The pace and direction of evolution in response to selection, drift, and mutation are governed by the genetic architecture that underlies trait variation. Consequently, much of evolutionary theory is predicated on assumptions about whether genes can be considered to act in isolation, or in the context of their genetic background. Evolutionary biologists have disagreed, sometimes heatedly, over which assumptions best describe evolution in nature. Methods for estimating genetic architectures that favor simpler (i.e., additive) models contribute to this debate. Here we address one important source of bias, model selection in line cross analysis (LCA). LCA estimates genetic parameters conditional on the best model chosen from a vast model space using relatively few line means. Current LCA approaches often favor simple models and ignore uncertainty in model choice. To address these issues we introduce Software for Analysis of Genetic Architecture (SAGA), which comprehensively assesses the potential model space, quantifies model selection uncertainty, and uses model weighted averaging to accurately estimate composite genetic effects. Using simulated data and previously published LCA studies, we demonstrate the utility of SAGA to more accurately define the components of complex genetic architectures, and show that traditional approaches have underestimated the importance of epistasis.