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Chapter 5_______________________________________________________
models, the vector of non-stochastic, Vq , s for the best and Vq ,t for the worst alternatives,
which can be recognized by the analyst, and the unobserved error term ε q,it . It is
imposed that this error term is independently and identically distributed (IID) with
extreme value type 1. Equation 5.8 models the choice decision for a Best-Worst
experiment.
Yq , st = U q , s − U q ,t = Vq , s − Vq ,t + ε q , st
for s, t = 1,..., J
and s ≠ t
5.8
In the Best-Worst choice task, with a choice set size of three alternatives,
answering the best and the worst options only once is enough to obtain a full ranking of
alternatives.
In this study, three approaches of Best-Worst Discrete Choice Experiment
(BWDCE) are dealt. One is the Simultaneous BWDCE, which considers that consumers
make their choice decision about the best and the worst alternatives in the choice set
only once (simultaneously). The other approach, which is proposed by Lancsar and
Louviere (2008), considers that respondents select first the best option and, then, the
worst alternative in the choice set and it is called Sequential BWDCE.
The last approach is an alternative method proposed by Louviere et al. (2009) in
order to improve the number of individual observations. They call this approach as the
Bottom-up model. This model does not make any assumption about the choice decision
(sequential or simultaneous), but it was originally proposed to be carried out with BestWorst DCE because consumers have better ability to identify extreme options.
As the number of observations per respondent is low, the intention of these
authors was to use a greater ability to identify alternatives by BW tasks to diminish the
choice variance, and as a consequence, increase the number of parameters statistically
different from zero.
5.A) Sequential Best-Worst Discrete Choice Experiment
Equation 5.9 represents the probability of ranking the three alternatives by
Sequential BW approach. Thus, the probability of A > B > C is equal to the MNL of
chosen the alternative A as the best option from a set {A, B and C} times the MNL of
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