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Genome wide complex trait analysis (GCTA) is extended to include environmental effects of the maternal genotype on offspring phenotype ("maternal effects", M-GCTA). The model includes parameters for the direct effects of the offspring genotype, maternal effects and the covariance between direct and maternal effects. Analysis of simulated data, conducted in OpenMx, confirmed that model parameters could be recovered by full information maximum likelihood (FIML) and evaluated the biases that arise in conventional GCTA when indirect genetic effects are ignored. Estimates derived from FIML in OpenMx showed very close agreement to those obtained by restricted maximum likelihood using the published algorithm for GCTA. The method was also applied to illustrative perinatal phenotypes from ~4,000 mother-offspring pairs from the Avon Longitudinal Study of Parents and Children. The relative merits of extended GCTA in contrast to quantitative genetic approaches based on analyzing the phenotypic covariance structure of kinships are considered.