Order of response surfaces for representation of a Monte Carlo epidemic model

Response hypersurfaces for two selected outcomes and for 6 model features were generated for Latin Hypercube (LH) samples of the parameter space of a discrete, micro-population, Monte Carlo model of an epidemic of an infectious disease agent. SAS stepwise, multivariate regression routines were used to generate response hypersurfaces of first, second and third order in the model features for each outcome. These are used as illustrative examples to examine the appropriateness of the order of the polynomial describing the response hypersurface. The response hypersurfaces are very dependent on the model outcomes and also on the selected ranges of the model features. Results indicate that there is little reason to prefer any particular order for the response hypersurfaces. Further, it is suggested that apparent interaction terms found when using quadratic and cubic response hypersurfaces may represent artifacts of the choice of a particular order for the response hypersurface. Nonetheless, the comparison of the 3 orders of response hypersurfaces can, under some circumstances, reveal basic characteristics of the sensitivity of the outcome to the model features.