In a genome-wide association study (GWAS) for a longitudinal quantitative trait, the trait is measured at multiple time points. GWAS is the examination of marker loci to identify loci associated with the progression of the quantitative trait. I use two models, a single locus model and a multi locus model, to simulate a longitudinal quantitative trait. I use the growth mixture modeling (GMM) method to assign each member of a sample into one of a small number of trajectory groups. The clinically important trajectory group is the one with fastest progression. The Bayesian posterior probability (BPP) of being in the clinically important group is used as a quantitative trait. I test for association with marker loci. I also use the modal BPP in the association test and perform a case/control association analysis. Finally, I compare these methods with the contingency table method. I evaluate the empirical type I error and empirical power using null simulations and power simulations. The principal results are that: (1) Both the BPP method and modal BPP method maintain the correct type I error rate, but the empirical null rejection rate is increasing less than the nominal rate as the nominal type I error rate increases. (2) Both the BPP and modal BPP methods have very high power to detect the disease locus in the single locus model. (3) Both the BPP and modal BPP methods have significant power to detect the disease loci in the multi locus model. The powers of detecting a specific locus are proportional to minor allele frequency (MAF) of loci. (4) Both the BPP and modal BPP methods are better than the contingency table method with regard to the empirical power and the power of the BPP is essentially equal to the power of the modal BPP.