Large amplitude oscillatory shear (LAOS) is a rheological test method for the characterization of viscoelastic nonlinear materials. The correlation between the characteristic parameters obtained from measurements and theoretical models is a complex issue, one that requires the extraction of significant data from the measurements in order to identify corresponding models. Alternatively, a process of deductive logic may be useful in predicting typical behaviors of the materials through modeling which can then be verified by the analysis of measured data. The aim of this work is to highlight the potential of this logical deductive approach regarding LAOS testing. For this purpose, a LAOS is analytically simulated for an isotropic viscoelastic material of a differential type, with cubic nonlinearities and a correspondence of the Fourier coefficients. This is how nonlinearity parameters of the model are obtained. It can be seen that each nonlinearity parameter depends on Fourier coefficients through one of the new measures introduced by Ewoldt et al. [ J. Rheol. 52, 1427-1458 (2008)] in 2008. Analysis of the function which represents shear stress suggests new interpretations of the experimental results and highlights how characteristics of the model can be compared with typical behaviors of the Lissajous-Bowditch plots. (C) 2016 The Society of Rheology.