Table 3. Comparison of various log detransformation bias correction factors.
| Correction factor | Field et al. (2013) all birds | Field et al. (2013) subset | Present data full dataset | Present data heavy and flightless | Present data flightless |
|---|---|---|---|---|---|
| No correction factor | 32.78883 | 21.05430 | 23.31936 | 18.25612 | 12.48232 |
| REML | 31.89988 | 21.04287 | 23.08221 | 18.15626 | 12.27288 |
| ML | 31.90159 | 21.05430 | 23.0887 | 18.15897 | 12.29152 |
| Finney’s | 31.90025 | 21.04537 | 23.08363 | 18.15685 | 12.27639 |
| Ratio | 32.15498 | 22.15854 | 22.92239 | 18.87176 | 11.32922 |
| UMVU | Inf1 | 21.20675 | 23.21062 | 18.21409 | 12.40849 |
| EV | 31.90125 | 21.06107 | 23.09212 | 18.16617 | 12.31257 |
| MM | 31.90565 | 21.09565 | 23.11133 | 18.17999 | 12.3658 |
| MB | 31.90124 | 21.06022 | 23.09162 | 18.16552 | 12.30875 |
| Smear | 31.12007 | 20.75643 | 22.93455 | 18.15139 | 12.12568 |
Notes:
The mean percent prediction error of the naive estimate (no correction factor) and nine different correction factors using all birds and a subset of the data of Field et al. (2013), as well as various combinations of the data presented herein. Abbreviations for the correction factors follow Clifford et al. (2013). Worst and best performing correction factors are indicated in red and green respectively.
1
The calculation of this correction factor returns “Inf” (=infinite),when the sample size exceeds a certain threshold, using the formula for the UMVU correction provided by Clifford et al. (2013), which is based on the hyperg_0F1 function in the gsl package in R.