Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared

Experimental designs for environmental valuation with choice-experiments: A Monte Carlo investigation

We review the practice of experimental design in the environmental economics literature concerned with choice experiments. We then contrast this with advances in the field of experimental design and present a comparison of statistical efficiency across four different experimental designs evaluated by Monte Carlo experiments. Two different situations are envisaged. First, a correct a priori knowledge of the multinomial logit specification used to derive the design and then an incorrect one. The data generating process is based on estimates from data of a real choice experiment with which preference for rural landscape attributes were studied. Results indicate the D-optimal designs are promising, especially those based on Bayesian algorithms with informative prior. However, if good a priori information is lacking, and if there is strong uncertainty about the real data generating process - conditions which are quite common in environmental valuation - then practitioners might be better off with conventional fractional designs from linear models. Under misspecification, a design of this type produces less biased estimates than its competitors

SAS Macros for Analysis of Unreplicated 2^k and 2^k-p Designs with a Possible Outlier

Many techniques have been proposed for judging the significance of effects in unreplicated 2^k and 2^k-p designs. However, relatively few methods have been proposed for analyzing unreplicated designs with possible outliers. Outliers can be a major impediment to valid interpretation of data from unreplicated designs. This paper presents SAS macros which automate a manual method for detecting an outlier and performing an analysis of data from an unreplicated 2^k or 2^k-p design when an outlier is present. This method was originally suggested by Cuthbert Daniel and is based on the normal or half normal plot of effects. This automated version was shown in simulation studies to perform better than other procedures proposed to do the same thing.

D-optimal Factorial Designs under Generalized Linear Models

Generalized linear models (GLMs) have been used widely for modelling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this paper, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multi-level predictors.Comment: 16 pages, 1 figur

Performance of likelihood-based estimation methods for multilevel binary regression models.

By means of a fractional factorial simulation experiment, we. compare the performance of penalised quasi-likelihood (PQL), non-adaptive Gaussian quadrature and adaptive Gaussian quadrature in estimating parameters for multilevel logistic regression models. The comparison is done in terms of bias, mean-squared error (MSE), numerical convergence and computational efficiency. It turns out that in terms of MSE, standard versions of the quadrature methods per-form relatively poorly in comparison with PQL.Bias; Binary regression; Convergence; Efficiency; Factorial; Fractional factorial experiment; Gaussian quadrature; Logistic regression; Methods; Model; Models; Monte Carlo simulation; Multilevel analysis; Parameters; Penalised quasi-likelihood; Performance; Regression; Simulation;

Robustness testing in the determination of seven drugs in animal muscle by liquid chromatography–tandem mass spectrometry

In this work, the robustness of the sample preparation procedure for the determination of six tranquilizers (xylazine, azaperone, propionylpromazine, chlorpromazine, haloperidol, and azaperol) and a beta-blocker (carazolol) in animal muscle by LC/MS–MS was assessed through the experimental design methodology. A 2III7 − 4 fractional factorial design was performed to evaluate the influence of seven variables on the final concentration of the seven drugs in the samples, in accordance with what is laid down in Commission Decision No 2002/657/EC. The variation considered for each of those seven factors is likely to happen when preparing the samples, being the values chosen as level − 1, the nominal operating conditions. The results of the experimentation were evaluated from different statistical strategies, such as hypothesis testing using an external variance previously estimated, Lenth's method, and Bayesian analysis. Both Lenth's and Bayes' approaches enabled to determine the effect of every variable even though no degrees of freedom were left to estimate the residual error. The same conclusion about the robustness of the extraction step was reached from the three methodologies, namely, none of the seven factors examined influenced on the method performance significantly, so the sample preparation procedure was considered to be robust.Ministerio de Ciencia e Innovación (CTQ2011-26022) and MINECO (CTQ2014- 53157-R)

Performance of likelihood-based estimation methods for multilevel binary regression models.

By means of a fractional factorial simulation experiment, we compare the performance of Penalised Quasi-Likelihood, Non-Adaptive Gaussian Quadrature and Adaptive Gaussian Quadrature in estimating parameters for multi-level logistic regression models. The comparison is done in terms of bias, mean squared error, numerical convergence, and computational efficiency. It turns out that, in terms of Mean Squared Error, standard versions of the Quadrature methods perform relatively poor in comparison with Penalized Quasi-Likelihood.Bias; Binary regression; Convergence; Efficiency; Factorial; Fractional factorial experiment; Gaussian quadrature; Logistic regression; Methods; Model; Models; Monte Carlo simulation; Multilevel analysis; Penalised quasi-likelihood; Performance; Regression; Simulation;

Bayesian Design and Analysis of Small Multifactor Industrial Experiments

PhDUnreplicated two level fractional factorial designs are a common type of experimental design used in the early stages of industrial experimentation. They allow considerable information about the e ects of several factors on the response to be obtained with a relatively small number of runs. The aim of this thesis is to improve the guidance available to experimenters in choosing a good design and analysing data. This is particularly important when there is commercial pressure to minimise the size of the experiment. A design is usually chosen based on optimality, either in terms of a variance criterion or estimability criteria such as resolution. This is given the number of factors, number of levels of each factor and number of runs available. A decision theory approach is explored, which allows a more informed choice of design to be made. Prior distributions on the sizes of e ects are taken into consideration, and then a design chosen from a candidate set of designs using a utility function relevant to the objectives of the experiment. Comparisons of the decision theoretic methods with simple rules of thumb are made to determine when the more complex approach is necessary. Fully Bayesian methods are rarely used in multifactor experiments. However there is virtually always some prior knowledge about the sizes of e ects and so using this in a Bayesian data analysis seems natural. Vague and more informative priors are 6 explored. The analysis of this type of experiment can be impacted in a disastrous way in the presence of outliers. An analysis that is robust to outliers is sought by applying di erent model distributions of the data and prior assumptions on the parameters. Results obtained are compared with those from standard analyses to assess the bene ts of the Bayesian analysis