Abstract
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.
Highlights
People’s choices depend on their personal characteristics, their socio-economic status and their aspirations
Following the work of [25] introducing Bayesian inference for logistic Gaussian process density estimation, we suggest a nonparametric conditional logit model, based on Gaussian processes, to allow for a large variety of complex preferences that vary between individuals without a combinatorial explosion of parametric basis functions
All other effects are modelled as functions drawn from Gaussian processes: U 1⁄4 log ZN þ fDðXI; XE; XC; XA; ZDÞ þ fIðXI; XE; XC; XA; ZIÞ ð18Þ
Summary
People’s choices depend on their personal characteristics, their socio-economic status and their aspirations. When those choices are connected to socioeconomic indicators such as income, wealth and ethnicity they can aggregate into profoundly important emergent social phenomena such as segregated neighbourhoods, schools and workplaces. It is vital to be able to accurately determine, at the individual level, the factors influencing socially relevant choices. To fully realise the power of large data sets requires models that are flexible enough to accommodate many different social phenomena while being statistically robust.
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