DEVACOE · Design of experiments for variance component estimation

Design of experiments for variance component estimation

Final Report (DEVACOE) 01/04/2010-31/01/2012 A.Final publishable summary report covering results, conclusions and socio-economic impact of the project. A1. Finished articles During the first year of the project, the researcher completed two articles in the field of optimal designs with restricted randomization: The first article is entitled 'Model selection using penalized generalized least squares under restricted randomization'. For model selection purposes in experimental contexts, researchers often use stepwise regression or subset selection. In situations involving restricted randomization, such as block experiments and split-plot experiments, this has to be done manually and often involves numerous model estimations. Moreover, these selection procedures ignore the stochastic errors inherited in the variable selection stage. This leads to incorrect standard errors. As an alternative, the use of penalized least squares estimation was proposed, which performs model selection and model estimation simultaneously. Therefore, the method enables to compute correct standard errors. A key property of the penalized least squares estimation approach is that it possesses the so-called oracle property, which means that it works as well as if the correct sub-model were known. The usefulness of the approach was demonstrated using various practical examples, and using an extensive simulation study. This article is currently under revision for publication in Journal of Quality Technology. The second submitted work is entitled 'Two new classes of second-order equivalent-estimation split-plot designs'. In many industrial experiments, complete randomization of the runs is impossible as, often, they involve factors whose levels are hard or costly to change. In such cases, the split-plot design is a cost-efficient alternative that reduces the number of independent settings of the hard-to-change factors. In general, the use of generalized least squares is required for model estimation based on data from split-plot designs. However, the ordinary least squares estimator is equivalent to the generalized least squares estimator for some split-plot designs, including some second-order split-plot response surface designs. These designs are called equivalent-estimation designs. An important consequence of the equivalence is that basic experimental design software can be used to analyze the data. Two new families of equivalent-estimation split-plot designs, one based on subset designs and another based on a class of rotatable response surface designs were constructed using supplementary difference sets. The resulting designs complement existing catalogs of equivalent-estimation designs and allow for a more flexible choice of the number of hard-to-change factors, the number of easy-to-change factors, the number and size of whole plots and the total sample size. This article is currently under revision for publication in IIE Transactions. During the second year of the project, the researcher completed an article on a new Bayesian composite design criterion for the construction of Bayesian optimal designs of experiments for estimating variance components in random effects models and for the joint estimation of fixed effects and variance components in linear mixed models. The focus in the article is on industrial experiments involving one or more restrictions on the randomization. The most commonly used experimental designs in those cases are blocked designs and split-plot designs, where the experimental runs are performed in groups. In general, modeling data from blocked and split-plot response surface experiments requires the use of generalized least squares and the estimation of two variance components. The literature on the optimal design of blocked and split-plot response surface experiments, however, focuses entirely on the precise estimation of the fixed factor effects and completely ignores the necessity to estimate the variance components as well. To overcome this problem, we propose a new Bayesian optimal design criterion which focuses on both the variance components and the fixed effects. A novel feature of the criterion is that it incorporates prior information about the variance components through log-normal or beta prior distributions. In our algorithm for generating optimal blocked and split-plot designs, we implement several lesser-known but computationally efficient quadrature approaches for the numerical approximation of the new optimal design criterion. This article is under consideration for publication in Technometrics. Moreover, during the second year of the project the researcher completed an article on Five-level Second Order Rotatable Designs. The focus in the article is on response surface methodology, which is widely used for developing, improving and optimizing processes in various fields. A method for constructing second-order rotatatable designs is proposed, in order to explore and optimize response surfaces based on an infinite class of supplementery difference sets. The produced designs achieve both properties of rotatability and estimation efficiency. Also, they possess good predictive properties. This article is currently under revision for publication in Communications in Statistics - Simulation and Computation. A2. Ongoing work The paper on the Bayesian composite optimal design criterion motivated the researcher to further investigate the usefulness of quadrature approaches that can be applied for the numerical approximation of Bayesian optimality criteria, with an aim to find good experimental designs at a lower computational cost. In the last months of the project, the researcher explored various quadrature techniques and studied how these can be applied for the evaluation of Bayesian criteria with several different choices for the a-priori distributions. An article describing this work is in preparation. Mention new criterion using full treatment model. Mention that an article is in preparation. Mention joint project proposal with Steven Gilmour, with the title of the project proposal and perhaps a short summary. A3. Socio-economic impact Because of the economic crisis that hits many businesses, industries and research institutes, it is more important than ever to use the most advanced methods to design experiments. The methodology we developed in the course of this project will allow the design of cost-efficient experiments that provide a maximum of information. As a result, this project helps ensuring that experimenting for product and process innovation and for advances in science in general remains an option for businesses, industries and research institutes in these times of crisis. B.Report covering the wider societal implications of the project, including gender equality actions, ethical issues, efforts to involve other actors and spread awareness as well as the plan for the use and dissemination of foreground. The researcher participated in several conferences, where she presented part of her work on the DEVACOE project and where she had the opportunity to meet and share ideas with experts in the field of design of experiments. The following is a list of conferences that the researcher attended. In case she gave a presentation, the title of the presentation is given as well. 1. 9th Workshop on Quality Improvement Methods at the Universitatskolleg Bommerholz, Dortmund, Germany - May 2010. Contributed Talk Title: A General Construction Method for Mixed-Level Supersaturated Designs. 2. 2010 Joint Statistical Meetings, Vancouver, Canada - August 2010. 3. 28th European Meeting of Statisticians (EMS2010), Athens, Greece - August 2010. Contributed Talk Title: A Group Screening Method for the Statistical Analysis of Data from Mixed-Level Supersaturated Designs. 4. 18th Meeting of the Belgian Statistical Society (BSS2010), Spa, Belgium - October 2010. Contributed Talk Title: Penalized Least Squares for Models with Correlated Responses. 5. 3rd International Conference of the ERCIM WG on Computing and statistics (CFE-ERCIM 2010), London, UK - December 2010. Contributed Talk Title: The Statistical Analysis of Optimal Mixed-Level Supersaturated Designs Using Group Screening. 6. European Network for Business and Industrial Statistics and Design of Industrial Experiments Spring Conference (ENBIS-DEINDE 2011), Turin, Italy - March 2011. Contributed Talk Title: A New Approach to the Optimal Design of Blocked and Split-Plot Experiments. 7. International Conference on Design of Experiments (ICODOE 2011), Memphis, USA - May 2011. Invited Talk Title: Optimal Design of Blocked and Split-Plot Experiments For Fixed-Effects and Variance-Component Estimation. 8. Spring Research Conference on Statistics in Industry and Technology (SRC 2011), Chicago, USA - June 2011. Invited Talk Title: Bayesian Optimal Design of Blocked and Split-Plot Experiments. 9. Designed Experiments: Recent advances in methods and applications (DEMA 2011), Cambridge, UK - August 2011. Contributed Talk Title: New Classes of Second-Order Equivalent-Estimation Split-Plot Designs. Invited Talk Title: Optimal design of blocked and split-plot experiments for fixed-effects and variance-components estimation 10. Design and Analysis of Experiments (DAE 2011), Cambridge, UK - October 2011. Invitation to participate in Design and Analysis of Experiments research program, Isaac Newton Institute for Mathematical Sciences. The researcher worked for two weeks at the Design and Analysis of Experiments program, where she had the chance to meet researchers on Design of Experiment, from all over the world, to discuss with them her research and to attend seminars. We are currently finalising a collaborative project with Professor Steven Gilmour from University of Southampton, for a joint Phd supervision on' Design and Analysis of Experiments for Hybrid Models'. The DEVACOE project was concerned with methodological, statistical work concerning the efficient collection of data, and therefore did not raise any ethical issues.

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