Suppose we want to compare following non-hierarchical log-linear models, $H_0:f(x, heta in Theta_alpha)$ vs $H_1:g(x, heta inTheta_eta)$ for $Theta_&alpha,;Theta_eta subsetTheta$ such that $Theta_alpha otsubset Theta_eta$. The goodness of fit test using the likelihood ratio test statistic for comparing these models could not be acceptable. By using the polyhedrons plots of Choi and Hong (1995), we propose a method to decide a better model between two non-hierarchical log-linear models $f(x, heta inTheta_alaph)$ and $g(x, heta in Theta_eta)$.