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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.