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Register a new userOptimal Designs for Second-Order Interactions in Paired Comparison Experiments with Binary Attributes
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Added by
Eric Nyarko Mr.
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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No Arabic abstract
In paired comparison experiments respondents usually evaluate pairs of competing options. For this situation we introduce an appropriate model and derive optimal designs in the presence of second-order interactions when all attributes are dichotomous.
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We propose a method for constructing optimal block designs for experiments on networks. The response model for a given network interference structure extends the linear network effects model to incorporate blocks. The optimality criteria are chosen to reflect the experimental objectives and an exchange algorithm is used to search across the design space for obtaining an efficient design when an exhaustive search is not possible. Our interest lies in estimating the direct comparisons among treatments, in the presence of nuisance network effects that stem from the underlying network interference structure governing the experimental units, or in the network effects themselves. Comparisons of optimal designs under different models, including the standard treatment models, are examined by comparing the variance and bias of treatment effect estimators. We also suggest a way of defining blocks, while taking into account the interrelations of groups of experimental units within a network, using spectral clustering techniques to achieve optimal modularity. We expect connected units within closed-form communities to behave similarly to an external stimulus. We provide evidence that our approach can lead to efficiency gains over conventional designs such as randomized designs that ignore the network structure and we illustrate its usefulness for experiments on networks.
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How to measure the incremental Return On Ad Spend (iROAS) is a fundamental problem for the online advertising industry. A standard modern tool is to run randomized geo experiments, where experimental units are non-overlapping ad-targetable geographical areas (Vaver & Koehler 2011). However, how to design a reliable and cost-effective geo experiment can be complicated, for example: 1) the number of geos is often small, 2) the response metric (e.g. revenue) across geos can be very heavy-tailed due to geo heterogeneity, and furthermore 3) the response metric can vary dramatically over time. To address these issues, we propose a robust nonparametric method for the design, called Trimmed Match Design (TMD), which extends the idea of Trimmed Match (Chen & Au 2019) and furthermore integrates the techniques of optimal subset pairing and sample splitting in a novel and systematic manner. Some simulation and real case studies are presented. We also point out a few open problems for future research.
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 based on Bayesian optimal designs offers robustness to our conclusions since these designs, unlike locally optimal designs, are efficient even if the parameters are misspecified. In this paper we develop approximate design theory for Bayesian $D$-optimality for nonlinear regression models with common parameters and investigate the cases of common location or common location and scale parameters separately. Analytical characterisations of saturated Bayesian $D$-optimal designs are derived for frequently used dose-response models and the advantages of our results are illustrated via a numerical investigation.
We propose a novel model-based approach for constructing optimal designs with complex blocking structures and network effects, for application in agricultural field experiments. The potential interference among treatments applied to different plots is described via a network structure, defined via the adjacency matrix. We consider a field trial run at Rothamsted Research and provide a comparison of optimal designs under various different models, including the commonly used designs in such situations. It is shown that when there is interference between treatments on neighbouring plots, due to the spatial arrangement of the plots, designs incorporating network effects are at least as, and often more efficient than, randomised row-column designs. The advantage of network designs is that we can construct the neighbour structure even for an irregular layout by means of a graph to address the particular characteristics of the experiment. The need for such designs arises when it is required to account for treatment-induced patterns of heterogeneity. Ignoring the network structure can lead to imprecise estimates of the treatment parameters and invalid conclusions.
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