Choice modelling with Gaussian processes in the social sciences: A case study of neighbourhood choice in Stockholm

We present a non-parametric extension of the conditional logit model, using Gaussian process priors. The conditional logit model is used in quantitative social science for inferring interaction effects between personal features and choice characteristics from observations of individual multinomial decisions, such as where to live, which car to buy or which school to choose. The classic, parametric model presupposes a latent utility function that is a linear combination of choice characteristics and their interactions with personal features. This imposes strong and unrealistic constraints on the form of individuals' preferences. Extensions using non-linear basis functions derived from the original features can ameliorate this problem but at the cost of high model complexity and increased reliance on the user in model specification. In this paper we develop a non-parametric conditional logit model based on Gaussian process logit models. We demonstrate its application on housing choice data from over 50,000 moving households from the Stockholm area over a two year period to reveal complex homophilic patterns in income, ethnicity and parental status.