A least absolute deviation critical decision path analysis with transport applications

This paper introduces a method that simultaneously analyzes travel variables from stated preferences that are measured under each of several different assumptions. The method uses least absolute deviation estimators and linear programming solutions and is flexible enough to permit inclusion of constraints for ordinal data and latent variables. Travel behavior is characterized by different indicators such as travel time, waiting time, mode choice and departure time. Consideration of different response variables simultaneously as part of a stated preference model requires a reclassification of variables as either endogenous or exogenous. This concept was introduced by the author as structural conjoint analysis earlier. Each endogenous variable may be defined as nominal, ordinal or cardinal and may be either explicitly measured or latent. Current econometric and psychometric techniques cannot accommodate this variety of data. The procedure is essentially a two-stage least absolute deviation simultaneous equation regression. The estimation technique is well known as are the various hypothesis tests. In the method each relationship between endogenous and exogenous variables is formulated separately carefully incorporating assumptions about each type of data. Thus there are different formulations for endogenous variables that are nominal and latent, ordinal and explicit, ordinal and latent, cardinal and explicit and cardinal and latent. Formulations for nominal latent, ordinal explicit and cardinal explicit variables were tested with simulated data for three separate hypothetical problems. Each problem consisted of at least two different types of variables and the technique was found to be able to reproduce the simulation function coefficients in virtually all cases.