Testing the sequential logit model against the nested logit model

In this paper, we show that the sequential logit (SL) model, in which a choice process is characterized as a sequence of independent multinomial logit models, is a limiting case of the nested logit (NL) model. For testing the SL model against the NL model, we propose Wald, likelihood ratio and Lagrange multiplier tests after suitably reparameterizing the NL model. It is found that when the NL model parameters are "weakly identified", the Wald test severely underrejects the true model, whereas the sizes of the LR and LM tests are not significantly affected.