Results from Genome-Wide Association Studies (GWAS) have shown that the genetic basis of complex traits often include many genetic variants with small to moderate effects whose identification remains a challenging problem. In this context multi-marker analysis at the gene and pathway level can complement traditional point-wise approaches that treat the genetic markers individually. In this paper we propose a novel statistical approach for multi-marker analysis based on the Rasch model. The method summarizes the categorical genotypes of SNPs by a generalized logistic function into a genetic score that can be used for association analysis. Through different sets of simulations, the false-positive rate and power of the proposed approach are compared to a set of existing methods, and shows good performances. The application of the Rasch model on Alzheimer's Disease (AD) ADNI GWAS dataset also allows a coherent interpretation of the results. Our analysis supports the idea that APOE is a major susceptibility gene for AD. In the top genes selected by proposed method, several could be functionally linked to AD. In particular, a pathway analysis of these genes also highlights the metabolism of cholesterol, that is known to play a key role in AD pathogenesis. Interestingly, many of these top genes can be integrated in a hypothetic signalling network.