Related papers: On The Study Of D-Optimal Saturated Designs For Me…
In this work we present the results of several simulations on main-effect factorial designs. The goal of such simulations is to investigate the connections between the $D$-optimality of a design and its geometrical structure. By means of a…
In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric…
We develop $D$-optimal designs for linear models with first-order interactions on a subset of the $2^K$ full factorial design region, when both the number of factors set to the higher level and the number of factors set to the lower level…
Two-level factorial designs are widely used in industrial experiments. For processes involving \(n\) factors, the construction of designs comprising \(2^n\) and \(2^{n-p}\) factorials, arranged in blocks of size \(2^q\) is investigated. The…
We develop two analytic approaches to solve D-optimal approximate designs under generalized linear models. The first approach provides analytic D-optimal allocations for generalized linear models with two factors, which include as a special…
We develop $D$-optimal designs for linear main effects models on a subset of the $2^K$ full factorial design region, when the number of factors set to the higher level is bounded. It turns out that in the case of narrow margins only those…
In this paper we study saturated fractions of a two-factor design under the simple effect model. In particular, we define a criterion to check whether a given fraction is saturated or not, and we compute the number of saturated fractions.…
We contemplate an experimental situation in a $2^k$-factorial experiment with acute resource crunch so that we need to conduct just a saturated design [SD] - with the understanding that precision of the estimates cannot be estimated from…
Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…
Factorial designs are widely used in agriculture, engineering, and the social sciences to study the causal effects of several factors simultaneously on a response. The objective of such a design is to estimate all factorial effects of…
We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this…
In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. We define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is…
We consider the problem of obtaining locally D-optimal designs for factorial experiments with qualitative factors at two levels each with binary response. Our focus is primarily on the 2^2 experiment. In this paper, we derive analytic…
We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects of interest differ from those under the…
Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…
A new class of two-level non-regular fractional factorial designs is defined. We call this class an {\it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine…
Choice designs for the main effects model, broader main effects model and main effects plus specified interaction effects model are discussed in this paper. Universally optimal choice designs are obtained for all of these models using…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and…
Factorial designs are widely used due to their ability to accommodate multiple factors simultaneously. The factor-based regression with main effects and some interactions is the dominant strategy for downstream data analysis, delivering…