Related papers: Optimal Design in Repeated Testing for Count Data
In this paper, we derive optimal designs for the Rasch Poisson counts model and the Rasch Poisson-Gamma counts model incorporating several binary predictors for the difficulty parameter. To efficiently estimate the regression coefficients…
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…
The Poisson-Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the $D$-optimality criterion for the Poisson-Gamma model is equivalent to a combined weighted optimality criterion of…
Analyzing ordinal data becomes increasingly important in psychology, especially in the context of item response theory. The generalized partial credit model (GPCM) is probably the most widely used ordinal model and finds application in many…
We investigate R-optimal designs for multi-response regression models with multi-factors, where the random errors in these models are correlated. Several theoretical results are derived for Roptimal designs, including scale invariance,…
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…
The subject of this work is multiple group random coefficients regression models with several treatments and one control group. Such models are often used for studies with cluster randomized trials. We investigate A-, D- and E-optimal…
We characterize $D$-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of…
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to…
Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
Subsampling is commonly used to overcome computational and economical bottlenecks in the analysis of finite populations and massive datasets. Existing methods are often limited in scope and use optimality criteria (e.g., A-optimality) with…
Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee's…
This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…
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…
Optimal block designs for additive models achieve their efficiency by dividing experimental units among relatively homogenous blocks and allocating treatments equally to blocks. Responses in many modern experiments, however, are drawn from…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
In this article, we investigate the robust optimal design problem for the prediction of response when the fitted regression models are only approximately specified, and observations might be missing completely at random. The intuitive idea…
We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show…