Exploiting correlation in the construction of D-optimal response surface designs.

Cost considerations and difficulties in performing completely randomized experiments often dictate the necessity to run response surface experiments in a bi-randomization format. The resulting compound symmetric error structure not only affects estimation and inference procedures but it also has severe consequences for the optimality of the designs used. Fir this reason, it should be taken into account explicitly when constructing the design. In this paper, an exchange algorithm for constructing D-optimal bi-randomization designs is developed and the resulting designs are analyzed. Finally, the concept of bi-randomization experiments is refined, yielding very efficient designs, which, in many cases, outperform D-optimal completely randomized experiments.Structure;

The impact of the soccer schedule on TV viewership and stadium attendance : evidence from the Belgian Pro League

In the past decade, television broadcasters have been investing a huge amount of money for the Belgian Pro League broadcasting rights. These companies pursue an audience rating maximization, which depends heavily on the schedule of the league matches. At the same time, clubs try to maximize their home attendance and find themselves affected by the schedule as well. Our paper aims to capture the Belgian soccer fans’ preferences with respect to scheduling options, both for watching matches on TV and in the stadium. We carried out a discrete choice experiment using an online survey questionnaire distributed on a national scale. The choice sets are based on three match characteristics: month, kickoff time, and quality of the opponent. The first part of this survey concerns television broadcasting aspects. The second part includes questions about stadium attendance. The choice data is first analyzed with a conditional logit model which assumes homogenous preferences. Then a mixed logit model is fit to model the heterogeneity among the fans. The estimates are used to calculate the expected utility of watching a Belgian Pro League match for every possible setting, either on TV or in the stadium. These predictions are validated in terms of the real audience rating and home attendance data. Our results can be used to improve the scheduling process of the Belgian Pro League in order to persuade more fans to watch the matches on TV or in a stadium

Trend-resistant design of experiments under budget constraints.

When experiments are to be performed in a time sequence, the observed responses are affected by a time trend. The construction of trend-resistant run orders is extensively described in the literature. However, run orders that are optimally balanced for time trends usually involve huge costs and they are often of low practical value in view of economical considerations. This paper presents a design algorithm for the construction of trend-resistant run orders under budget constraints. The algorithm offers the experimenter a general method for solving a wide range of practical design problems.

Improving the efficiency of individualized designs for the mixed logit choice model by including covariates.

Recent research shows that the inclusion of choice related demo- and sociographics in discrete choice models aids in modeling the choice behavior of consumers substantially. However, the increase in efficiency gained by accounting for covariates in the design of a choice experiment has thus far only been demonstrated for the conditional logit model. Previous findings are extended by using covariates in the construction of individualized Bayesian D-efficient designs for the mixed logit choice model. A simulation study illustrates how incorporating covariates affecting choice behavior yields more efficient designs and more accurate estimates and predictions at the individual level. Moreover, it is shown that the possible loss in design efficiency and therefore in estimation and prediction accuracy from including choice unrelated respondent characteristics is negligible.Covariate; Discrete choice experiment; Mixed logit choice model; Individual efficient design; Hierarchical Bayes estimation;

Semi-bayesian D-optimal designs and estimation procedures for mean and variance functions.

Semi-Bayesian D-optimal designs for fitting mean and variance functions are derived for some prior distributions on the variance function parameters. The impact of the mean of the prior and of the uncertainty about this mean is analyzed. Simulation studies are performed to investigate whether the choice of design has a substantial impact on the efficiency of the mean and the variance function parameter estimation and whether the D-optimality criterion is appropriate irrespective of the method applied to estimate the variance function parameters.Functions;

Using the Bayesian information criterion to develop two-stage model-robust and model-sensitive designs.

In this paper, we investigate use of the Bayesian Information Criterion (BIC) in the development of Bayesian two-stage designs robust to model uncertainty. The BIC is particularly appealing in this situation as it avoids the necessity of prior specification on the model parameters and can readily be computed from the output of standard statistical software packages.Bias; BIC; Design; Information; Integrated likelihood; Lack-of-fit; Model; Model-sensitive; Posterior probabilities; Prior probabilities; Probability; Software; Software packages; Two-stage procedures; Uncertainty;

(Dt,C) Optimal run orders.

Cost considerations have rarely been taken into account in optimum design theory. A few authors consider measurement costs, i.e. the costs associated with a particular factor level combination. A second cost approach results from the fact that it is often expensive to change factor levels from one observation to another. We refer to these costs as transition costs. In view of cost minimization, one should minimize the number of factor level changes. However, there is a substantial likelihood that there is some time order dependence in the results. Consequently, when considering both time order dependence and transition costs, an optimal ordering is not easy to find. There is precious little in the literature on how to select good time order sequences for arbitrary design problems and up to now, no thorough analysis of both costs is found in the literature. For arbitrary design problems, our proposed design algorithm incorporates cost considerations in optimum design construction and enables one to compute cost-efficient run orders that are optimally balanced for time trends. The results show that cost considerations in the construction of trend-resistant run orders entail considerable reductions in the total cost of an experiment and imply a large increase in the amount of information per unit cost.Optimal; Run orders;

Trend-resistant and cost-efficient cross-over designs for mixed models.

A mixed model approach is used to construct optimal cross-over designs. In a cross-over experiment the same subject is tested at different points in time. Consider as an example an experiment to investigate the influence of physical attributes of the work environment such as luminance, ambient temperature and relative humidity on human performance of acceptance inspection in quality assurance. In a mixed model context, the subject effects are assumed to be independent and normally distributed. Besides the induction of correlated observations within the same inspector, the mixed model approach also enables one to specify the covariance structure of the inspection data. Here, several covariance structures are considered either depending on the time variable or not. Unfortunately, a serious drawback of the inspection experiment is that the results may be influenced by an unknown time trend because of inspector fatigue due to monotony of the inspection task. In other circumstances, time trend effects can be caused by learning effects of the test subjects in behavioural and life sciences, heating or aging of material in prototype experiments, etc. An algorithm is presented to construct cross-over designs that are optimally balanced for time trend effects. The costs for using the subjects and for altering the factor levels between consecutive observations can also be taken into account. A number of examples illustrate utility of the outlined design methodology.Optimal; Models; Model;

Orthogonalized regressors and spurious precision.

The exposure of a stock's return to exchange-rate changes is conventionally estimated by regression. Often, the market return is included as an additional regressor. By first orthogonalizing the market return on the exchange rate one seems to have the best of both worlds: the market factor cannot subsume part of the exposure present in a stock's return, and these of the estimate beats both the simple -and the multiple- regression SE's. This last effect is illusory: since the simple and the pseudo-multiple regression always produce the same exposure estimate, given the sample, their precision must be identical too. Technically, the source of the problem is that the uncertainty about the market's exposure estimate is left out of the calculated SE. In published work, the calculated error variances should be corrected upward by 20 to 100 percent.Currency; Exchange; Exposure; Market; Market model; Multiple regression; Precision; Regression; Uncertainty; Variance; Work;