A Fisher scoring algorithm for the weighted regression method of QTL mapping

An improved weighted least square (LS) method for quantitative trait loci (QTL) mapping using the estimating equation (EE) algorithm was developed recently. The method is more efficient than both the LS and the weighted LS methods and slightly less efficient than the mixture model maximum likelihood (ML) method. The iteration process of the EE algorithm is implicit. We developed a Fisher-scoring algorithm for the weighted LS method. The iteration process is explicit and easy to program. In addition, the method automatically provides an approximate variance-covariance matrix for the estimated QTL parameters as a by-product of the iteration process. As a consequence, a W-test statistic can be used for testing the significance of QTL. To compare the Fisher scoring algorithm with the expectation maximization (EM)-based ML method, we also developed a slightly simplified method to compute the variance-covariance matrix of the estimated parameters under the EM algorithm.