Modelling Indifference in Binary SP Choice Experiments
J Amaya, V Cantillo, Universidad del Norte, ,CO; J de D Ortuzar, Pontificia Universidad Catolica de Chile, CL
We propose a model that describes the behaviour of individuals when they confront thresholds of indifference which let them obtain similar utilities in a binary SP survey where the individual is not forced to choose one alternative at first view
Choice behaviour is affected by complex factors; in addition, when facing new situations people might undergo a process of experimentation and learning, through trial and error. These represent a challenge to improve realism in modelling work. Furthermore, the choice process may present restrictions on the perception and evaluation of attributes that can vary within the population according to certain characteristics; we refer to these as thresholds. These thresholds of perception can be seen as "just noticeable differences". In this sense, perceptible changes would be values above a threshold whereas those below it would not cause a reaction in the individual because utilities do not change. It may also happen that utilities are so similar that are perceived as equal by the individual.
The use of binary Stated Preference (SP) surveys in which the individual can choose between only two alternatives is very frequent in applied work. However a good design requires that utilities are balanced, and this may imply cases where utilities are so close to be undistinguishable for the respondent; for this reason, it may be important to incorporate an "indifference option". In this paper we develop a discrete choice model to adequately treat this case.
In the classical theory of random utility an individual q would prefer one alternative to another if the utility of the former exceeds that of the latter by at least a non-negative threshold Deltaq, the minimum perceivable difference. If, however, the excess utility was less than the threshold level, a state of indifference would result. Formally, if Aiq and Ajq are the alternatives and, Uiq , Ujq their respective utilities (assumed continuous functions over the possible values of their attributes), the following three choices are possible and the individual can choose among them:
(i) Aiq is preferred to Ajq when Uiq>Ujq+Deltaq
(ii) Ajq is preferred to Aiq when Ujq>Uiq+Deltaq
(iii) Aiq is equally preferred to Ajq when ABS(Uiq-Ujq)<=Deltaq
To model the inclusion of an indifference option we consider thresholds that are dynamic and depend on the experiences and restrictions of the respondents. Thus, it is possible to postulate that these thresholds vary in the population, according with the concept of psychological threshold in the theory of consumer choice.
We propose a discrete choice model that describes the behaviour of individuals when they confront thresholds of indifference which let them obtain similar utilities from specific situations in a SP experiment. As an important contribution, our model introduces the indifference option so that the individual is not forced to choose one alternative at first view. We postulate that if thresholds exist they could be stochastic, random, differ among population and even be a function of socio-economic characteristics and choice conditions. Our formulation allows estimation of the parameters of the threshold probability distribution starting from information about choices.
We applied the model to synthetic data and to real data coming from a SP survey with rating data and found that if there is evidence about the existence of perception thresholds in the population, the use of models without this capability should lead to errors in prediction and in estimation, although this only occurs when the effect of the indifference threshold in the utility function is strong.
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