Modelling residential location choices with implicit availability of alternatives

Choice set generation is a challenging aspect of disaggregate level residential location choice modelling due to the large number of candidate alternatives in the universal choice set (hundreds to hundreds of thousands). The classical Manski method (Manski, 1977) is infeasible here because of the explosion of the number of possible choice sets with the increase in the number of alternatives. Several alternative approaches have been proposed in recent years to deal with this issue, but these have limitations alongside strengths. For example, the Constrained Multinomial Logit (CMNL) model (Martínez et al., 2009) offers gains in efficiency and improvements in model fit but has weaknesses in terms of replicating the Manski model parameters. The rth-order Constrained Multinomial Logit (rCMNL) model (Paleti, 2015) performs better than the CMNL model in producing results consistent with the Manski model, but the benefits disappear when the number of alternatives in the universal choice set increases. In this study, we propose an improved CMNL model (referred to as Improved Constrained Multinomial Logit Model, ICMNL) with a higher order formulation of the CMNL penalty term that does not depend on the number of alternatives in the choice set. Therefore, it is expected to result in better model fit compared to the CMNL and the rCMNL model in cases with large universal choice sets. The performance of the ICMNL model against the CMNL and the rCMNL model is evaluated in an empirical study of residential location choices of households living in the Greater London Area. Zone level models are estimated for residential ownership and renting decisions where the number of alternatives in the universal choice set is 498 in each case. The performance of the models is examined both on the estimation sample and the holdout sample used for validation. The results of both ownership and renting models indicate that the ICMNL model performs considerably better compared to the CMNL and the rCMNL model for both the estimation and validation samples. The ICMNL model can thus help transport and urban planners in developing better prediction tools.