. 2021 Apr 13;118(16):e2015188118. doi: 10.1073/pnas.2015188118

Table 1.

Parameter estimates and likelihood scores using each of three score functions for the four datasets described in Hierarchies in Data

	Root-Degree	PageRank	SpringRank
Math PhD Exchange
(N = 6,019)
$\hat{λ}$	0.87 (0.01)	0.96 (0.01)	0.91 (0.01)
${\hat{β}}_{1}$	1.28 (0.02)	0.74 (0.01)	2.99 (0.04)
${\hat{β}}_{2}$	−0.18 (0.01)	−0.07 (0.00)	−1.12 (0.04)
$L$	−14,379	−15,001	−14,927
Parakeets (G1)
(N = 838)
$\hat{λ}$	0.97 (0.08)	0.59 (0.08)	0.67 (0.14)
${\hat{β}}_{1}$	0.84 (0.05)	1.82 (0.08)	3.03 (0.16)
${\hat{β}}_{2}$	−0.12 (0.01)	−0.50 (0.03)	−1.74 (0.12)
$L$	−1,106	−1,053	−964
Parakeets (G2)
(N = 961)
$\hat{λ}$	0.42 (0.07)	0.13 (0.03)	0.40 (0.06)
${\hat{β}}_{1}$	0.62 (0.03)	0.82 (0.04)	2.86 (0.14)
${\hat{β}}_{2}$	−0.06 (0.01)	−0.12 (0.01)	−1.46 (0.12)
$L$	−975	−1,029	−924
Newcomb Fraternity
(N = 1,428)
$\hat{λ}$	0.56 (0.13)	0.81 (0.19)	0.71 (0.14)
${\hat{β}}_{1}$	0.95 (0.05)	1.21 (0.07)	2.33 (0.14)
${\hat{β}}_{2}$	−0.08 (0.03)	−0.25 (0.05)	−0.86 (0.16)
$L$	−1,850	−1,865	−1,841

Parenthetical values are SEs for each parameter estimate. For each dataset, the largest log-likelihood $L$ is indicated in bold. All parameter estimates are statistically distinct from zero at 95% confidence. N gives the total number of interactions in the data. See SI Appendix, Fig. S5 for simulated trajectories with the inferred parameters.