Martina Vandebroek

A comparison of criteria to design efficient choice experiments

To date, no attempt has been made to design efficient choice experiments by means of the G- and V-optimality criteria. These criteria are known to make precise response predictions, which is exactly what choice experiments aim to do. In this article, the authors elaborate on the G- and V-optimality criteria for the multinomial logit model and compare their prediction performances with those of the D- and A-optimality criteria. They make use of Bayesian design methods that integrate the optimality criteria over a prior distribution of likely parameter values. They employ a modified Fedorov algorithm to generate the optimal choice designs. They also discuss other aspects of the designs, such as level overlap, utility balance, estimation performance, and computational effectiveness.

D-optimal split-plot designs with given numbers and sizes of whole plots

The design of split-plot experiments has received considerable attention during the last few years. The goal of this article is to provide an efficient algorithm to compute D-optimal split-plot designs with given numbers of whole plots and given whole-plot sizes. The algorithm is evaluated and applied to a protein extraction experiment. In addition, it is shown that two-level factorial and fractional factorial designs are D-optimal for estimating first-order response surface models for specific numbers and sizes of whole plots.

Outperforming completely randomized designs

Split-plot designs have become increasingly popular in industrial experimentation because some of the factors under investigation are often hard-to-change. It is well-known that the resulting compound symmetric error structure not only affects estimation and inference procedures but also the efficiency of the experimental designs used. In this paper, we compute D-optimal first and second order split-plot designs and show that these designs, in many cases, outperform completely randomized designs in terms of D- and G-efficiency. This suggests that split-plot designs should be considered as an alternative to completely randomized designs even if running a completely randomized design is affordable.

Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity

Random effects or mixed logit models are often used to model differences in consumer preferences. Data from choice experiments are needed to estimate the mean vector and the variances of the multivariate heterogeneity distribution involved. In this paper, an efficient algorithm is proposed to construct semi-Bayesian D-optimal mixed logit designs that take into account the uncertainty about the mean vector of the distribution. These designs are compared to locally D-optimal mixed logit designs, Bayesian and locally D-optimal designs for the multinomial logit model and to nearly orthogonal designs Sawtooth CBC for a wide range of parameter values. It is found that the semi-Bayesian mixed logit designs outperform the competing designs not only in terms of estimation efficiency but also in terms of prediction accuracy. In particular, it is shown that assuming large prior values for the variance parameters for constructing semi-Bayesian mixed logit designs is most robust against the misspecification of the prior mean vector. In addition, the semi-Bayesian mixed logit designs are compared to the fully Bayesian mixed logit designs, which take also into account the uncertainty about the variances in the heterogeneity distribution and which can be constructed only using prohibitively large computing power. The differences in estimation and prediction accuracy turn out to be rather small in most cases, which indicates that the semi-Bayesian approach is currently the most appropriate one if one needs to estimate mixed logit models.

An Efficient Algorithm for Constructing Bayesian Optimal Choice Designs

Recently, Kessels et al. (2006) developed a way to produce Bayesian G- and V-optimal designs for the multinomial logitmodel. These designs allow for precise response predictions which is the goal of conjoint choice experiments. The authors showed that the G- and V- optimality criteria outperform the D- and A-optimality criteria for prediction. However, their G- and V-optimal design algorithm is computationally intensive, which is a barrier to its use in practice. In this paper, we present an efficient algorithm for calculating Bayesian optimal designs by means of the different criteria. Particularly, the speed of computation for the V-optimality criterion has improved dramatically.The new algorithm makes it possible to use Bayesian D-, A-, G- and V-optimal designs that are tailored to individual respondents in computerized conjoint choice studies.

D -optimal response surface designs in the presence of random block effects

The purpose of this paper is to help the reader in designing D-optimal blocked experiments. The block effects are assumed to be random. Therefore, in general, the optimal designs depend on the extent to which observations within one block are correlated. An algorithm is presented that produces D-optimal designs for these cases. However, in three specific situations, the optimal design does not depend on the degree of correlation. These situations include some cases where the block size is greater than or equal to the number of model parameters, the case of minimum support designs and orthogonally blocked first-order designs. In addition, a relationship is established between the design of experiments with random block effects and the design of experiments with fixed block effects. Finally, it is shown that orthogonal blocking is an optimal design strategy.

Practical inference from industrial split-plot designs

In many industrial response surface experiments, some of the factors investigated are not reset independently. The resulting experimental design then is of the split-plot type, and the observations in the experiment are in many cases correlated. A proper analysis of the experimental data therefore is a mixed model analysis involving generalized least-squares estimation. Many people, however, analyze the data as if the experiment was completely randomized and estimate the model using ordinary least squares. The purposes of this article are to quantify the differences in conclusions reached from the two methods of analysis and to provide the reader with guidance for analyzing split-plot experiments in practice. The problem of determining the denominator degrees of freedom for significance tests in the mixed model analysis is discussed as well.

Recommendations on the use of Bayesian Optimal Designs for Choice Experiments

In this paper, we argue that some of the prior parameter distributions used in the literature for the construction of Bayesian optimal designs are internally inconsistent. We rectify this error and provide practical advice on how to properly specify the prior parameter distribution. Also, we present two pertinent examples to illustrate that Bayesian optimal designs generally outperform utility-neutral optimal designs that are based on linear design principles.

Optimal designs for conjoint experiments

In conjoint experiments, each respondent receives a set of profiles to rate. Sometimes, the profiles are expensive prototypes that respondents have to test before rating them. Designing these experiments involves determining how many and which profiles each respondent has to rate and how many respondents are needed. To that end, the set of profiles offered to a respondent is treated as a separate block in the design and a random respondent effect is used in the model because profile ratings from the same respondent are correlated. Optimal conjoint designs are then obtained by means of an adapted version of an algorithm for finding D-optimal split-plot designs. A key feature of the design construction algorithm is that it returns the optimal number of respondents and the optimal number of profiles each respondent has to evaluate for a given number of profiles. The properties of the optimal designs are described in detail and some practical recommendations are given.

Recursions for the individual model

Abstract Recently, Waldmann considered an algorithm to compute the aggregate claims distribution in the individual life model which is an efficient reformulation of the original exact algorithm of De Pril. In this paper we will show that in practice the approximations as proposed by De Pril are still more efficient than the exact algorithm of Waldmann both in terms of the number of computations required and of the memory occupied by intermediate results. Furthermore we will generalize the algorithm of Waldmann to arbitrary claim amount distributions. We will compare this algorithm with respect to efficiency with the algorithms that were derived by De Pril for this model. It turns out that the approximations of De Pril are most efficient for practical computations.