Utility Covariances and Context Effects in Conjoint MNP Models
Marco Vriens1998, Marketing Science
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Abstract
Experimental conjoint choice analysis is among the most frequently used methods for measuring and analyzing consumer preferences. The data from such experiments have been typically analyzed with the Multinomial Logit (MNL) model. However, there are several problems associated with the standard MNL model because it is based on the assumption that the error terms of the underlying random utilities are independent across alternatives, choice sets, and subjects. The Multinomial Probit model (MNP) is well known to alleviate this assumption of independence of the error terms. Accounting for covariances in utilities in modeling choice experiments with the MNP is important because variation of the coefficients in the choice model may occur due to context effects. Previous research has shown that subjects' utilities for alternatives depend on the choice context, that is, the particular set of alternatives evaluated. Simonson and Tversky's tradeoff contrast principle describes the effect of the choice context on attribute importance and patterns of choice. They distinguish local contrast effects, which are caused by the alternatives in the offered set only, and background contrast effects, which are due to the influence of alternatives previously considered in choice experiments. These effects are hypothesized to cause correlations in the utilities of alternatives within and across choice sets, respectively.
Key takeaways
- We hypothesize that the difference in fit occurs because the RC model accommodates correlations among choice sets that are caused by background contrast effects, whereas the model that treats choice sets as independent (iRC) accounts for local contrast effects only.
- We can estimate the IP, RI, and RC models in two ways, each without and with assuming independence of the random utilities between choice sets, that is, using the likelihood in (6) or (9), respectively.
- Although the superior fit of the iRC and iRI models over the IP model may be indicative of local contrast effects, due to which utilities within choice sets are correlated and the IIA property does not hold, the superior fit of the RC and RI models may indicate again that background contrast effect are prevalent.
- The simpler iRC and IP models yield incorrect predictions because they do not accommodate effects of the covariance structure of utilities within and between choice sets.
- The iRC model that arises as a special case of the RC model by assuming that choice sets are independent does not suffer from the IIA property, but does not account for correlations between choice sets.
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