The use of correlation coefficients to evaluate the accuracy of spatial interaction models is inappropriate unless such models have been fitted using least squares techniques. In other cases the correlation involves an implicit intercept value and a regression coefficient that may significantly modify the interaction model's estimates. Researchers have not acknowledged the role of these two parameters when the correlation is used. A generalized root mean square error is proposed as an alternative indicator of accuracy that may be used with any model.There have been significant advances in the modeling of spatial interaction over the past thirty years (Black 1989). In general, spatial interaction models, which are more often called trip distribution models by planners, have their origins in an academic setting. Researchers evaluate the models developed using goodness-of-fit indices or statistics. If the models appear to be accurate they may be used in transport planning studies. In such applications the model is often calibrated to fit the study area flows. This calibration may involve the same indices or statistics used in the model's development, but more often it involves comparison of mean trip length or trip length frequency distributions for the observed and estimated flows and adjustments as merited.Advances in the development and testing of indices or statistics for measuring the accuracy or goodness-of-fit of models have not been as impressive as those in model development. Accuracy and goodness-of-fit are terms that have come to indicate the extent to which a set of model generated values replicate a set of observed data. It is apparent that these terms have something to say about error. For example, the better the goodness-of-fit or the more accurate the model, the lower the level of error. This note uses these terms interchangeably.
200Although there is no generally accepted indicator for assessing accuracy, the coefficients of correlation (r) and determination (r 2) are frequently utilized for this purpose. It will be demonstrated here that these coefficients are erroneous statistics for assessing the accuracy or goodness-of-fit of a flow model's elements, Eij , at replicating observed flows, Oij.The primary concern here is evaluating the accuracy of transport planning models during development. However, the increasing importance of geographic information systems in transportation and the anticipated availability of trip matrices from census collection efforts suggest that more accurate methods for assessing goodness-of-fit may be of concern for both the development and application fields in the near future.The note that follows briefly summarizes the application of correlation methods in flow modeling and notes criticisms that have been made regarding the use of these coefficients with flow matrices. An explanation and demonstration of why these coefficients do not usually measure the goodness-of-fit in the spatial interaction case follows. The note concludes with a recommended index of accuracy that...