Estimates, for a given number of tips, the mean gamma statistic as a
function of c and the mean normalized Colless index (see tree_shape())
as a function of beta. Because the topology and the internode intervals
are drawn independently, each curve is estimated from its own process alone:
gamma from intervals drawn with intervals_lineage_rate() and the Colless
index from topologies drawn with rtopology_beta(), without building trees.
The expected values are monotone (gamma increases with c and the Colless
index decreases with beta), but the estimated means need not be, especially
for few tips or few draws, so each curve is made monotone by isotonic
regression (stats::isoreg()) before it is inverted with shape_params().
Arguments
- n
Number of tips, a single integer of at least 4 (with 3 tips there is a single topology, so the Colless index cannot be calibrated).
- beta
Values of
betaat which the Colless index is estimated (at least two).- c
Values of
cat which gamma is estimated (at least two).- reps
Number of topologies or interval sets per value.
Value
An object of class shape_calibration: a list with n, reps and
the data frames colless (columns beta, colless and colless_mean)
and gamma (columns c, gamma and gamma_mean), where the _mean
columns hold the mean statistic at each value and colless and gamma
their monotone fit, which shape_params() inverts.
Examples
set.seed(1)
cal <- calibrate_shape(50, reps = 50)
cal$gamma
#> c gamma gamma_mean
#> 1 -2.00 -5.8035976 -5.8035976
#> 2 -1.75 -5.5579902 -5.5579902
#> 3 -1.50 -4.6638505 -4.6638505
#> 4 -1.25 -4.4493981 -4.4493981
#> 5 -1.00 -3.7145604 -3.7145604
#> 6 -0.75 -2.8344574 -2.8344574
#> 7 -0.50 -1.9903851 -1.9903851
#> 8 -0.25 -1.0701663 -1.0701663
#> 9 0.00 -0.1931103 -0.1931103
#> 10 0.25 1.5199069 1.5199069
#> 11 0.50 2.9293050 2.9293050
#> 12 0.75 4.0540840 4.0540840
#> 13 1.00 5.7964429 5.7964429