Parameters in the GPA model can be estimated using the Expectation-Maximization (EM) algorithm [48], which is computationally efficient because we have explicit solutions for estimation of all the parameters in the M-step. Standard errors for parameter estimates can be approximated using the empirical observed information matrix [49]. Note that in the GPA model, the sample size for estimating the empirical observed information matrix corresponds to the number of SNPs and as a result, we have a very large sample size () to estimate standard errors accurately. More details of the EM algorithm and the estimation of standard errors are provided in Sections 1 and 3 in Text S1.
