Related papers: A General Equivalence Theorem for Crossover Design…
We identify locally $D$-optimal crossover designs for generalized linear models. We use generalized estimating equations to estimate the model parameters along with their variances. To capture the dependency among the observations coming…
Locally optimal designs for generalized linear models are derived at certain values of the regression parameters. In the present paper a general setup of the generalized linear model is considered. Analytic solutions for optimal designs are…
This article discusses D-optimal Bayesian crossover designs for generalized linear models. Crossover trials with t treatments and p periods, for $t <= p$, are considered. The designs proposed in this paper minimize the log determinant of…
We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…
In crossover design experiments, the proportional model, where the carryover effects are proportional to their direct treatment effects, has draw attentions in recent years. We discover that the universally optimal design under the…
Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…
The gamma model is a generalized linear model for gamma-distributed outcomes. The model is widely applied in psychology, ecology or medicine. In this paper we focus on gamma models having a linear predictor without intercept. For a specific…
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…
This paper reviews the design of experiments for generalised linear models, including optimal design, Bayesian design and designs for models with random effects.
We present general results on D-optimal designs for estimating the mean response in repeated measures growth curve models with metric outcomes. For this situation, we derive a novel equivalence theorem for checking design optimality. The…
A model for cross-over designs with repeated measures within each period was developed. It is obtained using an extension of generalized estimating equations that includes a parametric component to model treatment effects and a…
In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on moment matrices (if criteria depend on designs via moment matrices) or with respect to the designs…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…
The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients.…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…
Subject dropout is very common in practical applications of crossover designs. However, there is very limited design literature taking this into account. Optimality results have not yet been well established due to the complexity of the…
Crossover designs randomly assign each unit to receive a sequence of treatments. By comparing outcomes within the same unit, these designs can effectively eliminate between-unit variation and facilitate the identification of both…
Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM…
The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies…