Spatial modelling of origin-destination commuting flows in 1 Switzerland 2 3 4 5

29 30 Objective and methodology 31 This paper presents a direct modelling approach for origin-destination public transportation commuting 32 flows with possible endogenous regressors for the case of Switzerland. Its purpose is to improve the 33 gravity modelling approach for OD flows by applying a spatial autoregressive regression model and 34 testing different spatial weighting schemes. To the best of our knowledge, there has been no prior 35 application of such advanced models in the context of transport demand modelling for public transport. 36 Methodologically, in the first step a gravity model is developed and tested for the presence of spatial 37 autocorrelation in its residuals. Subsequently, variants of a spatial lag model with different spatial 38 weighting schemes are developed. Furthermore, we test a variable based on mean income 39 differences on its ability to describe interregional demand patterns. In addition, we treat for the 40 endogenous nature of the newly constructed variable. We are also testing its ability to serve as the 41 basis for the construction of the spatial weight matrix, thus replacing the commonly used travel time / 42 distance metric. On the modelling front, we use an Ordinary least squares (OLS) estimator for the 43 gravity model, while a Generalized Method of Moments and Instrumental Variable (GMM/IV) (IV) 44 estimator for the spatial models is employed in order to obtain unbiased and consistent parameter 45 estimates. Last, we evaluate various models’ goodness-of-fit measures and in-sample predictive 46 accuracies by comparing among each other as well as to those of a state-of-the practice transport 47 model (as provided by national spatial planning bureau (NPVM)). This comparison can allow us to 48 draw solid conclusion with respect to the suitability of the presented method for predicting commuting 49 flows. 50 51 Case study 52 In brief, a case study for public transport commuting flows in Switzerland is designed to illustrate the 53 concept of OD flow modelling, based on travel-to-work trips data from the Federal Census of 2000. 54 The data cover 2896 Swiss municipalities and contains over 250’000 observations on their initial form. 55 However, it does not fill the whole flow matrix that contains 28962 = 8,386,816 flows. For the remaining 56 OD pairs we assume zero-valued travel flows. An important aspect is the issue with how to deal with 57 zero flows. A large fraction of zero-valued OD flows would definitely point towards a Poisson or a 58 (zero-inflated) negative Binomial interaction model. However, neither a Poisson nor a negative 59 Binomial spatial autoregressive regression model for OD flows has been developed so far. We include 60 income differences between Swiss communes as an explanatory variable in our models, since a 61 higher income gives incentives to commute. In conclusion, we filter the initial flow matrix for inter62 communal travel trips, income data available only in 1595 communes and all zero flows, which gives a 63 final sample size of 46,659 OD flows. Clearly, this is a limitation of our modelling approach but 64 nevertheless the findings can be of apparent value for pointing directions. 65 Modelling commuting behaviour requires a set of relevant explanatory variables that capture 66 the characteristics of origins and destinations, along with the mechanisms that generate the trips 67 among them. The dependent variable, inter-communal travel flows, is regressed on several 68 independent variables obtained or derived from the 2000 Federal Census, the Swiss national transport 69 model ARE (2005), and the Institute for Transport Planning and Systems (IVT) of ETH Zurich. We use 70 the following variables in our framework, which are also common in explaining public transport 71 demand in the literature (e.g. LeSage and Thomas-Agnan, 2015; Farmer, 2011; Axhausen et al., 72 2015). 73 74 Table 1: Model variables 75 76 Statistic Definition Flow Av. daily flows Network dist. minutes Income diff. rel CHF (in 1,000) Population (o) # inhabitants