@article{2021:goeken:hierarchic,
title = {Hierarchical Bayes Conjoint Choice Models - Model Framework, Bayesian Inference, Model Selection, and Interpretation of Estimation Results},
year = {2021},
note = {Choice-based conjoint (CBC) is nowadays the most widely used variant
of conjoint analysis, a class of methods for measuring consumer
preferences. The primary reason for the increasing dominance of the
CBC approach over the last 35 years is that it closely mimics real
choice behavior of consumers by asking respondents repeatedly to
choose their preferred alternative from a set of several offered
alternatives (choice sets). Within the framework of CBC analysis, the
multinomial logit (MNL) model is the most frequently used discrete
choice model due to the existence of closed form solutions for
conditional choice probabilities. The popularity of CBC and the MNL
model has grown even more since the introduction of hierarchical
Bayesian (HB) estimation techniques that accommodate individual
consumer heterogeneity in choice data, and which have now become
state-of-the-art in marketing theory and practice. Still, researchers
and practitioners have to make further decisions under this framework
(CBC, MNL, HB estimation), such as how to represent preference
heterogeneity. Here, using a normal distribution (and therefore a
unimodal distribution) has become the standard approach in the
marketing literature. However, the thin tails of the normal
distribution suggest that the standard HB-MNL model should not be the
“go-to” approach to approximate multimodal preference
distributions, because individual preference patterns lying at the
tails of the normal distribution (i.e., that do not fit well with the
assumption of a unimodal distribution) tend to be shrunk to the
population mean. This shrinkage, especially in multimodal data
settings, could mask important information (e.g., new or different
structures in the data). A mixture of normal distributions avoids this
limited flexibility of the most simple continuous approach of assuming
a unimodal prior heterogeneity distribution. There are currently two
prominent HB-CBC modeling approaches embedding the mixture-of-normals
(MoN) approach: the more widespread MoN-HB-MNL model, and the
Dirichlet process mixture (DPM)-HB-MNL model. In this article, we
review the prominent HB-MNL model (with its normal prior), the
MoN-HB-MNL model, and the DPM-HB-MNL model and apply them to an
empirical multi-country CBC data set. We compare the statistical
performance of the three models in terms of goodness-of-fit and
predictive accuracy, show how to include consumer background
characteristics in the upper level of these models, and illustrate how
to interpret the estimation results (with a special focus on
cross-county heterogeneity). In sum, our article serves as a kind of
user guide to the estimation and interpretation of Hierarchical Bayes
Conjoint Choice Models. For our data, we observed that all three
choice models (both with and without consumer background
characteristics) resulted in a one-component solution. The DPM-HB-MNL
model nevertheless yielded a higher cross-validated hit rate compared
to the MoN-HB-MNL and the HB-MNL models due to its even more flexible
prior assumptions. The two latter models tended to slightly overfit
our empirical data, which was reflected by higher goodness-of-fit
statistics but a lower predictive accuracy compared to the DPM-HB-MNL
model. We showed that this result could be attributed to the weaker
extent of Bayesian shrinkage of these two models. The DPM-HB-MNL model
showed a stronger shrinkage effect and seems therefore somewhat more
robust against overfitting. Including consumer background
characteristics in terms of country of origin information for the
respondents did not improve the statistical model performance
(especially not the predictive performance). Still, using the country
of origin information for respondents in a post-hoc segmentation
analysis helped us to explain some differences in brand preferences
between the five countries.},
journal = {Marketing ZFP},
pages = {49--66},
author = {Goeken, Nils and Kurz, Peter and Steiner, Winfried},
volume = {43},
number = {3}
}