MRP {parsec}

Mutial ranking probability matrix

Description

Function to evaluate Mutial Ranking Probability (MRP) matrix based on netrankr package.

Usage

MRP(Z, method = c("exact", "mcmc", "approx"), error = 10^(-3), nit = NULL)
## S3 method for class 'incidence'
MRP(Z, method = c("exact", "mcmc", "approx"), error = 10^(-3), nit = NULL)

Arguments

Z

an incidence matrix, an object of class incidence.

method

a string to choose the method applied to evaluate the MRP matrix. The default value is "exact". See section 'Details' below.

error

considered only if mcmc method is selected. The "distance" from uniformity in the sampling distribution of linear extensions.

nit

considered only if mcmc method is selected. Number of ITerations in the Bubley-Dyer algorithm, by default evaluated indicated in Bubley and Dyer (1999) depending on the value of error.

Details

Package netrankr provides three functions to evaluate MRP matrix. Note that MRP matrix definition in netrankr is a little different from the one used in Fattore and Arcagni (2018), therefore this function unifies the results to the second definition.

Parameter method allows the selection of which function of package netrankr to use: "exact" runs the function exact_rank_prob that provides the exact results, "mcmc" the function mcmc_rank_prob that provide the estimated results through the Bubley Dyer algorithm and "approx" runs the function approx_rank_relative that provide the Bruggemann and Carlsen (2011) approximated results. For small posets it is possible to evaluate the exact MRP matrix, for larger posets it is necessary to use the appoximated results.

Value

An object of class matrix representing the MRP matrix. Dimensions names are equal to incidence matrix ones.

References

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

Bubley R., Dyer M. (1999), Faster random generation of linear extensions, Discrete Math., 201, 81-88.

Fattore M., Arcagni A. (2018). Using mutual ranking probabilities for dimensionality reduction and ranking extraction in multidimensional systems of ordinal variables. Advances in Statistical Modelling of Ordinal Data, 117.

See Also

exact_rank_prob, mcmc_rank_prob, approx_rank_relative

Examples

L <- getlambda(A < B, C < B, B < D)
MRP(L)