The transdichotomous model is first proposed by Michael Fredman and Dan Willard . They wrote the motivation as
... On the other hand, with the inclusion of division and Boolean operations, they obtain a linear time algorithm. This linear time algorithm, however, suffers from an abuse of the unit cost assumption. In particular, the algorithm generates operands during the course of its computation whose individual lengths are $N^2$ times the length of the largest of the $N$ numbers to be sorted.
What seems to be needed is a computational model that avoids the potential abuses of the unit cost random access machine, but allows for unit cost operations among operands of “reasonable” size, i.e., operands of size commensurate with the sizes of the numbers to be sorted. Accordingly, we consider a reformulation of the sorting problem wherein our machine has a $b$-bit word size, and each of the $N$ input numbers is assumed to be a non-negative integer less than $2^b$ (and hence each tits into one word). Moreover, it is desirable that a sorting algorithm use only $O(N)$ words of memory.
That is to say, in contrast with RAM model, the transdichotomous model is less powerful because it does not allow unit cost operations on arbitrary large number. For example, in the sorting problem where the largest number is $m$, the transdichotomous model only allows unit cost operations on numbers no more than $m$.
 Fredman, M. L., & Willard, D. E. (1993). Surpassing the information theoretic bound with fusion trees. Journal of computer and system sciences, 47(3), 424-436.