The model developed thus far does not incorporate error correlation and/or random components in either the MDCEV vehicle type component or in the MNL make/model component. These can be accommodated by considering the vector in the baseline preference of the MDCEV component and the vector characterizing the parameters in the MNL models as being draws from multivariate normal distributions and . The unconditional probability of vehicle holdings and usage may then be written as:
vector in the baseline preference of 
vector characterizing the parameters in the MNL models as being draws from multivariate 
and 
. The unconditional probability of vehicle holdings and usage may then be written as: