In the above expression, is the overall observed utility component of vehicle type k, is an exogenous variable vector influencing the utility of vehicle make/model l of vehicle type k, is a corresponding coefficient vector to be estimated, and is an unobserved error component associated with make/model l of vehicle type k. We assume that the terms are identically distributed standard type I extreme value. Also, the error terms of the make/models belonging to the same vehicle type k may share common unobserved components (for example, a household may have a high overall preference for all SUV makes/models due to a preference for sitting high up when driving, ease in getting in/out, and projecting a social perception of being luxury-minded). This generates correlation across the error terms belonging to the same k. Let this correlation be determined by a dissimilarity parameter . Then, we can write the distribution function for as:
(5)
is the overall observed utility component 
is an exogenous variable vector influencing the utility of vehicle make/model l of vehicle type k, 
is a corresponding coefficient vector to be estimated, and 
is an unobserved error component associated with make/model l of vehicle type k. 
. Then, we can write 
as: