Design Issues for Generalized Linear Models: A Review

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 is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Extensions of D-optimal Minimal Designs for Symmetric Mixture Models.

The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé\u27s linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. IN THIS PAPER EXTENSIONS OF THE D-OPTIMAL MINIMAL DESIGNS ARE DEVELOPED FOR A GENERAL MIXTURE MODEL TO ALLOW ADDITIONAL INTERIOR POINTS IN THE DESIGN SPACE TO ENABLE PREDICTION OF THE ENTIRE RESPONSE SURFACE: Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two ten-point designs for the Lack of Fit test by simulations

An Integrated Probability-Based Approach for Multiple Response Surface Optimization

Nearly all real life systems have multiple quality characteristics where individual modeling and optimization approaches can not provide a balanced compromising solution. Since performance, cost, schedule, and consistency remain the basics of any design process, design configurations are expected to meet several conflicting requirements at the same time. Correlation between responses and model parameter uncertainty demands extra scrutiny and prevents practitioners from studying responses in isolation. Like any other multi-objective problem, multi-response optimization problem requires trade-offs and compromises, which in turn makes the available algorithms difficult to generalize for all design problems. Although multiple modeling and optimization approaches have been highly utilized in different industries, and several software applications are available, there is no perfect solution to date and this is likely to remain so in the future. Therefore, problem specific structure, diversity, and the complexity of the available approaches require careful consideration by the quality engineers in their applications

Extraction of Antioxidants from Blackberry (Rubus ulmifolius L.): Comparison between Ultrasound- and Microwave-Assisted Extraction Techniques

Berries are considered functional food because of their potential health benefits to consumers due to their high concentrations in bioactive compounds. The extraction process of their antioxidant compounds is a crucial step. In this work, ultrasound (UAE) and microwave (MAE) assisted extraction have been evaluated and compared for the recovery of total phenolic compounds (TPC) and total anthocyanins (TA) from blackberry. Since several variables have an influence on the extraction processes e ciency, a response surface method using a Box–Behnken design (BBD) was chosen for the optimization of UAE and MAE variables. Six variables (solvent, temperature, amplitude, cycle, pH, and sample:solvent ratio) were optimized for UAE while the optimization for MAE was performed on four variables (solvent, temperature, pH, and sample:solvent ratio). It has been proven that solvent and temperature have a significant influence on the extraction of both TA and TPC. Only 10 and 5 min were necessary to complete the UAE and MAE procedures, respectively. A precision study was also carried out, and coe cient of variation lower than 5% was determined. Non-significant di erences were obtained when using UAE and MAE at their respective optimum conditions. Thus, the results demonstrated a successful potential use of both techniques for the extraction of TA and TPC from blackberry. In conclusion, this work shows interesting perspectives for quality control analytical laboratories for the development of rapid extraction techniques to quantify these antioxidant compounds in blackberries

Optimal design of experiments for liquid–liquid equilibria characterization via semidefinite programming

Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated

Empirical modelling for sound absorption coefficient of Kenaf Fibre by using response surface method

This thesis discusses the use of Box Behnken Design (BBD) approach to plan experiments to find the Sound Absorption Coefficient (SAC) for Kenaf/Polypropylene (PP) and Kenaf/Epoxy sandwich sample with an overall objective of optimising the density (0.25g/cm3 - 0.65g/cm3), thickness (10mm - 50mm), pressure (1000kg - 5000kg), and frequency of sound (125Hz - 5000Hz). Based on the literature review, research that identifies the significance of independent variables of sound absorber capability using particular methodology remain scarce. Besides that, there was no research that adopted Design of Experiment (DOE) to be used before experimental work on acoustic areas related to natural fibre, specifically on Kenaf Fibre (KF). All research on identification of SAC was done by analysing previous research, by using calculation and experimental work and analysis. It was found that all research on KF and its sound characteristics such as SAC did not produce any empirical equation which could give benefits to other researchers on their study on the same characteristics. The researcher managed to achieve all the objectives of this research. The first objective of this study is to identify the significance of factors for a mixture of the composition between KF with PP and a mixture of the composition between KF with Epoxy to get the SAC by using the RSM as the DOE. The second objective is to compare the SAC between the simulation result and the experimental result based on the suggested test sample by the RSM and tested in an impedance test tube. The third objective is to develop and compare the empirical equation for the SAC from simulation result and experimental result by using the density, thickness, compression pressure, and frequency as the significant factors. RSM was adopted to validate the output parameters (responses) which were decided by the input process parameters. RSM also quantified the relationship between the variable input parameters and the corresponding output parameters and validated by Analysis of Variance (ANOVA) before experiments on 24 sets of sample that proposed by BBD were performed. Value of R2, Adjusted R2 and Predicted R2 with >95%, and p-value with 3244) + (0.00014 × ?@2AB23=7) + (0.000009583325 × D@244B@2)) is more reliable as a sound absorber if compared to KF with PP

Optimization of electrophoretic separations of thirteen phenolic compounds using single peak responses and an interactive computer technique

An interactive computer method is proposed for the electrophoretic separation of 13 phenolic compounds from extra-virgin olive oil using single peak response values. A central composite design was executed for optimization of the sodium tetraborate concentration, pH and applied voltage. Statistical models were determined for eight resolution responses and thirteen effective mobilities. Six of the resolution models had highly significant ANOVA lack of fit values, limiting their accuracies for use in Derringer´s desirability function search for optimal separation conditions. None of the 13 effective mobility models suffered from significant lack of fit. Since it is not possible to define effective mobility target values for the desirability function, an interactive computer program developed in our laboratories was applied to the single peak models. Mouse or cursor movements were executed to define experimental conditions in model simulations of the electropherogram. These simulations resulted in superior peak separations, especially for the apigenin and luteolin peaks, in 35 min, compared with those obtained in close to 50 min with the resolution models. Verification experiments performed 2 and 3 years later confirmed the robustness of the models.Um método computacional interativo foi desenvolvido para a separação eletroforética de 13 compostos fenólicos de azeite de oliva extravirgem, usando valores individuais de resposta para cada pico. Um planejamento composto central foi executado para a otimização da concentração de tetraborato de sódio, pH e voltagem aplicada. Foram determinados modelos estatísticos para oito respostas de resolução e treze de mobilidades efetivas. Seis modelos de resolução apresentaram significativa falta de ajuste após ANOVA, o que limitou sua acurácia para uso nas funções de desejabilidade de Derringer-Suich na busca pelas condições ótimas de separação. Nenhum dos 13 modelos de mobilidade efetiva apresentou falta de ajuste significativa. Visto que não foi possível definir valores alvos para as funções de desejabilidade, um programa de computador interativo, desenvolvido em nossos laboratórios, foi aplicado aos modelos individuais de cada pico. Movimentos do mouse ou do cursor foram executados para definir as condições experimentais nas simulações dos eletroferogramas. Essas simulações resultaram em uma melhor separação dos picos, especialmente para os picos de apigenina e luteolina, em 35 min, comparado aos obtidos para cerca de 50 min com os modelos de resolução. Experimentos de verificação executados 2 e 3 anos depois confirmaram a robustez dos modelos.17441753Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES