INTRODUCTION Despite recent advances in spatial analysis in transport, such as the accounting for spatial correlation in accident analysis, important research have not been fully addressed. Specifically, the paper examines the problems related to:  Spatial mismatching  The modifiable areal unit problem (MAUP)  Ecological fallacy  Spatial dependency Many of these problems in spatial analysis were previously investigated in ecological analysis, and they are relatively new to many transport researchers. AIM This paper intends to review and assess several data and methodological issues that affect spatial analysis in transport studies, before recommending strategies for addressing these issues in an integrated way, providing conclusions and suggesting future research directions. In the context of this paper, the term “spatial model” refers to a regression model that involves spatial data. SPATIAL MISMATCHING Geo-coded data usually come from different sources, and there may be inconsistencies in terms of the quality of spatial data among these different data sources thus causing a spatial mismatch problem. ECOLOGICAL FALLACY Closely related to the MAUP, the ecological fallacy states that results based on grouped aggregate data may not be applied to the individual units that form the aggregate dataset (Openshaw, 1984). Because of ecological fallacy, some researchers advocate analysing the data at an individual level. However, similar to ecological fallacy, a disaggregate level analysis may be subject to atomistic fallacy which refers to the fallacy of drawing inferences at aggregate level based on individual level data and is the counterpart of the ecological fallacy. SPATIAL DEPENDENCY Two types of spatial correlation exist: Spatial autocorrelation (“everything is related to everything else, but near things are more related than distant things”) “Within group” correlation as spatial units are often naturally clustered and it is expected that spatial units within the same group share similar characteristics Several spatial models that commonly employed to handle such correlation are: Simultaneous autoregressive (SAR) model Conditional autoregressive (CAR) model Spatial filtering model Multilevel modelling technique to account for “within group” correlation Any SAR model can be represented by a CAR model although the converse is not true. One problem which both CAR and SAR models encounter relates to how to specify a neighbouring structure. Different choices of neighbouring structure result in varying degrees of spatial associations, which requires future research for selecting an appropriate one. STRATEGIES OF ANALYSING SPATIAL DATA A good strategy is required to take account of the various issues involved in a spatial analysis. Table 3 below summarises the issues and recommends strategies. Chao Wang, Mohammed Quddus, Tim Ryley, Marcus Enoch, Lisa Davison Corresponding author’s Transport Studies Group, School of Civil and Building Engineering, Loughborough University, UK Spatial models in transport: a review and assessment of methodological issues ( ) Loughborough University Leicestershire, UK, LE11 3TU Tel: +44 (0) MODIFIABLE AREAL UNIT PROBLEM (MAUP) The modifiable areal unit problem (MAUP) refers to situations that occur when the boundary of zones (i.e. zone definition) used in a spatial analysis changes, the statistical inference and interpretation derived from the zones is also different (Openshaw, 1984). It is often the case that the definition of zones used in a spatial analysis is arbitrary and modifiable. For instance, zones are often defined based on political and administrative considerations (e.g. enumeration districts and electoral wards in the UK). The definition of the zones however may not have much geographic meaning, and therefore, the statistical inference based on the zones may also be questionable. MAUP can be illustrated using both real-world (Table 1) and simulated (Table 2) data: Aggregation 1Aggregation 2Aggregation 3 Coefz valueElasticityCoefz valueElasticityCoefz valueElasticity x Intercept Number of observations Pseudo R squared Table 2 The coefficients and elasticities of x under different grouping systems using simulated data (y~Poisson ( x)) LSOAWardDistrict Coefz valueCoefz valueCoefz value Population density (/km 2 ) Employment density (/km 2 ) Proportion of male IMD score Number of cars per person (for age 16-74) Proportion of people who are white Proportion of people in 0-15Reference case Proportion of people in Proportion of people in Proportion of people in Proportion of people in Proportion of people in Proportion of people who mainly work at home compared to all people aged & in employment Number of bus stops Number of train stations Number of tube stations Total area (km 2 ) Intercept Number of observations5, R squared Table 1 The coefficients under different aggregations using 2009 London Travel Demand Survey (LTDS) data and linear regression models Nature of the issueStrategies Spatial mismatching Often arises when spatial data were obtained from different sources, which compromise the data quality  Carefully check the data quality  Employ map-matching techniques such as weighting score method to correctly match spatial units MAUP The definition of zones and road segments is arbitrary and modifiable. Different definitions could lead to different statistical inference  Check the homogeneity of the data analysed  Sensitivity analysis testing parameter estimates under different data aggregations  Use uniform grid cells with a tested ‘optimal’ size  Utilise mathematical clustering scheme based on spatial homogeneity in demographic and transport characteristics Ecological fallacy Related to MAUP. Results based on aggregate data may not apply to individuals  As with MAUP, check if the homogeneity of the data  Use a better sampling/clustering scheme  Employ multilevel models for data that are explicitly defined in a hierarchical structure Spatial dependency Spatial data are correlated due to unobserved effects and data clustering  Check whether spatial data are correlated using various techniques such as Moran’s I test  Identify and employ an appropriate spatial model to control for the spatial autocorrelation, such as SAR, CAR and spatial filter models. For SAR and CAR models, different neighbouring structures need to be tested.  Employ multilevel modelling technique to account for data clustering Table 3 Issues and strategies in a spatial analysis CONCLUSIONS Several important data and methodological issues relating to spatial analyses employed in transport and future research directions have been discussed. Strategies for analysing spatial data has been offered Advanced spatial analysis should be employed in some transport research areas, such as estimating travel demand of demand responsive transport. REFERENCE Openshaw, S., The modifiable areal unit problem. Concepts and techniques in modern geography, (38).