Table 1 Average Pearson correlation and standard deviation for comparison approaches on 50 random train-test splits for the Maize dataset: multitrait linear mixed model with L1+trait-wise clustering penalty (mtLMM-clust), multitrait linear mixed model with L1 penalty (mtLMM-L1), multitrait linear model with L1+trait-wise clustering penalty (mtLM-clust),multitrait linear model with L1 penalty (mtLM-L1), single-trait RR-BLUP, applied to the rrBLUP R package (rrBLUP), multi-trait RR-BLUP, called Bayesian ridge regression (BRR) in the BGLR R package
Trait | mtLMM-clust | mtLMM-L1 | mtLM-clust | mtLM-L1 | rrBLUP | BRR |
|---|---|---|---|---|---|---|
\(\delta\)T3 | \(0.42 \pm 0.11\) | \(0.39 \pm 0.08\) | \(0.32 \pm 0.17\) | \(0.28 \pm 0.14\) | \(\varvec{ 0.43 \pm 0.13}\) | \(0.23 \pm 0.06\) |
\(\gamma\)T3 | \(\varvec{0.56 \pm 0.13}\) | \(0.54 \pm 0.15\) | \(0.35 \pm 0.12\) | \(0.25 \pm 0.17\) | \(0.41 \pm 0.14\) | \(0.27 \pm 0.05\) |
\(\alpha\)T3 | \(0.46 \pm 0.15\) | \(0.44 \pm 0.25\) | \(0.48 \pm 0.23\) | \(0.44 \pm 0.14\) | \(\varvec{0.51 \pm 0.13}\) | \(0.38 \pm 0.05\) |
\(\delta\)T | \(\varvec{0.48 \pm 0.17}\) | \(0.42 \pm 0.36\) | \(0.23 \pm 0.38\) | \(0.13 \pm 0.13\) | \(0.42 \pm 0.15\) | \(0.28 \pm 0.05\) |
\(\gamma\)T | \(0.29 \pm 0.12\) | \(0.26 \pm 0.23\) | \(0.25 \pm 0.26\) | \(0.23 \pm 0.13\) | \(\varvec{0.34 \pm 0.17}\) | \(0.23 \pm 0.06\) |
\(\alpha\)T | \(\varvec{0.68 \pm 0.14}\) | \(0.61 \pm 0.17\) | \(0.55 \pm 0.10\) | \(0.56 \pm 0.13\) | \(0.52 \pm 0.13\) | \(0.36 \pm 0.04\) |
PC8 | \(0.53 \pm 0.17\) | \(\varvec{0.54 \pm 0.27}\) | \(0.34 \pm 0.27\) | \(0.23 \pm 0.17\) | \(0.43 \pm 0.14\) | \(0.26 \pm 0.05\) |
Total T3 | \(\varvec{0.55 \pm 0.13}\) | \(0.52 \pm 0.19\) | \(0.26 \pm 0.17\) | \(0.25 \pm 0.15\) | \(0.42 \pm 0.14\) | \(0.32 \pm 0.05\) |
Total T | \(\varvec{0.34 \pm 0.15}\) | \(0.34 \pm 0.24\) | \(0.28 \pm 0.29\) | \(0.34 \pm 0.14\) | \(0.30 \pm 0.17\) | \(0.20 \pm 0.06\) |
Total T3Â +Â T | \(\varvec{0.40 \pm 0.11}\) | \(0.36 \pm 0.12\) | \(0.37 \pm 0.14\) | \(0.27 \pm 0.17\) | \(0.34 \pm 0.15\) | \(0.23 \pm 0.05\) |
\(\delta\)T/(\(\gamma\)TÂ +Â \(\alpha\)T) | \(\varvec{0.54 \pm 0.13}\) | \(0.53 \pm 0.19\) | \(0.27 \pm 0.23\) | \(0.14 \pm 0.10\) | \(0.44 \pm 0.15\) | \(0.32 \pm 0.05\) |
\(\delta\)T/\(\gamma\)T | \(\varvec{0.48 \pm 0.14}\) | \(0.48 \pm 0.18\) | \(0.43 \pm 0.23\) | \(0.14 \pm 0.11\) | \(0.33 \pm 0.17\) | \(0.26 \pm 0.05\) |
\(\delta\)T/\(\alpha\) T | \(\varvec{0.66 \pm 0.14}\) | \(0.62 \pm 0.09\) | \(0.52 \pm 0.12\) | \(0.46 \pm 0.12\) | \(0.59 \pm 0.09\) | \(0.35 \pm 0.05\) |
\(\gamma\)T/(\(\gamma\)TÂ +Â \(\alpha\)T) | \(\varvec{0.58 \pm 0.13}\) | \(0.55 \pm 0.14\) | \(0.57 \pm 0.16\) | \(0.48 \pm 0.12\) | \(0.55 \pm 0.11\) | \(0.33 \pm 0.06\) |
\(\delta\)T3/(\(\gamma\)T3Â +Â \(\alpha\)T3) | \(0.31 \pm 0.10\) | \(0.33 \pm 0.14\) | \(0.27 \pm 0.22\) | \(0.34 \pm 0.14\) | \(\varvec{0.38 \pm 0.17}\) | \(0.26 \pm 0.06\) |
\(\delta\)T3/\(\gamma\)T3 | \(0.29 \pm 0.13\) | \(0.28 \pm 0.23\) | \(0.21 \pm 0.29\) | \(0.34 \pm 0.14\) | \(\varvec{0.30 \pm 0.16}\) | \(0.23 \pm 0.06\) |
\(\delta\)T3/\(\alpha\)T3 | \(0.38 \pm 0.09\) | \(0.38 \pm 0.13\) | \(0.25 \pm 0.14\) | \(0.24 \pm 0.14\) | \(\varvec{0.42 \pm 0.13}\) | \(0.26 \pm 0.05\) |
\(\gamma\)T3/(\(\gamma\)T3Â +Â \(\alpha\)T3) | \(\varvec{0.45 \pm 0.13}\) | \(0.44 \pm 0.17\) | \(0.34 \pm 0.15\) | \(0.21 \pm 0.11\) | \(0.38 \pm 0.12\) | \(0.16 \pm 0.06\) |
\(\alpha\)T/\(\gamma\)T | \(0.52 \pm 0.12\) | \(0.49 \pm 0.18\) | \(0.52 \pm 0.19\) | \(0.54 \pm 0.11\) | \(\varvec{0.53 \pm 0.12}\) | \(0.35 \pm 0.05\) |
\(\alpha\)T3/\(\gamma\)T3 | \(0.41 \pm 0.12\) | \(\varvec{0.43 \pm 0.16}\) | \(0.32 \pm 0.12\) | \(0.29 \pm 0.13\) | \(0.39 \pm 0.12\) | \(0.14 \pm 0.06\) |
All | \(\varvec{0.47\pm 0.13}\) | \(0.45\pm 0.18\) | \(0.36\pm 0.20\) | \(0.31\pm 0.13\) | \(0.42\pm 0.14\) | \(0.27 \pm 0.05\) |