bis 31.03.2024
Modern information technology allows for collecting hugh amounts of data both in terms of units (size) as well as in terms of variables (multivariate observations) which are frequently called "Big Data”. However, the pure availability of Big Data does not necessary lead to further insight into causal structures within the data. Instead the sheer amount of data may cause severe problems for a statistical analysis. Moreover, in many situations parts (certain variables) of the data are cheap to obtain while other variables of interest may be expensive. Therefore prediction of the expensive variables would be desirable. This can be achieved by standard statistical methods when for a suitable subsample also the expensive variables are available. To reduce costs and/or improve the accuracy of the prediction there is a need for optimal sampling schemes. Concepts of optimal design theory originally related to technical experiments may be deployed in a non-standard way to generate efficient sampling strategies. Basic concepts like relaxation to continuous distributions of the data and symmetry properties may lead to substantial reduction in complexity and, hence, to feasible solutions. To make this general ideas more precise and to put them on a sound foundation to make them applicable to real data constitutes the aim of the present project.
Analyzing recurrent event process with a terminal event (informative censoring) - study design considerations
Duration: 01.04.2018 bis 31.03.2023
Recurrent events involve the occurrences of the same type of event repeatedly over time and are commonly encountered in clinical studies. Examples include seizures in epileptic studies, flares in gout studies or heart failure hospitalizations for patients suffering from chronic heart failure.
One considerable challenge in analyzing recurrent event data arises when informative censoring occurs. In a clinical trial for example, a patient may discontinue from the study because his/her condition is deteriorating such that an alternative treatment is needed. In this case, the mere fact that the patient discontinues may indicate that the event of interest is likely to occur sooner or more frequently than might have been expected under an independent censoring assumption. Informative censoring may also occur in combination with a terminal event that stops the recurrent event process. For example, in a chronic heart failure study death may stop the heart failure hospitalization process for a patient. As the determinants of heart failure hospitalization are shared with the risk factors for death we cannot neglect such dependence as resulting inference may otherwise be biased.
For designing a study aimed at assessing treatment effects on such endpoints and associated data analyses, many extensions of classical survival models are proposed. Of particular interest is the joint frailty model with correlated frailties, where separate marginal intensity models for both event processes are analyzed with each of the models having correlated random effects designating subject specific frailties.
This project will involve methodological work, applied data analysis but also simulation work.
Optimal Design of Experiments for Multi-variable Accelerated Degradation Tests (II)
Duration: 01.04.2022 bis 31.03.2023
The rapid advances in modern manufacturing technology, along with consumer needs for high quality products, have motivated the industry to design and manufacture products that can operate without failure for years or even tens of years. However, for such highly reliable products, it is not a trivial task to assess the product reliability within short test durations because sufficient life time data are generally required to accurately estimate product s lifetime distribution. Accordingly, time to failure testing at normal conditions is impractical. Therefore, repeated measures accelerated degradation tests are commonly utilized in manufacturing industries to assess the lifetime distribution of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. In this regard, data from tests at high levels of stress (e.g., temperature, voltage, or pressure) are extrapolated, through a physically reasonable statistical model, to obtain estimates of life time at lower, normal levels of stress. In addition, several factors, such as the inspection frequency, the sample size and the termination time, are closely related to the experimental cost and the estimation precision.
In this project various systems of bivariate degradation processes wiill be considered, where the correlation structureis given by a copula, and optimal designs will be determined for this situation.
Quasi-likelihood and Quasi-information for Non-linear and Generalized Linear Mixed Models (II)
Duration: 01.01.2023 bis 31.03.2023
Non-linear and generalized linear mixed models are effectively used for statistical analyses of data in a variety of applications in bio- or social sciences when the basic assumptions of commonly imposed linear models are not met. Such situations arise either when the data arise from an intrinsically non-linear relationship on parameters as in pharmacokinetics, in growth and dose-response curves or the response variable is reported on a non-metric scale like count data and nominal or ordinal response. Additionally mixed effects occur when repeated measurements are obtained within statistical units. This leads to a violation of the common assumption of independent observations. The non-linearity in combination with the mixed effects modeling makes an explicit calculation of the likelihood and thus of the Fisher information infeasible. As a surrogate quasi-likelihood and the resulting quasi-information will be considered which are easier to handle and result in feasible estimates and their uncertainty quantification. This approach further allows for the construction of reliable experimental designs which optimize the performance of the underlying experiments in advance. In so far this approach simplifies the complexity of the underlying estimation and design problem and can readily combined with other commonly used reduction principles in statistics like invariance and equivariance.
Sequential Adaptive Design
Duration: 01.04.2020 bis 31.03.2023
Non-linear regression plays an important role in adequate statistical modelling of data, when the influence of explanatory variables on the target variable of interest cannot be described by simple linear response function. In those models the information matrix of an experimental design depends on the parameter vector for which the true value is unknown. For such situations common approaches in optimal experimental design are locally optimal designs, Bayes-optimal designs or minimax designs. These concepts, however, require prior knowledge about the true value of the parameter. Sequential adaptive designs are learning procedures. They accumulate information about the true parameter value from previous observations in a sequential manner and can thus work without prior information. In these procedures adaptive updates are sequentially generated for the parameter estimates based on previously made observations. By means of these updated estimates the design is augmented appropriately. A popular algorithm of this kind is the adaptive Wynn algorithm for the asymptotic generation of D-optimal designs. In the joint work by Freise, Gaffke and Schwabe (2019a) the long lasting open problem concerning the convergence of this algorithm was (affirmatively) solved, at least, for the practically important class of generalized linear models. In the second work by Freise, Gaffke and Schwabe (2019b) this result was extended to another class of non-linear models and to other estimation methods. Currently the authors analyze a new algorithm for the asymptotic generation of D-optimal designs in which several observations are added simultaneously. Further aims of this project are the extension to further classes of non-linear models and further optimality criteria on the one hand side, and the test and the evaluation of the actual convergence properties of the algorithms on the other hand side.
Freise, F.; Gaffke, N.; Schwabe, R. (2019a). The adaptive Wynn-algorithm in generalized linear models with univariate response. Preprint arXiv:1907.02708
Freise, F.; Gaffke, N.; Schwabe, R. (2019b). Convergence of least squares estimators
in the adaptive Wynn algorithm for a class of nonlinear regression models. Preprint. arXiv:1909.03763
Quasi-likelihood and Quasi-information for Non-linear and Generalized Linear Mixed Models
Duration: 01.07.2019 bis 31.12.2022
Non-linear and generalized linear mixed models are effectively used for statistical analyses of data in a variety of applications in bio- or social sciences when the basic assumptions of commonly imposed linear models are not met. Such situations arise either when the data arise from an intrinsically non-linear relationship on parameters as in pharmacokinetics, in growth and dose-response curves or the response variable is reported on a non-metric scale like count data and nominal or ordinal response. Additionally mixed effects occur when repeated measurements are obtained within statistical units. This leads to a violation of the common assumption of independent observations. The non-linearity in combination with the mixed effects modeling makes an explicit calculation of the likelihood and thus of the Fisher information infeasible. As a surrogate quasi-likelihood and the resulting quasi-information will be considered which are easier to handle and result in feasible estimates and their uncertainty quantification. This approach further allows for the construction of reliable experimental designs which optimize the performance of the underlying experiments in advance. In so far this approach simplifies the complexity of the underlying estimation and design problem and can readily combined with other commonly used reduction principles in statistics like invariance and equivariance.
Optimal Design of Experiments for Multi-variable Accelerated Degradation Tests
Duration: 01.10.2017 bis 31.03.2022
The rapid advances in modern manufacturing technology, along with consumer needs for high quality products, have motivated the industry to design and manufacture products that can operate without failure for years or even tens of years. However, for such highly reliable products, it is not a trivial task to assess the product reliability within short test durations because sufficient life time data are generally required to accurately estimate product s lifetime distribution. Accordingly, time to failure testing at normal conditions is impractical. Therefore, repeated measures accelerated degradation tests are commonly utilized in manufacturing industries to assess the lifetime distribution of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. In this regard, data from tests at high levels of stress (e.g., temperature, voltage, or pressure) are extrapolated, through a physically reasonable statistical model, to obtain estimates of life time at lower, normal levels of stress. In addition, several factors, such as the inspection frequency, the sample size and the termination time, are closely related to the experimental cost and the estimation precision.
In this project first adequate and relevant computer experiments will be identified and robust methods of regression analysis will be developed. Then optimality criteria will be defined for experimental design based on the performance of the selected robust methods nad simulation based design will bedeveloped in order to obtain a unified approach to generate optimal or at least efficient designs for robust analysis in computer experiments.
Generation of Optimal and Efficient Designs of Experiments for Individualized Prediction in Hierarchical Models (II)
Duration: 16.02.2019 bis 15.03.2022
The aim of the present project is to develop an analytical approach for the determination of optimal designs for the problem of prediction in hierarchical random coefficient regression models as well as in generalized linear and nonlinear mixed models. Such models were initially introduced in bio- and agricultural sciences and are nowadays utilized in an increasing number of fields in statistical applications.
Mathematisches Komplexitätsreduktion (GRK 2297/1)
Duration: 01.04.2017 bis 30.09.2021
Das Projekt wird von den genannten Principal Investigators getragen. Diese sind den Instituten für Mathematische Optimierung (Averkov, Kaibel, Sager), für Algebra und Geometrie (Kahle, Nill, Pott), für Mathematische Stochastik (Kirch, Schwabe) und für Analysis und Numerik (Benner) der Fakultät zugeordnet. Benner ist zudem Direktor des Max-Planck Institutes für Dynamik komplexer technischer Systeme. Die Fakultät für Elektrotechnik und Informationstechnik ist über Findeisen beteiligt.
Im Kontext des vorgeschlagenen Graduiertenkollegs (GK) verstehen wir Komplexität als eine intrinsische Eigenschaft, die einen mathematischen Zugang zu einem Problem auf drei Ebenen erschwert. Diese Ebenen sind eine angemessene mathematische Darstellung eines realen Problems, die Erkenntnis fundamentaler Eigenschaften und Strukturen mathematischer Objekte und das algorithmische Lösen einer mathematischen Problemstellung. Wir bezeichnen alle Ansätze, die systematisch auf einer dieser drei Ebenen zu einer zumindest partiellen Verbesserung führen, als mathematische Komplexitätsreduktion.
Für viele mathematische Fragestellungen sind Approximation und Dimensionsreduktion die wichtigsten Werkzeuge auf dem Weg zu einer vereinfachten Darstellung und Rechenzeitgewinnen. Wir sehen die Komplexitätsreduktionin einem allgemeineren Sinne und werden zusätzlich auch Liftings in höherdimensionale Räume und den Einfluss der Kosten von Datenerhebungen systematisch untersuchen. Unsere Forschungsziele sind die Entwicklung von mathematischer Theorie und Algorithmen sowie die Identifikation relevanter Problemklassen und möglicher Strukturausnutzung im Fokus der oben beschriebenen Komplexitätsreduktion.
Unsere Vision ist ein umfassendes Lehr- und Forschungsprogramm, das auf geometrischen, algebraischen, stochastischen und analytischen Ansätzen beruht und durch effiziente numerische Implementierungen komplementiert wird. Die Doktorandinnen und Doktoranden werden an einem maßgeschneiderten Ausbildungsprogramm teilnehmen. Dieses enthält unter anderem Kompaktkurse, ein wöchentliches Seminar und ermutigt zu einer frühzeitigen Integration in die wissenschaftliche Community. Wir erwarten, dass das GK als ein Katalysator zur Etablierung dieser erfolgreichen DFG-Ausbildungskonzepte an der Fakultät für Mathematik dienen und zudem helfen wird, die Gleichstellungssituation zu verbessern.
Die Komplexitätsreduktion ist ein elementarer Aspekt der wissenschaftlichen Hintergründe der beteiligten Wissenschaftler. Die Kombination von Expertisen unterschiedlicher mathematischer Bereiche gibt dem GK ein Alleinstellungsmerkmal mit großen Chancen für wissenschaftliche Durchbrüche. Das GK wird Anknüpfungspunkte an zwei Fakultäten der OVGU, an ein Max Planck Institut und mehrere nationale und internationale Forschungsaktivitäten in verschiedenen wissenschaftlichen Communities haben. Die Studierenden im GK werden in einer Fülle von mathematischen Methoden und Konzepten ausgebildet und erlangen dadurch die Fähigkeit, herausfordernde Aufgaben zu lösen. Wir erwarten Erfolge in der Forschung und in der Ausbildung der nächsten Generation führender Wissenschaftler in Akademia und Industrie.
Equivariance and IMSE-optimality of Designs in Generalized Linear Models with Continuous Outcomes
Duration: 01.10.2020 bis 31.08.2021
In many applications where data are collected the assumption of an underlying Gaussian distribution is not appropriate. In particular, when the outcomes are not continuous, generalized linear models have been developed which provide reliable tools for binary (logistic regression) or count (Poisson regression) data. But even for continuous outcomes the assumption of Gaussian errors may be not adequate, and the data may be described more properly by some generalized linear model with non-linear link function. The present project aims at the construction of optimal designs fpt those models by using inherent symmetry properties to improve the quality of the data analysis.
Equivariance and IMSE-optimality of Designs in Generalized Linear Models with Continuous Outcomes
Duration: 01.04.2020 bis 30.09.2020
In many applications where data are collected the assumption of an underlying Gaussian distribution is not appropriate. In particular, when the outcomes are not continuous, generalized linear models have been developed which provide reliable tools for binary (logistic regression) or count (Poisson regression) data. But even for continuous outcomes the assumption of Gaussian errors may be not adequate, and the data may be described more properly by some generalized linear model with non-linear link function. The present project aims at the construction of optimal designs fpt those models by using inherent symmetry properties to improve the quality of the data analysis.
Geometry of optimal designs for nonlinear models in statistics
Duration: 01.04.2017 bis 31.03.2020
Geometric descriptions of optimal design regions are of growing interest in times of an increasing complexity of statistical models. The aim of the project is in searching for optimality regions of experimental designs for such statistical models, especially for generalized linear models with Poisson or logistic response. These regions are described by systems of polynomial inequalities in the parameter space, which means that they are nothing else than semialgebraic sets. Hence algebraic geometry can be used to study the properties of these optimality regions. For example, in the Bradley-Terry paired comparison model, which is a statistical model for comparisons of alternatives depending on a logistic response, we are interested in the optimality regions of so called saturated designs, i.e. designs with a minimal number of support points.
Optimal Design for Multivariate Generalized Linear Models with Continuous Outcomes (II)
Duration: 01.10.2019 bis 31.03.2020
In many applications where data are collected there is not only a single variable to be observed but there are several outcomes which are measured simultaneously and may be correlated with each other. Such multivariate observations are often described by an underlying multivariate Gaussian distribution. However, in some situations this approach is not appropriate. In particular, when the outcomes are not continuous, generalized linear models have been developed which provide reliable tools for binary (logistic regression) or count (Poisson regression) data. But even for continuous outcomes the assumption of Gaussian errors may be not adequate, and the data may be described more properly by some generalized linear model with non-linear link function. The present project aims at a proper description of asymptotic properties for such models under various correlation structures and the construction of optimal designs to improve the quality of the data analysis.
Sequential Adaptive Design
Duration: 01.01.2019 bis 31.03.2020
Non-linear regression plays an important role in adequate statistical modelling of data, when the influence of explanatory variables on the target variable of interest cannot be described by simple linear response function. In those models the information matrix of an experimental design depends on the parameter vector for which the true value is unknown. For such situations common approaches in optimal experimental design are locally optimal designs, Bayes-optimal designs or minimax designs. These concepts, however, require prior knowledge about the true value of the parameter. Sequential adaptive designs are learning procedures. They accumulate information about the true parameter value from previous observations in a sequential manner and can thus work without prior information. In these procedures adaptive updates are sequentially generated for the parameter estimates based on previously made observations. By means of these updated estimates the design is augmented appropriately. A popular algorithm of this kind is the adaptive Wynn algorithm for the asymptotic generation of D-optimal designs. In the joint work by Freise, Gaffke and Schwabe (2019a) the long lasting open problem concerning the convergence of this algorithm was (affirmatively) solved, at least, for the practically important class of generalized linear models. In the second work by Freise, Gaffke and Schwabe (2019b) this result was extended to another class of non-linear models and to other estimation methods. Currently the authors analyze a new algorithm for the asymptotic generation of D-optimal designs in which several observations are added simultaneously. Further aims of this project are the extension to further classes of non-linear models and further optimality criteria on the one hand side, and the test and the evaluation of the actual convergence properties of the algorithms on the other hand side.
Freise, F.; Gaffke, N.; Schwabe, R. (2019a). The adaptive Wynn-algorithm in generalized linear models with univariate response. Preprint arXiv:1907.02708
Freise, F.; Gaffke, N.; Schwabe, R. (2019b). Convergence of least squares estimators
in the adaptive Wynn algorithm for a class of nonlinear regression models. Preprint. arXiv:1909.03763
Optimal Design for Generalized Linear Mixed Models (II)
Duration: 01.10.2019 bis 31.01.2020
Mixed models are of increasing interest not solely in biosciences but also in problems in economic and social sciences in order to account for individual effects of the different observational units as representatives of a larger population in the statistical data analysis. Generalized linear mixed models are used to describe binary ("success - failure") or discrete responses ("counts"), which cannot represented in a meaningful way by standard linear mixed models for metric data. The occurring individual variability may then be assumed to come from a conjugate prior in addition to normally distributed random effects. These conjugate priors allow for a more explicit analysis of the data. As for all statistical studies the performance heavily depends on the observational or experimental design, i.e. on the choice of the observational units and time points. The aim of the present project is to develop optimal or, at least, efficient designs for generalized linear mixed models, which may incorporate both normally distributed random effects as well as those arising from a conjugate prior, and validate them.
Optimal Design for Discrete Choice Experiments with Higher Order Interactions
Duration: 01.10.2019 bis 31.12.2019
Discrete choice experiments are a popular marketing research method. They are used for eliciting consumer preferences and for estimating the utility people attach to the various attributes of a product. To this end, in each of a series of choice questions, respondents are asked to compare competing variants of the product and to choose the most attractive alternative. The questions are generated according to an experimental design and by using an efficient design more information can be obtained from the experiment. However, models and designs for discrete choice experiments do often not take higher order interactions into account which may describe synergy effects bewtween the attributes. The aim of this project is to develop and to validate optimal and efficient designs for discrete choice models with higher order interactions which account for these potential dependencies.
Optimal Design for Multivariate Generalized Linear Models with Continuous Outcomes
Duration: 01.10.2016 bis 30.09.2019
In many applications where data are collected there is not only a single variable to be observed but there are several outcomes which are measured simultaneously and may be correlated with each other. Such multivariate observations are often described by an underlying multivariate Gaussian distribution. However, in some situations this approach is not appropriate. In particular, when the outcomes are not continuous, generalized linear models have been developed which provide reliable tools for binary (logistic regression) or count (Poisson regression) data. But even for continuous outcomes the assumption of Gaussian errors may be not adequate, and the data may be described more properly by some generalized linear model with non-linear link function. The present project aims at a proper description of asymptotic properties for such models under various correlation structures and the construction of optimal designs to improve the quality of the data analysis.
Optimal Design for Spherical Design Regions
Duration: 01.01.2017 bis 30.09.2019
The validity of statistical models is often restricted to a local region for the explanatory variables. This region is typically assumed to be rectangular in many applications which means that the explanatory variables may vary independently of each other. In some situations, however, spherical regions are more meaningful which are described by a bounded Euclidean or Mahalanobis distance to a central point for the experimental settings.
The aim of the design of an experiment is to determine optimal or at least efficient settings for the explanatory variables in order to optimize the quality of the statistical analysis. In the case of classical models of linear regression characterizations of optimal designs are well established for spherical regions which use concepts of invariance and symmetry.
The purpose of the present project is to develop optimal designs on spherical regions for generalized linear models resp. nonlinear models which are nowadays frequently used in practical applications. First results obtained for Poisson count data show substantial deviations of the corresponding optimal designs from those for classical linear models.
Optimal Design for Generalized Linear Mixed Models
Duration: 01.10.2013 bis 30.09.2019
Mixed models are of increasing interest not solely in biosciences but also in problems in economic and social sciences in order to account for individual effects of the different observational units as representatives of a larger population in the statistical data analysis. Generalized linear mixed models are used to describe binary ("success - failure") or discrete responses ("counts"), which cannot represented in a meaningful way by standard linear mixed models for metric data. The occurring individual variability may then be assumed to come from a conjugate prior in addition to normally distributed random effects. These conjugate priors allow for a more explicit analysis of the data. As for all statistical studies the performance heavily depends on the observational or experimental design, i.e. on the choice of the observational units and time points. The aim of the present project is to develop optimal or, at least, efficient designs for generalized linear mixed models, which may incorporate both normally distributed random effects as well as those arising from a conjugate prior, and validate them.
Optimal Design for Discrete Choice Experiments with Blocked Observations
Duration: 01.10.2016 bis 30.09.2019
Discrete choice experiments are a popular marketing research method. They are used for eliciting consumer preferences and for estimating the utility people attach to the various attributes of a product. To this end, in each of a series of choice questions, respondents are asked to compare competing variants of the product and to choose the most attractive alternative. The questions are generated according to an experimental design and by using an efficient design more information can be obtained from the experiment. However, models and designs for discrete choice experiments do often not take into account potential correlations that are consequence of the fact that every respondent answers several questions. The aim of this project is to develop and to validate optimal and efficient designs for discrete choice models with block effects which account for these potential dependencies.
Optimal Design for online generated adaptive methode for intelligence testing (IV)
Duration: 01.09.2018 bis 31.05.2019
In this project adaptive procedure are developed for intelligence tests, which aim at measuring the general intelligence. Test items will be generated automatically and online by a rule-based item generator and adaptively presented. The items will be selected according to the parameter estimates in generalized linear logistic test models. The parameter estimations will be based on optimal designs in order to obtain maximal precision in measuring the intelligence by a minimal number of items to be presented. In detail four types of rule-based test procedures will be constructed for measuring the general intelligence and the necessary basic principles of statistics wikll be developed.
In Phase I rule based items were developed for measuring the working speed and empirically calibrated based on D-optimal dsigns in linear logistic test models with fixed and random factors. Furthermore a programming system was developed for the automatic generation of these items, their adaptive presentation and the estimation of person parameters.
In Phase II of this project the work of Phase I has been continued. In analogy to the items on working capacity developed in Phase I rule based items on working speed were constructed, which are suitable for an adaptive testing of this intelligence component. As speed tests were considered, it was necessary to use some extended versions of the Rasch Poisson Count Model as the statistical basis instead of the Logistic Rasch Model of Phase I. For these models again optimal designs were developed for both item calibration and adaptive testing.
In Phase III of this project time trends will be considered for the modelling of intelligence components in longitudinal studies. Also for this situation optimal designs will be constructed which can be used adaptively both within one session as well as over time. Additionally, optimal designs will be provided for the generation of item pools under constraints on the number of rules used.
Generation of Optimal and Efficient Designs of Experiments for Individualized Prediction in Hierarchical Models
Duration: 16.02.2017 bis 15.02.2019
The aim of the present project is to develop an analytical approach for the determination of optimal designs for the problem of prediction in hierarchical random coefficient regression models as well as in generalized linear and nonlinear mixed models. Such models were initially introduced in bio- and agricultural sciences and are nowadays utilized in an increasing number of fields in statistical applications.
Optimal Design for online generated adaptive methode for intelligence testing (III)
Duration: 01.01.2016 bis 31.12.2017
In this project adaptive procedure are developed for intelligence tests, which aim at measuring the general intelligence. Test items will be generated automatically and online by a rule-based item generator and adaptively presented. The items will be selected according to the parameter estimates in generalized linear logistic test models. The parameter estimations will be based on optimal designs in order to obtain maximal precision in measuring the intelligence by a minimal number of items to be presented. In detail four types of rule-based test procedures will be constructed for measuring the general intelligence and the necessary basic principles of statistics wikll be developed.
In Phase I rule based items were developed for measuring the working speed and empirically calibrated based on D-optimal dsigns in linear logistic test models with fixed and random factors. Furthermore a programming system was developed for the automatic generation of these items, their adaptive presentation and the estimation of person parameters.
In Phase II of this project the work of Phase I has been continued. In analogy to the items on working capacity developed in Phase I rule based items on working speed were constructed, which are suitable for an adaptive testing of this intelligence component. As speed tests were considered, it was necessary to use some extended versions of the Rasch Poisson Count Model as the statistical basis instead of the Logistic Rasch Model of Phase I. For these models again optimal designs were developed for both item calibration and adaptive testing.
In Phase III of this project time trends will be considered for the modelling of intelligence components in longitudinal studies. Also for this situation optimal designs will be constructed which can be used adaptively both within one session as well as over time. Additionally, optimal designs will be provided for the generation of item pools under constraints on the number of rules used.
Metaanalyse von unerwünschten Ereignissen in klinischen Studien basierend auf Aggregatdaten
Duration: 01.02.2015 bis 20.10.2017
Zur Charakterisierung der Nebenwirkungen von medizinischen Behandlungen ist es von Interesse, die Evidenz aus mehreren klinischen Studien zu kombinieren und auch historische Daten über die Kontrollgruppe zu berücksichtigen, weil in jeder einzelnen Studie oft nur wenige unerwünschte medizinische Ereignisse auftreten. Wenn für alle Studien detaillierte Patientendaten verfügbar sind, werden üblicherweise Überlebenszeitmethoden angewandt, um das Auftreten von unerwünschten Ereignissen unter Berücksichtigung der Dauer des Beobachtungszeitraums zu analysieren. Dies ist besonders dann wichtig, falls die Beobachtungsdauer sich zwischen Behandlungsgruppen unterscheidet oder falls die Austauschbarkeit von Modellparametern zwischen Studien von verschiedener Länge angenommen wird. Traditionelle Überlebenszeitmethoden können allerdings nicht angewandt werden, wenn für einige Studien lediglich Aggregatdaten verfügbar sind. Dies stellt ein Problem in der Metaanalyse dar, da Metanalysen meist auf Veröffentlichungen in medizinischen Fachzeitschriften beruhen, welche in aller Regel keine individuellen Patientendaten enthalten.
Ziel dieses Projektes ist es, statistische Methoden zu entwickeln und zu evaluieren, die Überlebenszeitmetaanalysen unter Berücksichtigung historischer Studien basierend auf Aggregatdaten ermöglichen.
Empirically and Hierarchically Bayesian Optimal Design for Logistic Regression Model with Random Effects
Duration: 15.03.2017 bis 15.09.2017
Binary data are often statistically analyzed by means of logistic regression models. To improve the quality of the analysis the design of the underlying experiment has to be optimized. Because of the nonlinearity of the modeling optimal designs depend on unknown parameters. To circumvent this problem Bayesian prior information may be introduced which can be modeled hierarchically and validated by empirical priors. Moreover, in the case of repeated measurements inter-individual variability has to be taken into account. All these concepts are to be summarized into a unified approach.
Optimal Design for Statistical Models with Censored Data
Duration: 01.04.2013 bis 30.06.2017
In many areas of engineering and biosciences the statistical analysis of censored data plays an important role. In these situations the censoring may be deterministic (fixed duration of the study, detection limits) or random (random duration of the study, random drop outs). The observed, partly censored variables may additionally be influenced by further factors (treatments and covariates), which can, for example, be described by a proportional hazards model.
While the statistical analysis of such data is quite well developed, there are relatively few results on the efficient design of such studies or experiments. The aim of the present project is to charcterize and to determine analytically optimal or. at least, efficient designs for a couple of relevant model situations in order to provide instructions for an efficient as possible utilization of the available resources in the case of censored data.
Optimal Design for the individual prediction of inter- and extrapolation in regression models with random parameters
Duration: 16.06.2016 bis 15.02.2017
In der statistischen Datenanalyse werden Modelle mit zufälligen Parametern in verschiedenen Anwendungsbereichen, insbesondere in den Biowissenschaften und der individualisierten Medizinforschung, häufig verwendet. In diesen Modellen ist neben der Schätzung des Populationsparameters die Vorhersage individueller zufälliger Effekte von Interesse. Der individualisierte Ansatz ist vor allem für die Studien, in denen nur wenige Beobachtungen pro Individuum möglich sind, z.B. in der Onkologie, von großer Bedeutung. Ziel dieses Projektes ist es, optimale oder zumindest effiziente und anwendbare Versuchspläne (Designs) für die Vorhersage von individuellen zufälligen Effekten für solche Experimentalsituationen zu konstruieren und zu validieren, in denen in unterschiedlichen Gruppen nur Querschnittsdesigns angewendet werden können.
Optimal Design for Dynamical Systems
Duration: 01.10.2013 bis 31.12.2016
Although technical systems may be highly developed the influence of technical settings on the response may often be observed only subject to statistical, i.e. random deviations. The resulting responce curves or surfaces can often not be explicitly represented, but canbe described by one or more differential equations, for which some of the model parameters are unknown. On the basis of observed data these model parameters have to be determined by suitable estimation methods. The performance of this estimation heavily depends on the design, i.e. on the choice of the experimental settings and the times of measurements. The aim of the present project is to develop strategies for the determination of optimal or, at least, efficient designs and to validate them.
Optimal Design for the individual prediction of inter- and extrapolation in regression models with random parameters
Duration: 15.10.2015 bis 15.06.2016
Regressionsmodelle mit zufälligen Parametern werden in statistischen Anwendungsbereichen, insbesondere in den Biowissenschaften, sowie in individualisierter Medizinforschung häufig verwendet. In diesen Modellen ist neben der Schätzung des Populationsparameters die Vorhersage individueller zufälliger Parameter von Interesse. Der individualisierte Ansatz ist vor allem für die Studien, in denen nur wenige Beobachtungen pro Individuum möglich sind, von großer Bedeutung. Letzteres ist für medizinische Fragestellungen, z.B. bei Untersuchungen von Blutentnahmen bei Patienten, besonders relevant. Ziel dieses Projektes ist es, optimale oder zumindest effiziente und anwendbare Versuchspläne (Designs) für die Vorhersage von Inter- und Extrapolation individueller Wirkungsfunktionen in Regressionsmodellen mit zufälligen Parametern zu entwickeln.
Adaptive Design
Duration: 01.04.2014 bis 31.01.2016
The quality of statistical experiments can be substantially improved by a suitable choice of the experimental conditions. The goal is to estimate the parameters as precise as possible with a minimal number of observations. For non-linear models one of the major problems is here that optimal designs will usually depend on the unknown parameters of interest. To use adaptive and sequential procedures based on the optimal designs can be a way out. The development and the analysis of such adaptive methods is the objective of the present project, where particular focus is on designs for dose-response models.The results can be applied for example in adaptive intelligence tests, which are investigated within the project "Optimal Design for online generated adaptive procedures for intelligence testing".
Optimal experimental design for indivdual customization in mixed models
Duration: 01.01.2011 bis 30.09.2015
In drug development primary interest is mainly in the charakteristics of a target population to facilitate the introduction of a product with potentially general efficacy. New trends, however, aim at an individualized approach. For this it is necessary to specify the charakteristics of single individueals as exact as possible based both on the subject specific observations as well as the properties of the population. The latter is of particular importance, if for ethical or technical reasons only very few (invasive) observations are possible per subject. For this problem optimal designs are to be generated, which allow for an efficient analysis of the observsations.
Theoretische Grundlagen der statistischen Datenanalyse mit "Partial Least Squares"
Duration: 01.02.2012 bis 06.06.2014
"Partial Least Squares" ist eine modernes Verfahren zur Dimensionsreduktion in hochdimensionalen Datensätzen, wie sie z.B. in den Neurowissenschaften bei MRT-Daten zur Analyse von Hirnaktivitäten oder bei der Bildanalyse anfallen. Ziel des vorliegenden Projektes ist es, geeignete theoretische Grundlagen und Modelle für die den Daten zu Grunde liegenden Strukturen zu entwickeln und zu validieren.
Adaptives Design
Duration: 01.04.2013 bis 31.03.2014
Durch eine geeigente Wahl der Versuchsbedingungen kann in vielen statistischen Experimenten eine wesentliche Verbesserung der Analyseergebnisse bzw.\ eine deutliche Verringerung der Kosten für die Durchführung des Experiments erzielt werden. Liegen nichtlineare Wirkungszusammenhänge zwischen den Versuchsbedingungen und der die Zielvariable beschreibenden Wirkungsfunktion vor, ergibt sich dabei das Problem, dass die optimalen Versuchspläne, d.h.\ die optimale Wahl der Versuchseinstellungen, in der Regel von den unbekannten und zu schätzenden Parametern abhängen. Während dies bei einstufig geplanten Experimenten ein schier unlösbares Problem darstellt, bieten adaptive und sequenzielle Verfahren, die "on-line" die Information zuvor gemachter Beobachtungen ausnutzen, einen vielversprechenden Ansatz, um auch in solchen Situationen mit möglichst wenigen Messungen zu möglichst genauen Schätzungen zu gelangen.Derartige Verfahren sollen im Rahmen des vorliegenden Projektes entwickelt und auf ihre Eigenschaften unter realen Versuchsbedingungen untersucht werden, wobei der Schwerpunkt auf Anwendungen in sogenannten Dosis-Wirkungs-Modellen liegt, bei denen eine binäre Zielvariable, die den Erfolg oder Misserfolg einer Behandlung beschreibt und daher nur zwei Ausprägungen annehmen kann, in Abhängigkeit von der Größe ("Dosis") einer oder mehrerer erklärenden Variablen untersucht wird.Neben Experimenten in der Psychophysik stellen adaptive Intelligenztests, wie sie im Projekt "Optimales Design für online generierte adaptive Intelligenztestverfahren" untersucht und weiterentwickelt werden, ein wichtiges Anwendungsgebiet dar.
Optimales Design bei zufälligen und festen Blockeffekten II
Duration: 01.10.2012 bis 15.02.2014
Auf Grund ökonomischer und ethischer Gründe besteht ein bedeutender Bedarf für optimale bzw. zumindest effiziente Designs in statistischen Experimenten. Dies bedeutet, dass experimentelle Einstellungen derart gewählt werden sollten, dass unter Verwendung möglichst weniger Ressourcen maximale Information erzielt werden kann.
In der Literatur gibt es im Wesentlichen zwei konkurrierende Ansätze: Der eine basiert auf kombinatorischen Überlegungen, die am besten für statistische Modelle der Varianzanalyse geeignet sind, bei denen die experimentellen Einstellungen nur wenige Faktor-Kombinationen annehmen können. der andere basiert auf analytschen Methoden und verwendet Methoden der konvexen Optimierung in einer quantitativ-stetigen Umgebung.
Das Ziel des vorliegenden Projektes ist es, diese beiden Konzepte zusammenzubringen in dem Sinnen, dass wir (stetige) analytische Methoden auf Modelle der Varianzanalyse mit typischerweise diskreter Struktur wie Block-Effekten übertragen wollen. Darüber hinaus wollen wir die analytischen Methoden, die für Modelle mit reinen festen Effekten entwickelt wurden, auf die praktisch relevanteren übertragen, bei denen individuelle Effekte der sogenannten Blöcke durch Randomisierung entstehen, was in der Literatur oft vernachlässigt wird.
MÄQNU: Multivariate Äquivalenztests und Tests auf Nichtunterlegenheit für hochdimensionale Endpunkte
Duration: 01.07.2010 bis 31.12.2013
Das Verbundprojekt untersucht statistische Tests auf Äquivalenz oder Nichtunterlegenheit. Während bislang meist nur Tests für einzelne Endpunkte durchgeführt und bei Bedarf konservativ über verschiedene Endpunkte gekoppelt werden, berücksichtigen wir die multivariate Verteilung und erhalten so effektivere Methoden, die auch die Analyse hochdimensionaler Endpunkte ermöglichen. Die Verfahren werden zusammen mit Industriepartnern zum Vergleich von Arzneimitteln und zur Untersuchung des Einflusses von Kulturpflanzen auf die mikrobielle Bodenflora angewendet. Im vorliegenden Teilprojekt wird analytisch das asymptotische Verhalten der in den anderen Teilbereichen vorgeschlagenen Testverfahren untersucht bzw. das Verhalten für kleine bis moderate Stichprobenumfänge durch Simulationen validiert. Neben mathematischen Entwicklungen zu den Grundlagen der Verfahren sind Untersuchungen zur Versuchsplanung durchzuführen und ein entsprechendes benutzerfreundliches Programm zu entwickeln.
Optimales Design für multivariate statistische Modelle mit scheinbar unzusammenhängenden Wirkungsfunktionen
Duration: 01.03.2013 bis 30.11.2013
In der statistischen Datenanalyse gewinnen multivariate lineare Modelle mit einer Vielzahl von Zielvariablen zunehmend an Bedeutung, da auf Grund der Entwicklung von Computer-Soft- und -Hardware mittlerweile gute Approximationen für die Auswertung derartiger, strukturierter Daten berechenbar sind. Ziel dieses Projektes ist es, optimale und effiziente Designs für statistische Experimeten bei verschiedenen zu Grunde liegenden multivariaten linearen Modellen zu bestimmen und zu validieren. Insbesondere stehen hier Modelle vom Typ der "Seemingly Unrelated Regression" (SUR), d.h. Modelle mit scheinbar unzusammenhängenden Wirkungen im Vordergrund.
Optimales Design für online generierte adaptive Intelligenztestverfahren (II)
Duration: 01.09.2011 bis 30.11.2013
In this project adaptive procedure are developed for intelligence tests, which aim at measuring the gneral intelligence. Test items will be generated automatically and online by a rule-based item generator and adaptively presented. The items will be selected according to the parameter estimates in generalized linear logistic test models. Theparameter estimations will be based on optimal designs in order to obtain maximal precision in measuring the intelligence by a minimal number of items to be presented. In detail four types of rule-based test procedures will be constructed for measuring the general intelligence and the necessary basic principles of statistics wikll be developed.
In Phase I rule based items were developed for measuring the working speed and empirically calibrated based on D-optimal dsigns in linear logistic test models with fixed and random factors. Furthermore a programming system was developed for the automatic generation of these items, their adaptive presentation and the estimation of person parameters.
In Phase II of this project the work of Phase I is continued. In analogy to the items on working capacity developed in Phase I rule based items on working speed will be constructed, which are sutiable for an adaptive testing of this intelligence component. As speed tests are considered, it is necessary to use some extended versions of the Rasch Poisson Count Model as the statiscal basis instead of the Logistic Rasch Model of Phase I. For these models again optimal designs will be developed for both item calibration and adaptive testing.
Adaptive Verfahren in der Planung und Auswertung statistischer Experimente
Duration: 01.04.2008 bis 31.03.2013
Durch eine geeigente Wahl der Versuchsbedingungen kann in vielen statistischen Experimenten eine wesentliche Verbesserung der Analyseergebnisse bzw.\ eine deutliche Verringerung der Kosten für die Durchführung des Experiments erzielt werden. Liegen nichtlineare Wirkungszusammenhänge zwischen den Versuchsbedingungen und der die Zielvariable beschreibenden Wirkungsfunktion vor, ergibt sich dabei das Problem, dass die optimalen Versuchspläne, d.h.\ die optimale Wahl der Versuchseinstellungen, in der Regel von den unbekannten und zu schätzenden Parametern abhängen. Während dies bei einstufig geplanten Experimenten ein schier unlösbares Problem darstellt, bieten adaptive und sequenzielle Verfahren, die "on-line" die Information zuvor gemachter Beobachtungen ausnutzen, einen vielversprechenden Ansatz, um auch in solchen Situationen mit möglichst wenigen Messungen zu möglichst genauen Schätzungen zu gelangen.Derartige Verfahren sollen im Rahmen des vorliegenden Projektes entwickelt und auf ihre Eigenschaften unter realen Versuchsbedingungen untersucht werden, wobei der Schwerpunkt auf Anwendungen in sogenannten Dosis-Wirkungs-Modellen liegt, bei denen eine binäre Zielvariable, die den Erfolg oder Misserfolg einer Behandlung beschreibt und daher nur zwei Ausprägungen annehmen kann, in Abhängigkeit von der Größe ("Dosis") einer oder mehrerer erklärenden Variablen untersucht wird.Neben Experimenten in der Psychophysik stellen adaptive Intelligenztests, wie sie im Projekt "Optimales Design für online generierte adaptive Intelligenztestverfahren" untersucht und weiterentwickelt werden, ein wichtiges Anwendungsgebiet dar.
Optimales Design für multivariate lineare statistische Modelle
Duration: 01.03.2008 bis 28.02.2013
In der statistischen Datenanalyse gewinnen multivariate lineare Modelle mit einer Vielzahl von Zielvariablen zunehmend an Bedeutung, da auf Grund der Entwicklung von Computer-Soft- und -Hardware mittlerweile gute Approximationen für die Auswertung derartiger, strukturierter Daten berechenbar sind. Ziel dieses Projektes ist es, optimale und effiziente Designs für statistische Experimeten bei verschiedenen zu Grunde liegenden multivariaten linearen Modellen zu bestimmen und zu validieren.
Optimales Design bei zufälligen und festen Blockeffekten
Duration: 01.10.2009 bis 30.09.2012
Auf Grund ökonomischer und ethischer Gründe besteht ein bedeutender Bedarf für optimale bzw. zumindest effiziente Designs in statistischen Experimenten. Dies bedeutet, dass experimentelle Einstellungen derart gewählt werden sollten, dass unter Verwendung möglichst weniger Ressourcen maximale Information erzielt werden kann. In der Literatur gibt es im Wesentlichen zwei konkurrierende Ansätze: Der eine basiert auf kombinatorischen Überlegungen, die am besten für statistische Modelle der Varianzanalyse geeignet sind, bei denen die experimentellen Einstellungen nur wenige Faktor-Kombinationen annehmen können. der andere basiert auf analytschen Methoden und verwendet Methoden der konvexen Optimierung in einer quantitativ-stetigen Umgebung. Das Ziel des vorliegenden Projektes ist es, diese beiden Konzepte zusammenzubringen in dem Sinnen, dass wir (stetige) analytische Methoden auf Modelle der Varianzanalyse mit typischerweise diskreter Struktur wie Block-Effekten übertragen wollen. Darüber hinaus wollen wir die analytischen Methoden, die für Modelle mit reinen festen Effekten entwickelt wurden, auf die praktisch relevanteren übertragen, bei denen individuelle Effekte der sogenannten Blöcke durch Randomisierung entstehen, was in der Literatur oft vernachlässigt wird.
Approximation statistischer Information in nichtlinearen Modellen mit zufälligen Effekten
Duration: 01.01.2011 bis 31.03.2012
Die statistische Information spielt eine wichtige Rolle in der Bewertung der Qualität von statistischen Analyseverfahren. Während die Theorie für lineare Modelle mit und ohne zufällige Effekte und für nichtlineare Modelle ohne zufällige Effekte weit entwickelt ist, gibt es für nichtlineare Modelle mit zufälligen Effekten nur mehr oder minder gute Näherungen in der Literatur. Ziel des Projektes ist es, die bestehenden Näherungsverfahren auf ihre Praxistauglichkeit zu untersuchen und neue Approximationen zu entwickeln. Diese können dann zur effizienten Planung von Experimenten z.B. in der Pharmakokinetik eingesetzt werden.
Statistische Datenanalyse mit "Partial Least Squares"
Duration: 01.02.2007 bis 31.01.2012
"Partial Least Squares" ist eine modernes Verfahren zur Dimensionsreduktion in hochdimensionalen Datensätzen, wie sie z.B. in den Neurowissenschaften bei MRT-Daten zur Analyse von Hirnaktivitäten oder bei der Bildanalyse anfallen. Ziel des vorliegenden Projektes ist es, geeignete Modelle für die den Daten zu Grunde liegenden Strukturen zu entwickeln und zu validieren.
SKAVOE: Sicherere und kosteneffizientere Arzneimittelentwicklung unter Verwendung von optimalen Experimentdesigns
Duration: 01.07.2007 bis 31.12.2010
In eine Gesellschaft mit einem hoch entwickelten Gesundheitssystem besteht die Forderung und Notwendigkeit, innovative Medikamentenentwicklungen schnellstmöglich für den Menschen nutzbar zu machen. Dies impliziert die ständige Suche nach neuen Wirkstoffen, was mit einem hohen Zeitaufwand und erheblichen Investitionen verbunden ist. Durch den Einsatz effizienter Experimentaldesigns auf den verschiedenen Stufen der Arzneimittelentwicklung können dabei beträchtliche Ressourcen eingespart werden. Dies erlaubt nicht nur eine schnellere Positionierung neuer Medikamente auf dem Markt und damit einen ökonomischen Vorteil, sondern eine aus ethischen Gründen wünschenswerte schnellere Verfügbarkeit wirksamerer und sicherer Medikamente sowie eine ebenfalls aus ethischen Gründen erstrebenswerte geringere Belastung von Probanden und Patienten in der Erprobungsphase. Die Entwicklung derartiger effizienter Experimentaldesigns ist Inhalt des vom Bundesministerium für Bildung und Forschung im Rahmen des Schwerpunktprogramms zur Förderung der naturwissenschaftlichen Grundlagenforschung auf dem Gebiet Mathematik für Innovationen in Industrie und Dienstleistungen bewilligten Verbundprojekts SKAVOE (Sicherere und kosteneffizientere Arzneimittelentwicklung unter Verwendung von optimalen Experimentdesigns).Das Verbundprojekt fokussiert auf verschiedene Bereiche des Entwicklungsprozesses für zukünftige Arzneimittel (präklinisches, genetisches Screening von Substanzen mittels Microarrays, klinische Dosis-Findungsstudien und dynamische Modelle der Populations-Pharmakokinetik für Expositionsdaten). Im Magdeburger Teilprojekt werden vorrangig effiziente Experimentaldesigns für Modelle zur Bioverfügbarkeit von Wirkstoffen im menschlichen Körper nach einer Medikamentengabe entwickelt, mit deren Hilfe die Dosierung von Medikamenten im Hinblick auf Wirksamkeit und Arzneimittelsicherheit optimiert werden kann.
Optimales Design in der Conjoint-Analyse
Duration: 01.10.2006 bis 31.07.2010
Conjoint analysis is a popular tool in marketing research. Stated choice experiments are performed to evaluate the influence of various options on the comsumers' preferences. The quality of the outcome of such experiments heavily depends on its design, i.e. on which questions are asked. The aim of the present project is to develop and validate optimal and efficient designs for questionnaires in this context.
Optimales Design für online generierte adaptive Intelligenztestverfahren
Duration: 01.08.2007 bis 30.04.2010
In diesem Projekt sollen adaptive Intelligenztests zur Messung der allgemeinen Intelligenz entwickelt werden. Die Items werden durch einen automatischen Itemgenerator regelbasiert und online generiert und adaptiv dargeboten. Selektiert werden die Items anhand der Parameterschätzungen für erweitete linear-logistische Testmodelle. Die Parameterschätzungen erfolgen anhand optimaler Designs, so dass mit einem Minimum an darzubietenden Items ein Maximum an Präzision bei der Intelligenzmessung erzielt werden kann. Konkret sollen vier Arten regelgeleiteter Testverfahren zur Messung von allgemeiner Intelligenz konstruiert und hierfür die erforderlichen statistischen Grundlagen entwickelt werden.
Optimales Design für verallgemeinerte lineare gemischte Modelle
Duration: 01.11.2005 bis 31.01.2010
In der statistischen Datenanalyse gewinnen verallgemeinerte lineare Modelle mit sowohl zufälligen als auch festen Effekten zunehmend an Bedeutung, da auf Grund der Entwicklung von Computer-Soft- und -Hardware mittlerweile gute Näherungen für die Anpassung derartiger, mehr reaklistischer Modelle an die Daten berechenbar sind. Ziel dieses Projektes ist es, optimale und effiziente Designs für statistische Experimeten bei zu Grunde liegenden verallgemeinerten linearen gemischten Modellen zu bestimmen und zu validieren.
Optimales Design in klinischen Dosisfindungsstudien zur Sicherheit und Wirksamkeit
Duration: 01.09.2006 bis 30.06.2009
Das Ziel von klinischen Dosisfindungsstudien ist es, eine Dosis (oder eine Spanne von Dosen) zu identifizieren, die sowohl die untersuchte Krankheit wirksam behandelt, als auch sicher ist im Hinblick auf Nebenwirkungen. Traditionell werden erst Studien zur Sicherheit durchgeführt (Phase I), bevor solche zur Wirksamkeit betrachtet werden (Phase II). Werden die Versuche beider Phasen kombiniert, kann die Effizienz des Prozesses der Medikamentenentwicklung erhöht werden. Das Design solcher Versuche weist Schwierigkeiten auf: einerseits hängt der optimale Versuchsplan von den unbekannten Paramentern und dem zu Grunde liegenden (meist nichtlinearen) Modell ab, andererseits ergeben sich aus ethischen Gründen vielerlei Restriktionen, die das Versuchsdesign beeinflussen. Das Ziel dieses Projektes ist es, Designs für das beschriebene Problem zu finden, die sowohl Optimalitätskriterien erfüllen als auch für reale Dosisfindungsstudien in die Praxis umgesetzt werden können.
Statistische Analyse multivariater Stichproben in endlichen Populationen
Duration: 01.04.2004 bis 31.03.2009
Bei Schadenssummenbestimmungen in Wirtschaftsstrafsachen ist es von Bedeutung, zuverlässige Schätzungen für Mindestschadenssummen zu ermitteln, die sich als mit den Schadenswerten gewichtete Summen von Anteilschätzungen für verschiedene Komponenten von multivariaten Schadenszahlen ergeben. Ziel dieses Projektes ist es, unter geeigneten Modellannahmen diese Mindestschadenssummen unter Berücksichtigung von eventuellen Abhängigkeitren zwischen den Komponenten hitreichend präzise zu ermitteln und diese Verfahren unter Modellabweichungen zu überprüfen.
Effiziente Versuchsplanung in der Conjoint Analyse
Duration: 15.06.2004 bis 31.07.2007
Die Conjoint Analyse ist ein häufig benutztes Verfahren zur Analyse von Präferenzen und Entscheidungen in vielen Bereichen wie Marketing, Personalmanagement, sensorische Messungen in der Lebensmittelindustrie etc. Durch den Einsatz effizienter Versuchspläne, d.h. effizienter Auswahlen der darzubietenden Stimuli, kann die Zahl der Darbietungen und damit die Erhebungszeit deutlich reduziert werden. Im Rahmen der beiden ersten Phasen dieses Projektes wurden für verschiedene conjoint-analytische Modelle effiziente Versuchspläne entwickelt, die eine erheblich höhere relative Effizienz als die bisher häufig in der Praxis eingesetzten Designs besitzen. In mehreren Experimenten und Simulationsstudien konnte nachgewiesen werden, dass die theoretisch gesicherte höhere Effizienz dieser Designs auch empirisch zu reliableren und valideren Nutzenschätzungen in der Praxis führt. Mittlerweise wurden heterogene Discrete-Choice-Modelle als sehr leistungsfähige Verfahren der Conjoint Analyse entwickelt. In der nächsten Phase dieses Projekts sollen daher effiziente Designs für Discrete-Choice-Modelle mit zufälligen Effekten und/oder latenten Klassen entwickelt werden. Da effiziente Versuchspläne zu einer sehr hohen Aufgabenkomplexität führen können, ist weiterhin eine theoretische und empirische Bewertung der Versuchspläne aus Sicht der Informationsverarbeitung erforderlich.
Biometrische Methoden zur Frühdiagnostik, Verlaufskontrolle und Visualisierung perimetrisch fassbarer Sehbahnläsionen
Duration: 01.04.2004 bis 31.03.2007
Modellierung von Messverfahren für die Sehfähigkeit in Abhängigkeit von der Lokation im Gesichtsfeld, der Stärke von Lichtstimuli und des zeitlichen Krankheitsverlaufs durch Dosis-Wirkungsbeziehungen; Bestimmung altersabhängiger Normwerte unter besonderer Berücksichtigung von Messwiederholungen und zufälligen Probandeneffekten; Modellierung und Planung psychophysischer Experimente unter Berücksichtigung falsch-positiver und falsch-negativer Reaktionen;Entwicklung adaptiver Verfahren zur Stimuluswahl aus der Basis von a-priori Vorwissen über die verteilung der individuellen Schwellenwerte
Modellierung und Planung populationspharmakokinetischer Studien
Duration: 15.02.2003 bis 31.12.2006
Versuchsplanung für pharmakokinetische Phase-I- und Phase-III-Studien zur Kontrolle der Bioverfügbarkeit von Medikamenten (Hormon-Therapie) und zum Nachweis der Bioäquivalenz; Modellierung der Bioverfügbarkeit durch kinetische Modelle mit zufälligen Probandeneffekten bei Messwiederholungen
Adaptive Designs für mehrstufige klinische Studien mit Interims-Analyse
Duration: 01.04.2003 bis 30.09.2006
Adaptive Designs, wo Entscheidungen auf Basis von während der Studie gesammelten Informationen getroffen werden, können die Flexibilät einer Studie erhöhen und die erwartete Fallzahl verringern. Insbesondere findet diese Vorgehensweise Anwendung bei Interimsanalysen in der pharmazeutischen Forschung, bei denen nach Durchführung eines vorher festgelegten Teils der Studie über eine Fortführung bzw. einen Abbruch entschieden werden soll. Ziel dieses Projektes ist es, ein allgemeines Rahmenwerk für adaptive Tests mit zwei Stufen zu finden und Software für deren Umsetzung zu entwickeln. Die Ausweitung auf mehr als zwei Stufen soll ebenfalls behandelt werden.
Effiziente Planung in der nichtparametrischen Regression
Duration: 01.04.2004 bis 31.03.2006
effiziente Planung von Experimenten für nichtlineare Wirkungszusammenhänge und nichtparametrische Regressionsansätze, verallgemeinerte lineare und additive Modelle; Berücksichtigung von Approximationsfehlern. lokalen und globalen Strukturen; Konstruktion "guter Gitter" zur Verwendung als effizienter Versuchspläne
Effiziente Versuchsplanung in der Conjoint Analyse
Duration: 01.12.2001 bis 30.11.2003
Die Conjoint Analyse ist ein häufig benutztes Verfahren zur Analyse von Präferenzen und Entscheidungen in vielen Bereichen wie Marketing, Personalmanagement, sensorische Messungen in der Lebensmittelindustrie etc. Durch den Einsatz effizienter Versuchspläne, d.h. effizienter Auswahlen der darzubietenden Stimuli, kann die Zahl der Darbietungen und damit die Erhebungszeit deutlich reduziert werden. Im Rahmen einer ersten Phase dieses Projektes wurden D-optimale Versuchspläne für lineare und logistische Paarvergleichsmodelle basierend auf Teilprofilen entwickelt. Diese Pläne besitzen eine erheblich höhere relative Effizienz als die bisher häufig in der Praxis eingesetzten Designs. In experimentellen Studien konnte nachgewiesen, dass diese höhere Effizienz auch zu reliableren und valideren Resultaten führt. Diese Ergebnisse konnten auch durch Simulationsstudien bestätigt werden. In der gegenwärtigen Phase dieses Projekts werden für allgemeinere Paarvergleichsmodelle und Discrete Choice-Modelle effiziente (u.a. adaptiv optimale) Designs entwickelt und anhand von experimentellen Studien sowie Simulationsstudien überprüft. Dabei soll in den experimentellen Studien das neu eingeführte Konzept der "wahren Werte" eingesetzt und weiterentwickelt werden.
2024
Peer-reviewed journal article
Experimental designs for accelerated degradation tests based on linear mixed effects models
Shat, Helmi; Schwabe, Rainer
In: Communications in statistics. Theory and methods - London : Taylor and Francis, Bd. 53 (2024), Heft 6, S. 2154-2177 [Online first]
A p-step-ahead sequential adaptive algorithm for D-optimal nonlinear regression design
Freise, Fritjof; Gaffke, Norbert; Schwabe, Rainer
In: Statistical papers - Berlin : Springer, Bd. 65 (2024), Heft 5, S. 2811-2834
Non-peer-reviewed journal article
Optimal design in repeated testing for count data
Parsamaram, Parisa; Holling, Heinz; Schwabe, Rainer
In: Arxiv - Ithaca, NY : Cornell University . - 2024, insges. 26 S.
Poisson Regression in one Covariate on Massive Data
Reuter, Torsten; Schwabe, Rainer
In: De.arxiv.org - [Erscheinungsort nicht ermittelbar] : Arxiv.org . - 2024, insges. 16 S.
2023
Peer-reviewed journal article
Optimal design for estimating the mean ability over time in repeated item response testing
Freise, Fritjof; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam : North-Holland Publ. Co., Bd. 225 (2023), S. 266-282
D-optimal and nearly D-optimal exact designs for binary response on the ball
Radloff, Martin; Schwabe, Rainer
In: Statistical papers - Berlin : Springer, Bd. 64 (2023), S. 1021-1040
Optimal subsampling design for polynomial regression in one covariate
Reuter, Torsten; Schwabe, Rainer
In: Statistical papers - Berlin : Springer, Bd. 64 (2023), S. 1095-1117
V-optimality of designs in random effects Poisson regression models
Niaparast, Mehrdad; MehrMansour, Sahar; Schwabe, Rainer
In: Metrika - Berlin : Springer . - 2023
Habilitation
Optimal experimental designs in multiple-group mixed models
Prus, Maryna; Schwabe, Rainer
In: Magdeburg: Universitätsbibliothek, Habilitationsschrift Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2023 Kumulative Habilitationsschrift, 1 Online-Ressource (verschiedene Blattzählung, 1,92 MB) [Literaturangaben][Literaturangaben]
Non-peer-reviewed journal article
D-optimal subsampling design for massive data linear regression
Reuter, Torsten; Schwabe, Rainer
In: De.arxiv.org - [S.l.] : Arxiv.org . - 2023, Artikel 2307.02236, insges. 21 S.
A p-step-ahead sequential adaptive algorithm for D-optimal nonlinear regression design
Freise, Fritjof; Gaffke, Norbert; Schwabe, Rainer
In: De.arxiv.org - [S.l.] : Arxiv.org . - 2023, Artikel 2307.02086, insges. 32 S.
2022
Book chapter
Optimal stress levels in accelerated degradation testing for various degradation models
Shat, Helmi; Schwabe, Rainer
In: Konferenz: ICRA8, Vienna, Austria, 2019, Mindful Topics on Risk Analysis and Design of Experiments - Cham: Springer International Publishing; Pilz, Jürgen . - 2022, S. 113-134
Peer-reviewed journal article
Optimal time plan in accelerated degradation testing
Shat, Helmi; Schwabe, Rainer
In: Communications in statistics / Theory and methods - London : Taylor and Francis . - 2022
Dissertation
Optimum design in nonlinear and generalized linear mixed models
Parsamaram, Parisa; Schwabe, Rainer
In: Magdeburg: Universitätsbibliothek, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2022, 1 Online-Ressource (123 Seiten, 912,62 MB) [Literaturverzeichnis: Seite 120-123]
Optimal designs for accelerated degradation testing
Shat, Helmi; Schwabe, Rainer; Gaffke, Norbert
In: Magdeburg: Universitätsbibliothek, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2022, 1 Online-Ressource (viii, 148 Blätter, 1,16 MB) [Literaturverzeichnis: Blatt 133-141]
Non-peer-reviewed journal article
Optimal designs for discrete choice models via graph Laplacians
Röttger, Frank; Kahle, Thomas; Schwabe, Rainer
In: De.arxiv.org - [S.l.]: Arxiv.org . - 2022, insges. 23 S.
2021
Peer-reviewed journal article
Optimal design for probit choice models with dependent utilities
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Statistics - London [u.a.] : Taylor & Francis, Bd. 55 (2021), Heft 1, S. 173-194
Equivariance and invariance for optimal designs in generalized linear models exemplified by a class of gamma models
Idais, Osama; Schwabe, Rainer
In: Journal of statistical theory and practice - Cham: Springer International Publishing, Bd. 15 (2021), insges. 32 S.
The semialgebraic geometry of saturated optimal designs for the Bradley-Terry model
Kahle, Thomas; Röttger, Frank; Schwabe, Rainer
In: Algebraic statistics - Berkeley, Calif.: Mathematical Sciences Publishers, Bd. 12 (2021), 1, S. 97-114
D-optimal designs for Poisson regression with synergetic interaction effect
Freise, Fritjof; Graßhoff, Ulrike; Röttger, Frank; Schwabe, Rainer
In: TEST - Heidelberg [u.a.]: Springer, Bd. 30 (2021), S. 1004-1025
The adaptive Wynn algorithm in generalized linear models with univariate response
Freise, Fritjof; Gaffke, Norbert; Schwabe, Rainer
In: The annals of statistics: an official journal of the Institute of Mathematical Statistics - Hayward, Calif.: IMS Business Off., Bd. 49 (2021), 2, S. 702-722
Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models
Freise, Fritjof; Gaffke, Norbert; Schwabe, Rainer
In: Metrika - Berlin : Springer, Bd. 84 (2021), Heft 6, S. 851-874
Analytic solutions for locally optimal designs for gamma models having linear predictors without intercept
Idais, Osama; Schwabe, Rainer
In: Metrika - Berlin: Springer, Bd. 84 (2021), 1, S. 1-26
2020
Peer-reviewed journal article
Doptimal design for the Rasch counts model with multiple binary predictors
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: The British journal of mathematical and statistical psychology - Hoboken, NJ [u.a.]: Wiley, Bd. 73.2020, 3, S. 541-555
Geometrie optimaler Versuchspläne
Kahle, Thomas; Röttger, Frank; Schwabe, Rainer
In: Mitteilungen der Deutschen Mathematiker-Vereinigung/ Deutsche Mathematiker-Vereinigung - Berlin: DMV, Bd. 28.2020, 2, S. 71-76
Optimality regions for designs in multiple linear regression models with correlated random coefficients
Graßhoff, Ulrike; Holling, Heinz; Röttger, Frank; Schwabe, Rainer
In: Journal of statistical planning and inference: JSPI - Amsterdam: North-Holland Publ. Co., Bd. 209.2020, S. 267-279
Optimal design in hierarchical random effect models for individual prediction with application in precision medicine
Prus, Maryna; Benda, Norbert; Schwabe, Rainer
In: Journal of statistical theory and practice - Cham: Springer International Publishing, Bd. 14 (2020), 2, S. 1-12
Optimal designs for two-level main effects models on a restricted design region
Freise, Fritjof; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam : North-Holland Publ. Co., Bd. 204 (2020), S. 45-54
Optimal designs for Poisson count data with Gamma block effects
Schmidt, Marius; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam : North-Holland Publ. Co., Bd. 204 (2020), S. 128-140
Dissertation
Optimale Versuchsplanung für Zähldaten mit zufälligen Blockeffekten
Schmidt, Marius; Schwabe, Rainer
In: Magdeburg, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2020, IV, 119 Seiten [Literaturverzeichnis: Seite 116-119][Literaturverzeichnis: Seite 116-119]
Geometry of optimal design and limit theorems
Röttger, Frank; Kahle, Thomas; Schwabe, Rainer
In: Magdeburg, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2020, IX, 105 Seiten [Literaturverzeichnis: Seite 99-105][Literaturverzeichnis: Seite 99-105]
2019
Peer-reviewed journal article
Optimal designs for the generalized partial credit model
Bürkner, Paul-Christian; Schwabe, Rainer; Holling, Heinz
In: The British journal of mathematical and statistical psychology - Hoboken, NJ [u.a.]: Wiley, 1965, Bd. 72.2019, 2, S. 271-293
Optimal designs for second-order interactions in paired comparison experiments with binary attributes
Nyarko, Eric; Schwabe, Rainer
In: Journal of statistical theory and practice - Cham: Springer International Publishing, 2007, Bd. 13.2019, 4, S. 1-16
Locally D-optimal designs for a wider class of non-linear models on the k-dimensional ball - with applications to logit and probit models
Radloff, Martin; Schwabe, Rainer
In: Statistical papers - Berlin: Springer, 1988, Bd. 60.2019, 2, S. 515-527
Locally D-optimal designs for non-linear models on the k-dimensional ball
Radloff, Martin; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam: North-Holland Publ. Co, 1977, Bd. 203.2019, S. 106-119
Locally optimal designs for gamma models
Gaffke, Norbert; Idais, Osama; Schwabe, Rainer
In: Journal of statistical planning and inference: JSPI - Amsterdam: North-Holland Publ. Co., 1977, Bd. 203.2019, S. 199-214
Optimal designs for K-factor two-level models with first-order interactions on a symmetrically restricted design region
Freise, Fritjof; Schwabe, Rainer
In: Statistical papers - Berlin: Springer, 1988, Bd. 60.2019, 2, S. 495-513
Quasi-Newton algorithm for optimal approximate linear regression design: Optimization in matrix space
Gaffke, Norbert; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam : North-Holland Publ. Co., Bd. 198 (2019), S. 62-78
Dissertation
Optimal designs for paired comparison experiments
Nyarko, Eric; Schwabe, Rainer
In: Magdeburg, 2019, vi, 115 Seiten, 30 cm[Literaturverzeichnis: Seite 111-115]
Editor
Journal of statistical theory and practice
Schwabe, Rainer
In: 2019
Non-peer-reviewed journal article
Experimental designs for accelerated degradation tests based on gamma process models
Shat, Helmi; Schwabe, Rainer
In: De.arxiv.org - [S.l.]: Arxiv.org, 1991, 2019, Artikel 1912.04202, insgesamt 16 Seiten
2018
Abstract
Optimal designs for count data with random parameters
Schmidt, Marius; Schwabe, Rainer
In: IWS 2018: 9th International Workshop on Simulation : Barcelona, Spain, June 25 - June 29, 2018 : book of abstracts - Barcelona, 2018 . - 2018, S. 118-119[Workshop: 9th International Workshop on Simulation, IWS 2018, Barcelona, Spain, June 25 - June 29, 2018]
Locally D-optimal designs for non-linear models on the k on the k-dimensional ball
Radloff, Martin; Schwabe, Rainer
In: IWS 2018: 9th International Workshop on Simulation : Barcelona, Spain, June 25 - June 29, 2018 : book of abstracts - Barcelona, 2018 . - 2018, S. 102-103[Workshop: 9th International Workshop on Simulation, IWS 2018, Barcelona, Spain, June 25 - June 29, 2018]
The revival of reduction principles in the generation of optimal designs for non-standard situations
Schwabe, Rainer; Freise, Fritjof; Idais, Osama; Nyarko, Eric; Radloff, Martin; Schmidt, Dennis
In: IWS 2018: 9th International Workshop on Simulation : Barcelona, Spain, June 25 - June 29, 2018 : book of abstracts - Barcelona, 2018; Fonseca, P. . - 2018, S. 120-121[Workshop: 9th International Workshop on Simulation, IWS 2018, Barcelona, Spain, June 25 - June 29, 2018]
Geometry of parameter regions for optimal designs
Röttger, Frank; Kahle, Thomas; Schwabe, Rainer
In: IWS 2018: 9th International Workshop on Simulation : Barcelona, Spain, June 25 - June 29, 2018 : book of abstracts - Barcelona, 2018; Fonseca, P. . - 2018, S. 107-108[Workshop: 9th International Workshop on Simulation, IWS 2018, Barcelona, Spain, June 25 - June 29, 2018]
Non-peer-reviewed journal article
Locally D-optimal designs for non-linear models on the k-dimensional ball with applications to logit and probit models
Radloff, Martin; Schwabe, Rainer
In: De.arxiv.org - [S.l.]: Arxiv.org, 1991 . - 2018, insges. 11 S.
Optimal design in hierarchical models with application in multi-center trials models
Prus, Maryna; Benda, Norbert; Schwabe, Rainer
In: De.arxiv.org - [S.l.]: Arxiv.org, 1991 . - 2018, insges. 9 S.
2017
Peer-reviewed journal article
D-optimal design for a model with interaction between a qualitative and a quantitative factor in the presence of random block effects
Alonso Cabrera, Jesús; Schwabe, Rainer
In: Journal of statistical theory and practice - Cham : Springer International Publishing, Bd. 11.2017, 4, S. 759-770
Adaptive designs for quantal dose-response experiments with false answers
Benda, Norbert; Bürkner, Paul-Christian; Freise, Fritjof; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical theory and practice - Cham : Springer International Publishing, Bd. 11.2017, 3, S. 361-374
Optimal design for multiple regression with information driven by the linear predictor
Schmidt, Dennis; Schwabe, Rainer
In: Statistica Sinica - Taipei: Statistica Sinica, Institute of Statistical Science, Academia Sinica, Bd. 27.2017, 3, S. 1371-1384
Dissertation
Versuchsplanung für nichtlineare multiple Regressionsmodelle mit Anwendung auf zensierte Daten
Schmidt, Dennis; Schwabe, Rainer
In: Magdeburg, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2017, IV, 127 Seiten
Meta-analysis of aggregate data on medical events
Holzhauer, Björn; Schwabe, Rainer
In: Magdeburg, Dissertation Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik 2017, V, 152 Seiten, Illustrationen, Diagramme, 21 cm
2016
Book chapter
Invariance and equivariance in experimental design for nonlinear models
Radloff, Martin; Schwabe, Rainer
In: Kongress: 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016, mODa 11 - Advances in Model-Oriented Design and Analysis - Cham: Springer . - 2016, S. 217-224
Statistical optimal design theory
Holling, Heinz; Schwabe, Rainer
In: Handbook of Item Response Theory, Volume Two: Statistical Tools/ van der Linden - s.l.: CRC Press, 2016; van der Linden, Wim J. . - 2016, S. 313-340
Interpolation and extrapolation in random coefficient regression models - optimal design for prediction
Prus, Maryna; Schwabe, Rainer
In: Kongress: 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016, mODa 11 - Advances in Model-Oriented Design and Analysis - Cham: Springer . - 2016, S. 209-216
Optimal design for the rasch poisson-gamma model
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: Kongress: 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016, mODa 11 - Advances in Model-Oriented Design and Analysis - Cham: Springer . - 2016, S. 133-141
Peer-reviewed journal article
Optimal designs for the prediction of individual parameters in hierarchical models
Prus, Maryna; Schwabe, Rainer
In: Journal of the Royal Statistical Society / B - London: Wiley-Blackwell, 2016
Algebraic geometry of Poisson regression
Kahle, Thomas; Oelbermann, Kai-Friederike; Schwabe, Rainer
In: Journal of algebraic statistics - Istanbul, 2012, Bd. 7.2016, 1, S. 29-44
Activation of mitochondrial complex II-dependent respiration is beneficial for α-synucleinopathies
Fröhlich, Christina; Zschiebsch, Katja; Gröger, Victoria; Paarmann, Kristin; Steffen, Johannes; Thurm, Christoph; Schropp, Eva-Maria; Brüning, Thomas; Gellerich, Frank Norbert; Radloff, Martin; Schwabe, Rainer; Lachmann, Ingolf; Krohn, Markus; Ibrahim, Saleh; Pahnke, Jens
In: Molecular neurobiology - Totowa, NJ: Humana Press, 1987, Bd. 53 (2016), 7, S. 4728-4744
2015
Book chapter
Poisson model with three binary predictors - When are saturated designs optimal?
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: Stochastic Models, Statistics and Their Applications - Cham: Springer; Steland, Ansgar *1967-* . - 2015, S. 75-81 - (Springer proceedings in mathematics & statistics; 122)
Design for discrete choice experiments
Grossmann, Heiko; Schwabe, Rainer
In: Handbook of design and analysis of experiments - Boca Raton: CRC Press, a Chapman & Hall book . - 2015, S. 787-832 - (CRC Handbooks of Modern Statistical Methods; 7)
On the impact of correlation on the optimality of product-type designs in SUR models
Soumaya, Moudar; Schwabe, Rainer
In: Stochastic Models, Statistics and Their Applications - Cham: Springer; Steland, Ansgar *1967-* . - 2015, S. 159-167 - (Springer Proceedings in Mathematics & Statistics; 122)
Peer-reviewed journal article
Optimal cutpoints for random observations
Schmidt, Marius; Schwabe, Rainer
In: Statistics: a journal of theoretical and applied statistics - London [u.a.]: Taylor & Francis, Bd. 49.2015, 6, S. 1366-1381
Optimal design for multivariate observations in seemingly unrelated linear models
Soumaya, Moudar; Gaffke, Norbert; Schwabe, Rainer
In: Journal of multivariate analysis: JMVA - Orlando, Fla: Acad. Press, Bd. 142.2015, S. 48-56
Erratum to: On optimal designs for censored data
Schmidt, Dennis; Schwabe, Rainer
In: Metrika: international journal for theoretical and applied statistics - Berlin: Springer, Bd. 78.2015, 3, S. 259
On optimal designs for censored data
Schmidt, Dennis; Schwabe, Rainer
In: Metrika: international journal for theoretical and applied statistics - Berlin: Springer, Bd. 78.2015, 3, S. 237-257
Dissertation
Optimal designs for the prediction in hierarchical random coefficient regression models
Prus, Maryna; Schwabe, Rainer
In: Magdeburg, Univ., Fak. für Mathematik, Diss., 2015, V, 87 S., graph. Darst.
2014
Peer-reviewed journal article
Algorithms for approximate linear regression design with application to a first order model with heteroscedasticity
Gaffke, Norbert; Graßhoff, Ulrike; Schwabe, Rainer
In: Computational statistics & data analysis - Amsterdam: Elsevier Science, 1983, Bd. 71.2014, S. 1113-1123
A catalogue of designs for partial profiles in paired comparison experiments with three groups of factors
Großmann, Heiko; Graßhoff, Ulrike; Schwabe, Rainer
In: Statistics. - London [u.a.] : Taylor & Francis, Bd. 48.2014, 6, S. 1268-1281
Discussion of Methods for planning repeated measures accelerated degradation tests by Brian P. Weaver and William Q. Meeker
Schwabe, Rainer; Prus, Maryna; Graßhoff, Ulrike
In: Applied stochastic models in business and industry - Chichester: Wiley, 1999, Bd. 30.2014, 6, S. 677-679
Dissertation
Theoretische Grundlagen der partiellen kleinsten Quadrate
Hasan, Hayan; Schwabe, Rainer
In: Magdeburg, Univ., Fak. für Mathematik, Diss., 2014, 98 S.
Optimal design in the presence of random or fixed block effects
Alonso Cabrera, Jesús Eduardo; Schwabe, Rainer
In: Magdeburg, Univ., Fak. für Mathematik, Diss., 2014, VII, 83 S., graph. Darst., 30 cm
Editor
Journal of statistical theory and practice
Schwabe, Rainer
In: Colchester, Taylor & Francis Group, ISSN: 1559-8608 ; 8.2014
Metrika
Schwabe, Rainer
In: Berlin ; Heidelberg, Springer, ISSN: 0026-1335, 35026, 2014
2013
Book chapter
Optimal design for count data with binary predictors in item response theory
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: mODa 10 – Advances in Model-Oriented Design and Analysis / Uciński , Dariusz - Heidelberg : Springer International Publishing ; Uciński, Dariusz . - 2013, S. 117-124 Kongress: International Workshop in Model-Oriented Design and Analysis 10 (Łagów Lubuski, Poland) : 2013.06.10-14
Sample size calculation for diagnostic tests in generalized linear mixed models
Mielke, Tobias; Schwabe, Rainer
In: Ucinski, Dariusz: : mODa 10 - Advances in Model-Oriented Design and Analysis. - Heidelberg : Springer International Publishing, S. 171-178, 2013Kongress: mODa; 10 (Łagów Lubuski) : 2013.06.10-14
Sample size calculation for diagnostic tests in generalized linear mixed models
Mielke, Tobias; Schwabe, Rainer
In: mODa 10 – Advances in Model-Oriented Design and Analysis / Uciński , Dariusz - Heidelberg : Springer International Publishing ; Uciński, Dariusz . - 2013, S. 171-178 Kongress: International Workshop in Model-Oriented Design and Analysis 10 (Łagów Lubuski, Poland) : 2013.06.10-14
Optimal designs for the prediction of individual effects in random coefficient regression
Prus, Maryna; Schwabe, Rainer
In: mODa 10 – Advances in Model-Oriented Design and Analysis / Uciński , Dariusz - Heidelberg : Springer International Publishing ; Uciński, Dariusz . - 2013, S. 211-218 Kongress: International Workshop in Model-Oriented Design and Analysis 10 (Łagów Lubuski, Poland) : 2013.06.10-14
Peer-reviewed journal article
Optimal design for quasi-likelihood estimation in Poisson regression with random coefficients
Niaparast, Mehrdad; Schwabe, Rainer
In: Journal of statistical planning and inference. - Amsterdam : North-Holland Publ. Co, Bd. 143.2013, 2, S. 296-306
Optimal design for discrete choice experiments
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference. - Amsterdam : North-Holland Publ. Co, Bd. 143.2013, 1, S. 167-175
An introduction to optimal design
Holling, Heinz; Schwabe, Rainer
In: Zeitschrift für Psychologie. - Göttingen : Hogrefe, Bd. 221.2013, 3, S. 124-144
Editor
Journal of statistical theory and practice
Schwabe, Rainer
In: Greensboro, Grace Scientific Publ., ISSN: 1559-8608 ; 5.2011, 2013
Article in conference proceedings
Optimal Design for Count Data with Binary Predictors in Item Response Theory
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: 2013, S. 117-124, 10.1007/978-3-319-00218-7_14
Sample Size Calculation for Diagnostic Tests in Generalized Linear Mixed Models
Schwabe, Rainer
In: 2013, 10.1007/978-3-319-00218-7_20
Non-peer-reviewed journal article
Optimal designs for censored data
Schmidt, Dennis; Schwabe, Rainer
In: Magdeburg: Univ., Fak. für Mathematik, 2013, 20 S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2013,20)
Optimal designs for the prediction of individual parameters in hierarchical models
Prus, Maryna; Schwabe, Rainer
In: Magdeburg: Univ., Fak. für Mathematik, 2013, [19] S. - (Preprint; Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg; 2013,21)
2012
Peer-reviewed journal article
Optimal designs for the Rasch model
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: Psychometrika: a journal of quantitative psychology - New York: Springer-Verl., Bd. 77.2012, 4, S. 710-723
Original article in peer-reviewed international journal
Designs for first-order interactions in paired comparison experiments with two-level factors
Großmann, Heiko; Schwabe, Rainer; Gilmour, Steven G.
In: Journal of statistical planning and inference. - Amsterdam : Elsevier, Bd. 142.2012, 8, S. 2395-2401
Discussion on the Paper by Gilmour and Trinca
Holling, Heinz; Schwabe, Rainer
In: Journal of the Royal Statistical Society / C/ Royal Statistical Society - London: Royal Statistical Society, Bd. 61.2012, 3, S. 385[In Artikel: Gilmour, S.G.; Trinca, L. A.: Optimum design of experiments for statistical inference]
Optimal design for linear regression models in the presence of heteroscedasticity caused by random coefficients
Graßhoff, Ulrike; Doebler, Anna; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference: JSPI / ed. in chief J. N. Srivastava: JSPI - Amsterdam: Elsevier, Bd. 142.2012, 5, S. 1108-1113
2011
Book chapter
D-optimal design for a seemingly unrelated linear model
Soumaya, Moudar; Schwabe, Rainer
In: Optimal design of experiments. - Wien : BOKU, S. 170-174, 2011Kongress: International Conference; (Vienna, Austria) : 2011.09.25-30
Optimal designs for individual prediction in random coefficient regression models
Prus, Maryna; Schwabe, Rainer
In: Optimal design of experiments. - Wien : BOKU, S. 122-129, 2011Kongress: International Conference; (Vienna, Austria) : 2011.09.25-30
Editor
Statistica Sinica
Schwabe, Rainer
In: Taipei [u.a.], ISSN: 1017-0405 ; 21.2011
Original article in peer-reviewed international journal
'The usefulness of Bayesian optimal designs for discrete choice experiments' by Roselinde Kessels, Bradley Jones, Peter Goos and Martina Vandebroek
Holling, Heinz; Schwabe, Rainer
In: Applied stochastic models in business and industry. - Chichester : Wiley, Bd. 27.2011, 3, S. 189-192
2010
Original article in peer-reviewed periodical-type series
Some considerations on the Fisher information in nonlinear mixed effects models
Mielke, Tobias; Schwabe, Rainer
In: mODa 9 . - Heidelberg [u.a.] : Physica [u.a.], ISBN 978-3-7908-2409-4, S. 129-136Kongress: mODa; 9 (Bertinoro, Italy) : 2010.06.14-19
Self-avoiding generating sequences for Fourier lattice designs
Bates, Ronald A.; Maruri-Aguilar, Hugo; Riccomagno, Eva; Schwabe, Rainer; Wynn, Henry P.
In: Algebraic methods in statistics and probability II . - Providence, RI : American Math. Soc., ISBN 978-0-8218-4891-3, S. 37-47; Contemporary mathematics; 516, 2010Kongress: AMS Special Session Algebraic Methods in Statistics and Probability; (Urbana-Champaign, Ill.) : 2009.03.27-29
Optimal designs for linear logistic test models
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: mODa 9 . - Heidelberg [u.a.] : Physica [u.a.], ISBN 978-3-7908-2409-4, S. 97-104Kongress: mODa; 9 (Bertinoro, Italy) : 2010.06.14-19
2009
Original article in peer-reviewed international journal
Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors
Großmann, Heiko; Graßhoff, Ulrike; Schwabe, Rainer
In: Journal of statistical planning and inference . - Amsterdam : Elsevier, Bd. 139.2009, 3, S. 1171-1179
Original article in peer-reviewed periodical-type series
On optimal design for a heteroscedastic model arising from random coefficients
Graßhoff, Ulrike; Holling, Heinz; Schwabe, Rainer
In: 6th St. Petersburg Workshop on Simulation; 1: . - St. Petersburg : VVM com. Ltd., ISBN 978-5-9651035-4-6, S. 387-392, 2009Kongress: St. Petersburg Workshop on Simulation; 6 (St. Petersburg) : 2009.06.28-07.04
Some new design for first-order interactions in 2[K] paired comparison experiments
Großmann, Heiko; Schwabe, Rainer; Gilmour, Steven G.
In: 6th St. Petersburg Workshop on Simulation; 1: . - St. Petersburg : VVM com. Ltd., ISBN 978-5-9651035-4-6, S. 394-399, 2009Kongress: St. Petersburg Workshop on Simulation; 6 (St. Petersburg) : 2009.06.28-07.04
2008
Original article in peer-reviewed international journal
Optimal design for the BradleyTerry paired comparison model
Graßhoff, Ulrike; Schwabe, Rainer
In: Statistical methods & applications . - Berlin : Springer, Bd. 17.2008, 3, S. 275-289
Original article in peer-reviewed periodical-type series
On optimal designs in random intercept models
Schwabe, Rainer; Schmelter, Thomas
In: PROBASTAT <5, 2006, Smolenice> : PROBASTAT '06 . - Bratislava : Math. Inst., Slovak Acad. of Sciences, S. 145-153; Tatra Mountains mathematical publications; 39Kongress: PROBASTAT; 5 (Smolenice Castle) : 2006.06.05-09
2007
Original article in peer-reviewed international journal
Full macular translocation versus photodynamic therapy with verteporfin in the treatment of neovascular age-related macular degeneration - 1-year results of a prospective, controlled, randomised pilot trial (FMT-PDT)
Gelisken, Faik; Voelker, Michael; Schwabe, Rainer; Besch, Dorothea; Aisenbrey, Sabine; Szurman, Peter; Grisanti, Salvatore; Herzau, Volker; Bartz-Schmidt, Karl U.
In: Graefe's archive for clinical and experimental ophthalmology - Berlin : Springer, Bd. 245 (2007), Heft 8, S. 1085-1095
Design optimality in multi-factor generalized linear models in the presence of an unrestricted quantitative factor
Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference - Amsterdam : Elsevier, Bd. 137 (2007), Heft 12, S. 3882-3893
Self-face recognition in schizophrenia
Kircher, Tilo T.; Seiferth, Nina Y.; Plewnia, Christian; Baar, Sophia; Schwabe, Rainer
In: Schizophrenia research . - Amsterdam : Elsevier, Bd. 94.2007, 1/3, S. 264-272
Full macular translocation versus photodynamic therapy with verteporfin in the treatment of neovascular age-related macular degeneration - 1-year results of a prospective, controlled, randomised pilot trial (FMT-PDT)
Gelisken, Faik; Voelker, Michael; Schwabe, Rainer; Besch, Dorothea; Aisenbrey, Sabine; Szurman, Peter; Grisanti, Salvatore; Herzau, Volker; Bartz-Schmidt, Karl U.
In: Graefe's archive for clinical and experimental ophthalmology . - Berlin : Springer, ISSN 0721-832x, Bd. 245.2007, 8, S. 1085-1095
Self-face recognition in schizophrenia
Kircher, Tilo T. J.; Seiferth, Nina Yvonne; Plewnia, Christian; Baar, Sophia; Schwabe, Rainer
In: Schizophrenia research - Amsterdam : Elsevier, Bd. 94 (2007), Heft 1/3, S. 264-272
Original article in peer-reviewed periodical-type series
A comparison of efficient designs for choices between two options
Großmann, Heiko; Holling, Heinz; Graßhoff, Ulrike; Schwabe, Rainer
In: mODa 8 - Advances in model oriented design and analysis - Heidelberg [u.a.] : Physica-Verl. , 2007, S. 83-90 - (Contributions to Statistics)
Some curiosities in optimal designs for random slopes
Schmelter, Thomas; Benda, Norbert; Schwabe, Rainer
In: mODa 8 - advances in model-oriented design and analysis - Heidelberg [u.a.] : Physica-Verl. , 2007, S. 189-195 - (Contributions to Statistics)
A comparison of efficient designs for choices between two options
Großmann, Heiko; Holling, Heinz; Graßhoff, Ulrike; Schwabe, Rainer
In: mODa 8 - advances in model-oriented design and analysis - Heidelberg [u.a.] : Physica-Verl. , 2007, S. 83-90 - (Contributions to Statistics)
Some curiosities in optimal designs for random slopes
Schmelter, Thomas; Benda, Norbert; Schwabe, Rainer
In: mODa 8 - Advances in model oriented design and analysis . - Heidelberg [u.a.] : Physica-Verl., ISBN 3-7908-1951-4, S. 189-195; Contributions to Statistics, 2007
2006
Original article in peer-reviewed international journal
Optimal designs for asymmetric linear paired comparisons with a profile strength constraint
Großmann, Heiko; Holling, Heinz; Graßhoff, Ulrike; Schwabe, Rainer
In: Metrika . - Berlin : Springer, Bd. 64.2006, 1, S. 109-119; Abstract
Halton and Hammersley sequences in multivariate nonparametric regression
Rafajlowicz, Ewaryst; Schwabe, Rainer
In: Statistics & probability letters . - Amsterdam : Elsevier Science, Bd. 76.2006, 8, S. 803-812; Abstract
2005
Book chapter
Utility balance and design optimality in logistic models with one unrestricted quantitative factor.
Schwabe, Rainer; Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz
In: Ermakov, S. M. (Hrsg.) ; Melas, V. B. (Hrsg.) ; Pepelyshev, A. N. (Hrsg.): Simulation 2005 (5th Workshop St. Petersburg, Russia June 26 - July 2, 2005). - proceedings. St. Petersburg : Univ., 2005, S. 605 - 610
On the empirical relevance of optimal designs for the measurement of preferences.
Grossmann, Heiko; Holling, Heinz; Brocke, Michaela; Grasshoff, Ulrike; Schwabe, Rainer
In: Berger, Martijn P. F. (Hrsg.) ; Wong, Weng Kee (Hrsg.): Applications of optimal designs. Hoboken, NJ : Wiley, 2005, S. 45 - 65
2004
Original article in peer-reviewed international journal
Optimal designs for main effects in linear paired comparison models.
Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Journal of statistical planning and inference [Amsterdam] 126(2004), S. 361 - 376
Digital image analysis for diagnosis of cutaneous melanoma : development of a highly effective computer algorithm based on analysis of 837 melanocytic lesions.
Blum, A.; Luedtke, H.; Ellwanger, U.; Schwabe, Rainer; Rassner, G.; Garbe, C.
In: British journal of dermatology : the journal of the British Assosiation of Dermatologists [Oxford] 151(2004), S. 1029 - 1037
Original article in peer-reviewed national journal
Sehschärfenprüfung bei Kindern im Vorschulalter : ein Vergleich zwischen Sheridan- Gardiner-Test und Räder-Test.
Mildenberger, I.; Schwabe, Rainer; Schiefer, U.
In: Klinische Monatsblätter für Augenheilkunde [Stuttgart] 221(2004), S. 577 - 582
2003
Original article in peer-reviewed international journal
On the analysis of paired observations.
Grasshoff, Ulrike; Schwabe, Rainer
In: Statistics & probability letters [Amsterdam] 65(2003), S. 7 - 12
Optimal paired comparison design for first-order interactions.
Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Statistics [Basingstoke] 37(2003), Nr. 5, S. 373 - 386
Experimental design for (semi-)local regression.
Rafajlowicz, E.; Schwabe, Rainer
In: Communications in statistics : theory and methods [New York, NY] 32(2003), S. 1035 - 1055
A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space.
Koval, Valery; Schwabe, Rainer
In: Stochastic processes and their applications [Amsterdam] 105(2003), S. 299 - 313
Equidistributed designs in nonparametric regression.
Rafajlowicz, E.; Schwabe, Rainer
In: Statistica sinica [Taipei] 13(2003), Nr. 1, S. 129 - 142
Efficient product designs for quadratic models on the hypercube.
Schwabe, Rainer; Wong, Weng Kee
In: Sankhyá : the Indian journal of statistics [Calcutta] 65(2003), Nr. 3, S. 649 - 659
Original article in peer-reviewed periodical-type series
Optimal 2(K) paired comparison designs for partial profiles.
Schwabe, Rainer; Grasshoff, Ulrike; Grossmann, Heiko; Holling, Heinz
In: Tatra mountains mathematical publications [Bratislava] 26(2003), S. 79 - 86
2002
Book chapter
Versuchsplanung.
Schwabe, Rainer
In: Guido, Walz (Redakt.): Lexikon der Mathematik : in sechs Bänden. Bd. 5 : Sed bis Zyl. Heidelberg : Spektrum, Akademischer Verl., 2002, S. 332 - 337
Original article in peer-reviewed international journal
The two-factor method : a new approach to categorizing the clinical stages of malnutrition in geriatric patients.
Weinrebe, Wolfram; Graef-Gruss, Rudolf; Schwabe, Rainer; Stippler, Dietmar; Fuesgen, Ingo
In: Journal of the american geriatrics society [Malden, Mass.] 50(2002), Nr. 12, S. 2105
Original article in peer-reviewed periodical-type series
Advances in optimum experimental design for conjoint analysis and discrete choice models.
Grossmann, Heiko; Holling, Heinz; Schwabe, Rainer
In: Franses, P. H. (Hrsg.) ; Montgomery, A. L. (Hrsg.): Econometric models in marketing. Amsterdam : JAI, 2002, S. 93 - 117 (Advances in econometrics 16)
Summer semester 2022
Arbeitsgruppenseminar LSF
Oberseminar zur Stochastik LSF
Winter semester 2021/22
Summer semester 2021
Arbeitsgruppenseminar LSF
Oberseminar zur Stochastik LSF
Sommersemester 2018
Biological Statistics (GC 116): LSF Elearning
Modellierung 2 (FMA): LSF
Oberseminar zur Stochastik: LSF
Ringvorlesung Statistik in den Anwendungen. LSF
Seminar für Abschlussarbeiten: LSF
Seminar zur Statistik: LSF Elearning
Statistische Methoden: LSF
Wintersemester 2017/18
Einführung in die Wahrscheinlichkeitstheorie und Statistik: LSF Elearning
- Einführung in die Wahrscheinlichkeitstheorie und Statistik (2 Ü Math): LSF
- Einführung in die Wahrscheinlichkeitstheorie und Statistik (Ü LA): LSF
Multivariate Statistik: LSF Elearning
Informationsveranstaltung für den Masterstudiengang Statistik: LSF
Oberseminar zur Stochastik: LSF
Seminar für Abschlussarbeiten: LSF
Seminar zur Statistik B (Consulting): LSF
Summer semester 2022
Arbeitsgruppenseminar LSF
Oberseminar zur Stochastik LSF
Winter semester 2021/22
Summer semester 2021
Arbeitsgruppenseminar LSF
Oberseminar zur Stochastik LSF
Sommersemester 2018
Biological Statistics (GC 116): LSF Elearning
Modellierung 2 (FMA): LSF
Oberseminar zur Stochastik: LSF
Ringvorlesung Statistik in den Anwendungen. LSF
Seminar für Abschlussarbeiten: LSF
Seminar zur Statistik: LSF Elearning
Statistische Methoden: LSF
Wintersemester 2017/18
Einführung in die Wahrscheinlichkeitstheorie und Statistik: LSF Elearning
- Einführung in die Wahrscheinlichkeitstheorie und Statistik (2 Ü Math): LSF
- Einführung in die Wahrscheinlichkeitstheorie und Statistik (Ü LA): LSF
Multivariate Statistik: LSF Elearning
Informationsveranstaltung für den Masterstudiengang Statistik: LSF
Oberseminar zur Stochastik: LSF
Seminar für Abschlussarbeiten: LSF
Seminar zur Statistik B (Consulting): LSF