Implements a variety of functions to approximate expected ranks for partial rankings.

`approx_rank_expected(P, method = "lpom")`

- P
A partial ranking as matrix object calculated with neighborhood_inclusion or positional_dominance.

- method
String indicating which method to be used. see Details.

A vector containing approximated expected ranks.

The *method* parameter can be set to

- lpom
local partial order model

- glpom
extension of the local partial order model.

- loof1
based on a connection with relative rank probabilities.

- loof2
extension of the previous method.

Which of the above methods performs best depends on the structure and size of the partial
ranking. See `vignette("benchmarks",package="netrankr")`

for more details.

Brüggemann R., Simon, U., and Mey,S, 2005. Estimation of averaged
ranks by extended local partial order models. *MATCH Commun. Math.
Comput. Chem.*, 54:489-518.

Brüggemann, R. and Carlsen, L., 2011. An improved estimation of averaged ranks
of partial orders. *MATCH Commun. Math. Comput. Chem.*,
65(2):383-414.

De Loof, L., De Baets, B., and De Meyer, H., 2011. Approximation of Average
Ranks in Posets. *MATCH Commun. Math. Comput. Chem.*, 66:219-229.

```
P <- matrix(c(0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, rep(0, 10)), 5, 5, byrow = TRUE)
# Exact result
exact_rank_prob(P)$expected.rank
#> V1 V2 V3 V4 V5
#> 1.333333 2.111111 2.888889 4.222222 4.444444
approx_rank_expected(P, method = "lpom")
#> [1] 1.2 2.0 3.0 4.5 4.5
approx_rank_expected(P, method = "glpom")
#> [1] 1.250000 2.166667 2.833333 4.333333 4.416667
```