# Using a spatial autoregressive model with spatial autoregressive disturbances to investigate origin-destination trip flows

## TL;DR

This paper introduces a new model to study trip flows by considering spatial effects in both the main model and the error term.

## Contribution

The paper is the first to develop and test a SARAR model with OD filters for trip distribution analysis.

## Key findings

- SARAR models with OD filters can disentangle spatial dependence in trip flows.
- SARAR models outperform SAR and SEM models statistically in trip distribution analysis.
- The study provides empirical evidence from Hangzhou, China, supporting the hypotheses.

## Abstract

Spatial interaction models with spatial origin-destination (OD) filters are powerful tools to characterize trip flows in space, which is a classic and important problem in regional science. To the authors’ knowledge, existing studies adopting OD filters mostly specify the spatial dependence as an autoregressive process, which may not be the full picture of spatial effects. To examine the problem, this paper proposes the hypotheses that 1) spatial OD dependences can take place in both the spatial autoregressive term and the spatial error term in a spatial interaction model. 2) Estimating a spatial autoregressive model with spatial autoregressive disturbances (SARAR) model with OD filters would disentangle where the spatial dependence exists and by how much. 3) The marginal effects obtained from SARAR models would be preferred to analysts when SARAR models outperform spatial autoregressive (SAR) models and spatial error models (SEM) from the statistical point of view. To assess these hypotheses, this paper specifies, estimates, and applies SARAR models with OD filters to investigate trip distributions. By comparing against alternative models, this paper investigates the estimation results in SAR, SEM and SARAR models using an empirical data collected from Hangzhou, China. The contribution of this paper is to be the first in developing an SARAR model with OD filters for trip distribution analyses and examining its performance.