# lmm: Learn a Mallows Model In PerMallows: Permutations and Mallows Distributions

## Description

Learn the parameter of the distribution of a sample of n permutations comming from a Mallows Model (MM).

## Usage

 ```1 2``` ```lmm(data, sigma_0_ini = identity.permutation(dim(data)), dist.name = "kendall", estimation = "approx", disk = FALSE) ```

## Arguments

 `data` the matrix with the permutations to estimate `sigma_0_ini` optional the initial guess for the consensus permutation `dist.name` optional the name of the distance used by the model. One of: kendall (default), cayley, hamming, ulam `estimation` optional select the approximated or the exact. One of: approx, exact `disk` optional can only be true if estimating a MM under the Ulam distance. Insted of generating the whole set of SYT and count of permutations per distance, it loads the info from a file in the disk

## Value

A list with the parameters of the estimated distribution: the mode and the dispersion parameter

## References

"Ekhine Irurozki, Borja Calvo, Jose A. Lozano (2016). PerMallows: An R Package for Mallows and Generalized Mallows Models. Journal of Statistical Software, 71(12), 1-30. doi:10.18637/jss.v071.i12"

## Examples

 ```1 2 3 4 5 6``` ```data <- matrix(c(1,2,3,4, 1,4,3,2, 1,2,4,3), nrow = 3, ncol = 4, byrow = TRUE) lmm(data, dist.name="kendall", estimation="approx") lmm(data, dist.name="cayley", estimation="approx") lmm(data, dist.name="cayley", estimation="exact") lmm(data, dist.name="hamming", estimation="exact") lmm(data, dist.name="ulam", estimation="approx") ```

### Example output

```Loading required package: Rcpp
\$mode
 1 2 4 3

\$theta
 1.176725

\$mode
 1 2 3 4

\$theta
 1.906813

\$mode
 1 2 3 4

\$theta
 1.906813

\$mode
 1 2 3 4

\$theta
 1.071962

\$mode
 1 2 4 3

\$theta
 2.057118
```

PerMallows documentation built on May 2, 2019, 6:14 a.m.