Extended Data Fig. 1: Comparison of likelihoods.
From: Evaluating and improving heritability models using summary statistics
Plots compare likelihood ratio test (LRT) statistics (twice the improvement in log likelihood relative to the null model) computed using the likelihood from restricted maximum likelihood (REML) with those from loglSS, our new approximate likelihood, and loglOld, the approximate likelihood we reported in the original version of SumHer (see Supplementary Note for details). We only analyze the 14 UKBb GWAS, because to perform REML requires individual-level data, and we only consider the GCTA, LDAK and LDAK-Thin Models, because REML is only feasible for simple heritability models. To ensure a fair comparison, when running SumHer we restrict the reference panel to the 4.7 M GWAS SNPs. The bottom plots are zoomed versions of the top plots (obtained by excluding height, the most heritable trait). We see that the LRT statistics from loglSS are highly concordant with those from REML, indicating that the weights used when calculating loglSS perform well. We observe lower concordance between the LRT statistics from loglOld and those from REML, reflecting that loglOld was based on the assumption that test statistics were Gaussian distributed, rather than Gamma distributed.
