International Choice Modelling Conference, International Choice Modelling Conference 2017

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Using a spatial error latent class approach to address spatial dependence in latent class membership
Danny Campbell, Wiktor Budziński, Mikołaj Czajkowski, Nick Hanley

Last modified: 28 March 2017

Abstract


Finite mixture models are now widely used to analyse revealed and stated preference data. Their appeal is the flexibility that they afford to the analyst. With the correct assumptions, they can uncover preference heterogeneity, the presence of error variance heteroscedasticity and a range of processing strategies, most predominately attribute non-attendance. At the heart of these models is the assumption that respondents belong in a given class. However, it is obviously not possible to knowmembership beforehand with certainty and, thus, it remains latent. To work around this, based on observed choice behaviour, probabilistic conditions are imposed on each class. In doing so, the presence of each classcan be established up to a probability, with the full probability per respondent allocated across all classes.

Typically, the class membership function includes class-specific constant, and a vector of class-specific parameters for the individual characteristics for respondents and an error term that is iid type I extreme value distributed so that the unconditional class probabilities can be retrieved using a multinomial logit specification. Notwithstanding the ability to include individual characteristics in the latent class membership function, there is a possibility that the unobserved factors that explain membership to latent classes may be spatially related. If so, the errors are spatially arranged, meaning that the assumption that the error terms are independent of one another is violated. Not addressing this means the model is mis-specified in the systematic component of the latent class membership function—in particular, the omission of variables that are spatially clustered. Overlooking this will, therefore, lead to bias, poor prediction andmissed opportunities for insight.

In this paper we develop a new latent class modelling framework, whereby spatial dependence can enter through the membership function errors. We refer to this as a spatial error latent class model.The key assumption of this model is that spatial autocorrelation is treated as a nuisance and as an estimation problem, and as something to be estimated. This is accommodated by decomposing the overall membership error into two components, namely a aspatial error term that is iid type I extreme value distributed that satisfies the standard assumption, and a spatial error term that captures thepattern of spatial dependence between errors for connected observations.

In this paper, we confirm the incidence of positive spatial clustering of latent class probabilities (i.e., class membership errors for an observation tend to vary systematically in size with the errors for othernearby observations). Given that this clustering of residuals violates the assumption that the error terms are independent of one another, it raises concerns on the appropriateness of the widespread use of aspatial latent class models. Importantly, we show that not addressing this also has implications for model fit, marginal willingness to pay estimation and for policy evaluation.


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