Setting prices in mixed logit model designs
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Setting prices in mixed logit model designs Andreas Falke1 · Harald Hruschka1
© Springer Science+Business Media New York 2015
Abstract We investigate different procedures to set prices in designs for choicebased conjoint analysis using the mixed logit model which captures latent consumer heterogeneity. Besides discrete attributes, we include a linear price term in the deterministic utility function thereby treating price as continuous variable. We consider two different price intervals and several price sets which contain either two or three prices. We compare these alternatives to set prices by simulating choices for different constellations on the basis of the mixed logit model. Furthermore, we generate ten designs simultaneously instead of just one. Using these simulated choices, we estimate the parameters of the mixed logit model in the next step. To reduce the needed sample size and computation time caused by accounting for latent consumer heterogeneity, we apply Halton draws and set a minimum potential design for prior draws. ANOVA with root mean squared error between estimated and true price coefficient values of individual consumers as dependent variable shows that using more extreme prices as interval bounds and one intermediate price positioned to the right of the interval performs best. Keywords Semi-Bayesian mixed logit design · Heterogeneity · Estimation accuracy · D-optimality
Andreas Falke
[email protected] 1
University of Regensburg, Universitaetsstrasse 31, 93053 Regensburg, Germany
Mark Lett
1 Introduction Because of its flexibility, choice-based conjoint analysis has become a popular tool to get insights to consumer preferences for attributes of services or goods Gustafsson et al. (2006). Until a few years ago, data obtained by this kind of experiment have been analyzed using homogeneous multinomial logit models, which have several flaws, not considering latent consumer heterogeneity being the most serious one. In recent years, eliminating this particular lack has become a focal point in the marketing literature. Using the mixed logit model and assuming coefficients to be multivariate normal distributed are the solution most researchers use to take latent heterogeneity into account. There are a few papers whose authors develop and investigate methods to construct design for the mixed logit model which allows for latent heterogeneity. S´andor and Wedel (2002) assume that parameter values are known and therefore ignore parameter uncertainty. These authors also compare designs for the mixed logit to designs constructed for the homogeneous logit model. Yu et al. (2009), on the other hand, follow a semi-Bayesian approach and take coefficient uncertainty into account. They also investigate several less complex design procedures, e.g., for the homogeneous logit model or procedures based on orthogonal designs. S´andor and Wedel (2002) as well as Yu et al. (2009) construct mixed logit designs using a D-error-related efficiency criterion (see Section 2 for more details). In a n
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