Tree uncertainty benchmark

Comparison of single-tree MI vs multi-tree MI on avonet300 (300 species, mixed-type traits).

Downstream model: log(Mass) ~ log(Wing.Length) + log(Beak.Length_Culmen)

Single-tree: MCC tree, m = 50 MC-dropout draws.
Multi-tree: 10 posterior trees × 5 draws = 50 total datasets.

Pooled estimates (Rubin's rules)

Missing fraction: 20%

TermMethodEstimateSEdfFMIRIV
(Intercept) Single-tree MI -7.7734 0.4264 680.1 0.293 0.418
(Intercept) Multi-tree MI (50 trees) -7.7447 0.3106 544.9 0.311 0.451
log(Wing.Length) Single-tree MI 2.2892 0.1356 602.9 0.301 0.434
log(Wing.Length) Multi-tree MI (50 trees) 2.2720 0.1115 339.2 0.389 0.633
log(Beak.Length_Culmen) Single-tree MI 0.3313 0.1301 512.9 0.322 0.474
log(Beak.Length_Culmen) Multi-tree MI (50 trees) 0.3504 0.1103 348.2 0.389 0.639

Missing fraction: 40%

TermMethodEstimateSEdfFMIRIV
(Intercept) Single-tree MI -7.3682 0.4327 379.4 0.368 0.578
(Intercept) Multi-tree MI (50 trees) -7.2205 0.4985 136.7 0.628 1.940
log(Wing.Length) Single-tree MI 2.1998 0.1470 247.3 0.451 0.808
log(Wing.Length) Multi-tree MI (50 trees) 2.1008 0.1642 147.8 0.610 1.829
log(Beak.Length_Culmen) Single-tree MI 0.3292 0.1492 224.3 0.476 0.898
log(Beak.Length_Culmen) Multi-tree MI (50 trees) 0.4260 0.1541 162.8 0.567 1.330

Missing fraction: 60%

TermMethodEstimateSEdfFMIRIV
(Intercept) Single-tree MI -7.0156 0.4859 327.5 0.410 0.713
(Intercept) Multi-tree MI (50 trees) -6.8702 0.7352 88.0 0.760 3.476
log(Wing.Length) Single-tree MI 2.0410 0.1474 341.5 0.392 0.642
log(Wing.Length) Multi-tree MI (50 trees) 1.9386 0.2334 91.7 0.753 3.606
log(Beak.Length_Culmen) Single-tree MI 0.4547 0.1382 308.1 0.405 0.674
log(Beak.Length_Culmen) Multi-tree MI (50 trees) 0.5650 0.2022 112.0 0.687 2.463

SE ratio (multi-tree / single-tree)

Values > 1 indicate that phylogenetic uncertainty widens standard errors beyond what single-tree MI provides.

Missing %TermSE (single)SE (multi)Ratio
20% (Intercept) 0.4264 0.3106 0.73
20% log(Wing.Length) 0.1356 0.1115 0.82
20% log(Beak.Length_Culmen) 0.1301 0.1103 0.85
40% (Intercept) 0.4327 0.4985 1.15
40% log(Wing.Length) 0.1470 0.1642 1.12
40% log(Beak.Length_Culmen) 0.1492 0.1541 1.03
60% (Intercept) 0.4859 0.7352 1.51
60% log(Wing.Length) 0.1474 0.2334 1.58
60% log(Beak.Length_Culmen) 0.1382 0.2022 1.46

Wall time: 279.4 min. Generated: 2026-04-17 16:01

Reference: Nakagawa S, de Villemereuil P (2019). Systematic Biology 68(4): 632-641.