Interpreting correlated random parameters in choice experiments

The random parameter logit (RPL) model with uncorrelated coefficients is a restrictive version of the mixed logit model, but it is one of the most frequently used models for analysing stated choice data in environmental valuation. The body of applied literature using a more flexible version, the RPL model with correlated coefficients, has been noticeably growing in the last years, but it has still been used less frequently due to its computational complexity and non-trivial interpretation. The correlation matrix of the coefficients in this model captures not only the correlation due to a behavioural phenomenon but also the correlation caused by scale heterogeneity. These two effects cannot be identified empirically. Nevertheless, this paper proposes a simple procedure that enables an interpretation of some of the estimated correlations, which can help to disentangle the unobserved preference heterogeneity. The proposed procedure consists of two simple steps. Firstly, the signs of the attributes corresponding to the utility coefficients that have a negative mean coefficient are reversed. Secondly, only negative correlations are interpreted. We propose a theoretical model accounting for correlations induced both by hypothetical behavioural phenomena and by scale heterogeneity and apply the proposed procedure to three typical cases of environmental valuation.