Heiko Großmann

Advances in optimum experimental design for conjoint analysis and discrete choice models

The authors review current developments in experimental design for conjoint analysis and discrete choice models emphasizing the issue of design efficiency. Drawing on recently developed optimal paired comparison designs, theoretical as well as empirical evidence is provided that established design strategies can be improved with respect to design efficiency.

A catalogue of designs for partial profiles in paired comparison experiments with three groups of factors

A common strategy for avoiding information overload in multi-factor paired comparison experiments is to employ pairs of options which have different levels for only some of the factors in a study. For the practically important case where the factors fall into three groups such that all factors within a group have the same number of levels and where one is only interested in estimating the main effects, a comprehensive catalogue of D-optimal approximate designs is presented. These optimal designs use at most three different types of pairs and have a block diagonal information matrix.

Efficient Designs for Paired Comparisons with a Polynomial Factor

In psychological research paired comparisons, which demand judges to evaluate the trade-off between two alternatives, have been shown to yield valid estimates of the judges’ preferences. For this situation we present optimal and efficient designs in a response surface setting where the alternatives are modelled by a polynomial.

Partial-profile choice designs for estimating main effects and interactions of two-level attributes from paired comparison data

A new method to generate designs for estimating main effects and two-factor interactions of two-level attributes from choice experiments is presented for the situation where the choice sets are pairs and the alternatives are specified by a subset of the attributes. Partial-profile designs are constructed by using Hadamard matrices and factorial and incomplete block designs as building blocks. Their information matrix under the multinomial logit model is derived under the indifference assumption of equal choice probabilities by exploiting the relationship between the multinomial logit model for pairs and the linear paired comparison model. The information matrix depends only on the incomplete block designs but not on the other building blocks. Efficient partial-profile designs with relatively small numbers of choice sets are found by performing computer searches inspired by these results.

Functional Data Analysis in Designed Experiments

F-type tests for functional ANOVA models implicitly assume that the response curves are generated by a completely randomized design. By using the split-plot design as an example it is illustrated how these tests can be extended to more complex ANOVA models. In order to derive the test statistics and their approximate null distributions, Hasse diagrams for representing the structure of the experiment are combined with a stochastic process perspective. The application of the more general F-type tests is illustrated for simulated data.

Differences between Analytic and Algorithmic Choice Designs for Pairs of Partial Profiles

Choice experiments are widely used for measuring how the attributes of goods or services influence preference judgments. To this end, a suitable experimental design is used to combine attribute levels into options or profiles and to further arrange these into choice sets. Often incomplete descriptions of the options, which are known as partial profiles, are used in order to reduce the amount of information respondents need to process. For the situation where the choice sets are pairs, where only the main effects of the attributes are of interest and where the attributes fall into two groups such that all attributes within a group have the same number of levels, optimal designs which were obtained analytically are compared with algorithmically generated designs. For the situations considered, there are sometimes substantial differences between the efficiencies of the two types of design.

A Comparison of Efficient Designs for Choices Between Two Options

Optimal designs for choice experiments with choice sets of size two are frequently derived under the assumption that all model parameters in a multinomial logit model are equal to zero. In this case, optimal designs for linear paired comparisons are also optimal for the choice model. It is shown that the methods for constructing linear paired comparison designs often require a considerably smaller number of choice sets when the parameters of primary interest are main effects.

A Conjoint Measurement Based Rationale for Inducing Preferences

For additive models of preferences or choices among multi-attribute options an approach to inducing preferences is presented which offers new opportunities for empirical investigations of choice behavior as well as the validation of preference elicitation techniques. The approach is founded in measurement theory and draws on finite conjoint measurement and random utility theory. Preferences are induced by teaching respondents to choose among multi-attribute options in accordance with a weak order that can be represented by a unique set of utility values. It is shown that the utility values can be recovered with estimation procedures for probabilistic choice models. As the utility values are known a priori, they can serve as a standard of comparison for estimates in empirical investigations. The measurement theoretic background and a procedure for teaching preferences are described in detail. Data from two experiments provide evidence that accurate numerical utility values can be induced with tasks that require only qualitative judgments but do not reveal any numerical information.

Testing Gait with Ankle-Foot Orthoses in Children with Cerebral Palsy by Using Functional Mixed-Effects Analysis of Variance.

Existing statistical methods extract insufficient information from 3-dimensional gait data, rendering clinical interpretation of impaired movement patterns sub-optimal. We propose an alternative approach based on functional data analysis that may be worthy of exploration. We apply this to gait data analysis using repeated-measurements data from children with cerebral palsy who had been prescribed fixed ankle-foot orthoses as an example. We analyze entire gait curves by means of a new functional F test with comparison to multiple pointwise F tests and also to the traditional method - univariate repeated-measurements analysis of variance of joint angle minima and maxima. The new test maintains the nominal significance level and can be adapted to test hypotheses for specific phases of the gait cycle. The main findings indicate that ankle-foot orthoses exert significant effects on coronal and sagittal plane ankle rotation; and both sagittal and horizontal plane foot rotation. The functional F test provided further information for the stance and swing phases. Differences between the results of the different statistical approaches are discussed, concluding that the novel method has potential utility and is worthy of validation through larger scale patient and clinician engagement to determine whether it is preferable to the traditional approach.

Efficient Paired Comparison Designs for Utility Elicitation

In applications data are often available from the comparison of two alternatives rather than the direct valuation of a single object on its own. Experiments have to be designed for these paired comparisons in a different way than for standard situations. In this note we deal with a problem arising from organizational psychology and present an application of design considerations to the estimation of utility functions.