Identification conditions and an improved estimation method for a D-dimensional mixed coefficients multinomial logit model are discussed. This model is a generalisation of the Adams and Wilson (1997) random coefficients multinomial logit and it can be used to fit multdimensional forms of a wide range of Rasch measurement models. The computational demands of the numerical integration required in fitting such models have limited previous implementations to three and perhaps four-dimensional problems (Glas, 1992; Adams, Wilson and Wang, 1997). This paper illustrates a Monte Carlo integration method that permits the estimation of models with much higher dimensionality. The example in this paper fits models of six dimensions.
Volodin, Nikolai and Adams, Ray J., "The estimation of polytomous item response models with many dimensions" (2002).