MODELING THE ENDOGENEITY OF LANE-MEAN SPEEDS AND LANE-SPEED DEVIATIONS: A STRUCTURAL EQUATIONS APPROACH VENKATARAMAN SHANKAR Washington State Department of Transportation, Room 2B, Transportation Building, Box 47329, Olympia, WA 98504, U.S.A. and FRED MANNERING* Department of Civil and Environmental Engineering, 121 More Hall, Box 352700, University of Washington, Seattle, WA 98195, U.S.A. (Received 22 April 1997; in revised form 2 December 1997) AbstractÐThis paper attempts to macroscopically address endogeneity issues related to lane-mean trac speeds and lane-speed deviations. Methodologically, we seek to provide a better understanding of mean speeds and speed deviations across the lanes of a multilane highway. In so doing, the work may eventually be applied to better understand highway safety and the eects that lane-mean and lane speed deviations have on highway safety. We propose a structural model that relates mean speed and speed deviations by lane and is contemporaneously in¯uenced by environmental, temporal, and trac ¯ow factors. Spot speed and vehicle classi®cation data measured by lane in both the eastbound and westbound directions of Interstate 90 (I-90) in Washington State are used to develop the empirical relationships. The ®ndings show that lane-mean speeds are endogenously related with adjacent lane speeds and exogenously related with associated environmental, trac ¯ow and temporal factors, while lane-speed deviations are endogenously related not only with adjacent lane speed deviations but also, through forward causality, lane-mean speeds and exogenously related with environmental, trac ¯ow and temporal factors as well. The approach shows signi®cant promise in unravel- ing cause±eect relationships aecting macroscopic trac ¯ow continuums. # 1998 Elsevier Science Ltd. All rights reserved Keywords: structural equations, three-stage least squares, speed deviation 1. INTRODUCTION Prior speed±¯ow relationship studies have focused on single-regime or multi-regime functional relationships that were generally univariate or bivariate in nature. Linkages between speed and ¯ow were generally studied over dierent trac density ranges. Engineering intuition suggests that such approaches oer only a limited understanding of the underlying processes governing speed± ¯ow relationships. Particularly in the context of intelligent transportation systems (ITS) where the use of technological components will likely result in fundamental shifts of assumed speed±¯ow relationships. In the presence of ITS, it is important that the causality underlying the processes aecting trac speed±¯ow relationships and consequently safety be uncovered, because systemic aects associated with such technologies are potentially wide-ranging and often simultaneous. Prior theories and empirical validations have established speed±¯ow relationships that are uni- directional and regime-based (see for example, Greenshields, 1935; Edie, 1961; May and Keller, 1968). Suggestions on structural modeling (i.e. a simultaneous equations approach), with its potential to provide an improved understanding of the interrelationships among the contemporaneous in¯uences of lane-mean speeds, lane-speed deviations, environmental condi- tions, geometric elements, vehicle types, and temporal and seasonal factors, have been conceptual for the most part. Instead, signi®cant eort has been focused on the use of independent ordinary Transpn Res.-A, Vol. 32, No. 5, pp. 311±322, 1998 # 1998 Elsevier Science Ltd. All rights reserved Pergamon Printed in Great Britain PII: S0965-8564(98)00003-2 0965-8564/98 $19.00+0.00 311 *Author for correspondence. Fax: 001 206 543 1543; e-mail:¯m@u.washington.edu