Failures of the additive infinitesimal model continue to provide incentive to study other modes of gene action, in particular, epistasis. Epistasis can be modeled as a QTL by genetic background interaction. Association mapping models lend themselves to fitting such an interaction because they often include both main marker and genetic background factors. In this study, I review a model that fits the QTL by background interaction as an added random effect in the now standard mixed model framework of association analyses. The model is applied to four-generation pedigrees where the objective is to predict the genotypic values of fourth-generation individuals that have not been phenotyped. In particular, I look at how well epistatic effects are estimated under two levels of inbreeding. Interaction detection power was 8% and 65% for pedigrees of 240 randomly mated individuals when the interaction generated 6% and 20% of the phenotypic variance, respectively. Power increased to 21% and 94% for these conditions when evaluated individuals were inbred by selfing four times. The interaction variance was estimated in an unbiased way under both levels of inbreeding, but its mean squared error was reduced by 40% to 70% when estimated in inbred relative to randomly mated individuals. The performance of the epistatic model was also enhanced relative to the additive model by inbreeding. These results are promising for the application of the model to typically self-pollinating crops such as wheat and soybean.