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Linear mixed effect models are powerful tools used to account for population structure in genome-wide association studies (GWASs) and estimate the genetic architecture of complex traits. However, fully-specified models are computationally demanding and common simplifications often lead to reduced power or biased inference. We describe Grid-LMM (https://github.com/deruncie/GridLMM), an extendable algorithm for repeatedly fitting complex linear models that account for multiple sources of heterogeneity, such as additive and non-additive genetic variance, spatial heterogeneity, and genotype-environment interactions. Grid-LMM can compute approximate (yet highly accurate) frequentist test statistics or Bayesian posterior summaries at a genome-wide scale in a fraction of the time compared to existing general-purpose methods. We apply Grid-LMM to two types of quantitative genetic analyses. The first is focused on accounting for spatial variability and non-additive genetic variance while scanning for QTL; and the second aims to identify gene expression traits affected by non-additive genetic variation. In both cases, modeling multiple sources of heterogeneity leads to new discoveries., Author summary The goal of quantitative genetics is to characterize the relationship between genetic variation and variation in quantitative traits such as height, productivity, or disease susceptibility. A statistical method known as the linear mixed effect model has been critical to the development of quantitative genetics. First applied to animal breeding, this model now forms the basis of a wide-range of modern genomic analyses including genome-wide associations, polygenic modeling, and genomic prediction. The same model is also widely used in ecology, evolutionary genetics, social sciences, and many other fields. Mixed models are frequently multi-faceted, which is necessary for accurately modeling data that is generated from complex experimental designs. However, most genomic applications use only the simplest form of linear mixed methods because the computational demands for model fitting can be too great. We develop a flexible approach for fitting linear mixed models to genome scale data that greatly reduces their computational burden and provides flexibility for users to choose the best statistical paradigm for their data analysis. We demonstrate improved accuracy for genetic association tests, increased power to discover causal genetic variants, and the ability to provide accurate summaries of model uncertainty using both simulated and real data examples.