Standard approaches to evaluate the impact of single nucleotide polymorphisms (SNP) on quantitative phenotypes use linear models. However, these normal-based approaches may not optimally model phenotypes which are better represented by Gaussian mixture distributions (e.g., some metabolomics data). We develop a likelihood ratio test on the mixing proportions of two-component Gaussian mixture distributions and consider more restrictive models to increase power in light of a priori biological knowledge. Data were simulated to validate the improved power of the likelihood ratio test and the restricted likelihood ratio test over a linear model and a log transformed linear model. Then, using real data from the Framingham Heart Study, we analyzed 20,315 SNPs on chromosome 11, demonstrating that the proposed likelihood ratio test identifies SNPs well known to participate in the desaturation of certain fatty acids. Our study both validates the approach of increasing power by using the likelihood ratio test that leverages Gaussian mixture models, and creates a model with improved sensitivity and interpretability.