A more complete theoretical model of testing Lorentz violation by the comparison of atomic clocks is developed in the Robertson-Mansouri-Sexl kinematic framework. As this frame postulates the deviation of the coordinate transformation from the Lorentz transformation, from the viewpoint of the transformation violations on time and space, the LI violating effect in the atomic clock comparison can be explained as two parts: time-delay effect $alpha frac {v^2}{c^2}$ and structure effect $-frac {beta+2delta}{3} frac {v^2}{c^2}$. Standard model extension is a widely used dynamic frame to characterize the Lorentz violation, in which a space-orientation dependence violating background field is regarded as the essential reason for the Lorentz violation effect. Compared with the RMS frame which only indicates the kinematic properties with the coordinate transformation, this dynamic frame provides a more complete and clear description for the Lorentz violation effect.
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