A type of large eddy simulation model is proposed which consists of threehierarchies, i.e. transport, magnetohydrodynamics (MHD) and turbulence. Theseclasses are categorized by the poloidal and toroidal mode number (m, n). A(0, 0) mode represents transport, low (m, n) modes represent MHD and high(m, n) modes represent turbulence. Mutual interactions between threeclasses are possible via nonlinearities such as Reynolds stress, renormalizededdy viscosity and so on. As a starting point, a two-hierarchical model of MHDand turbulence is derived and applied for the analysis of magnetic islanddynamics in the presence of a strong pressure gradient. It is found that thegrowth of the magnetic island is accelerated by the anomalous resistivity,whereas it causes the rotation of the magnetic island to decelerate.