Properties, advantages, and drawbacks of the block logit model

This paper proposes a block logit (BL) model, which is an alternative approach to incorporating covariance between the random utilities of alternatives into a GEV random utility maximization model. The BL is similar to the nested logit (NL), in that it is a restricted form of a network GEV (NGEV) model. The NL is a NGEV model where all of the allocation parameters have been fixed with a value equal to zero or one. The BL model proposed in this paper imposes the other possible constraint on the parameters of a NGEV model, so that the restrictions are placed not on the allocation parameters, but on the logsum parameters. The BL model can be used in much the same way as the NL model, to generate choice models that exhibit inter-alternative correlations in random utilities. It can reproduce similar covariance structures to those generated by NL models, but can also create a wider variety of possible covariance matrices than the NL, because it allows overlapping blocks. The estimation of parameters for the BL model is difficult, as the likelihood function for BL models is non-continuous. This paper examines the shape of the BL log likelihood function in some detail, and compares the relative performance of estimation procedures for NL and BL models using mode choice data.