Table 1.

Empirical Bayes matrix factorization model selection

EBNM Appr.	No. Fact.	LL	PVE	R ${}_{\text{adj}}^2$	$r_{(Y_{\mathit{tst}},{\widehat{Y}}_{\mathit{tst}})}$	RMSE
Ad. Shr.	102	−581716.3	59.41	0.438	0.322	1.451
Point Nor.	106	−583809.9	59.36	0.429	0.514	0.978
Laplace	100	−584317.2	58.82	0.434	0.520	0.970

Each model was fit using degressed BLUPs for 1668 metabolites. Ad. Shr.: adaptive shrinkage family of densities described by Stephens (2016). Cross-validation (CV) was based on a threefold orthogonal CV described by Wang and Stephens (2018) and Owen and Wang (2016) with 10 independent resamplings. Point Nor.: point-normal family of densities which are a normal distribution with a point mass at zero; LL indicates log-likelihood; PVE: percent variance explained; R${}_{\text{adj}}^2$: adjusted R²; $r_{(Y_{\mathit{tst}},{\widehat{Y}}_{\mathit{tst}})}$ is the Pearson’s correlation between predicted and observed values for observations in the testing set; RMSE: root mean square error.