Efficient evaluation of the residual sum of squares for quantitative trait locus models in the case of complete marker genotype information

Motivation: A core computation of many popular quantitative trait locus, QTL, mapping methods is determining the residual sum of squares, RSS, for a regression of trait values on (pseudo-)marker genotypes. A single evaluation is easily performed using the standard method QR factorization, but together the RSS computations take considerable time and often constitute the major part of the computational effort. Results: We present an algorithm for RSS evaluation that is mathematically equivalent to evaluation via QR factorization but 10100 times faster depending on the model and data dimensions. It can be used for all standard QTL models. Our method opens the possibility for more detailed data analysis and more extensive model