New algorithms for generating balanced efficient stated preference designs

Abstract

In transport we need to understand and quantify the importance people attach to the different attributes of travel and how changes in these attributes might affect what they do. The traditional approach was to use an orthogonal fractional factorial design but this places severe limitations on the number of variables and their levels as the number of choice situations generally increases exponentially with increasing number of attributes. This led to the recent design approach based on the principle of ‘efficiency’ rather than the traditional principle of ‘orthogonality’. Efficient designs are typically nonorthogonal; however they are efficient in the sense that the variances and covariances of the parameter estimates are minimized. However, existing algorithms such as modified Fedorov or RSC-algorithm for generating such designs do not guarantee that the optimized design is level balanced, especially if the starting design is unbalanced. A balanced design is desirable for least two reasons; In the presence of an unbalanced design, psychological side effects are likely to determine biased results since it is very likely that a respondent could think that there is a reason why a level appears more often than others in a presented set of choice situations; Having attribute level balance ensures that the parameters can be estimated well on the whole range of levels, instead of just having data points at only one or a few of the attribute levels, which intuitively provides a good basis for estimation.

We have proposed new algorithms for generating balanced efficient designs. Experimental analyses show that designs generated by our proposed algorithms are in additional to being balanced, statistically more efficient than the modified Fedorov algorithm.