  By a further investigation on the structure of the coefficient matrix of the
globally hyperbolic regularized moment equations for Boltzmann equation in [Z.
Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571], we propose a
uniform framework to carry out model reduction to general kinetic equations, to
achieve certain moment system. With this framework, the underlying reason why
the globally hyperbolic regularization in [Z. Cai, Y. Fan and R. Li, Comm.
Math. Sci., 11 (2013), pp. 547-571] works is revealed. The even fascinating
point is, with only routine calculation, existing models are represented and
brand new models are discovered. Even if the study is restricted in the scope
of the classical Grad's 13-moment system, new model with global hyperbolicity
can be deduced.
