redist.mcmc.mpi is used to simulate Congressional redistricting plans using Markov Chain Monte Carlo methods.

redist.mcmc.mpi(adjobj, popvec, nsims, ndists = NA, initcds = NULL,
loopscompleted = 0, nloop = 1, nthin = 1,
eprob = 0.05,
lambda = 0, popcons = NA, grouppopvec = NA,
areasvec = NA, countymembership = NA,
borderlength_mat = NA, ssdmat = NA,
compactness_metric = "fryer-holden", rngseed = NA,
constraint = NA, constraintweights = NA,
betaseq = "powerlaw",
betaseqlength = 10, adjswaps = TRUE,
freq = 100, savename = NA, maxiterrsg = 5000,
contiguitymap = "rooks", verbose = FALSE)

## Arguments

adjobj An adjacency matrix, list, or object of class "SpatialPolygonsDataFrame." A vector containing the populations of each geographic unit. The number of simulations run before a save point. The number of congressional districts. The default is NULL. A vector containing the congressional district labels of each geographic unit. The default is NULL. If not provided, random and contiguous congressional district assignments will be generated using redist.rsg. Number of save points reached by the algorithm. The default is 0. The total number of save points for the algorithm. The default is 1. Note that the total number of simulations run will be nsims * nloop. The amount by which to thin the Markov Chain. The default is 1. The probability of keeping an edge connected. The default is 0.05. The parameter determining the number of swaps to attempt each iteration of the algorithm. The number of swaps each iteration is equal to Pois(lambda) + 1. The default is 0. The strength of the hard population constraint. popcons = 0.05 means that any proposed swap that brings a district more than 5% away from population parity will be rejected. The default is NULL. A vector of populations for some sub-group of interest. The default is NULL. A vector of precinct areas for discrete Polsby-Popper. The default is NULL. A vector of county membership assignments. The default is NULL. A matrix of border length distances, where the first two columns are the indices of precincts sharing a border and the third column is its distance. Default is NULL. A matrix of squared distances between geographic units. The default is NULL. The compactness metric to use when constraining on compactness. Default is fryer-holden, the other implemented option is polsby-popper. Allows the user to set the seed for the simulations. Default is NULL. Which constraint to apply. Accepts any combination of compact, segregation, population, similarity, or none (no constraint applied). The default is NULL. The weights to apply to each constraint. Should be a vector the same length as constraint. Default is NULL. Sequence of beta values for tempering. The default is powerlaw (see Fifield et. al (2015) for details). Length of beta sequence desired for tempering. The default is 10. Flag to restrict swaps of beta so that only values adjacent to current constraint are proposed. The default is TRUE. Frequency of between-chain swaps. Default to once every 100 iterations Filename to save simulations. Default is NULL. Maximum number of iterations for random seed-and-grow algorithm to generate starting values. Default is 5000. Use queens or rooks distance criteria for generating an adjacency list from a "SpatialPolygonsDataFrame" data type. Default is "rooks". Whether to print initialization statement. Default is TRUE.

## Value

redist.mcmc.mpi returns an object of class "redist". The object redist is a list that contains the folowing components (the inclusion of some components is dependent on whether tempering techniques are used):

partitions

Matrix of congressional district assignments generated by the algorithm. Each row corresponds to a geographic unit, and each column corresponds to a simulation.

distance_parity

Vector containing the maximum distance from parity for a particular simulated redistricting plan.

mhdecisions

A vector specifying whether a proposed redistricting plan was accepted (1) or rejected (0) in a given iteration.

mhprob

A vector containing the Metropolis-Hastings acceptance probability for each iteration of the algorithm.

pparam

A vector containing the draw of the p parameter for each simulation, which dictates the number of swaps attempted.

constraint_pop

A vector containing the value of the population constraint for each accepted redistricting plan.

constraint_compact

A vector containing the value of the compactness constraint for each accepted redistricting plan.

constraint_segregation

A vector containing the value of the segregation constraint for each accepted redistricting plan.

constraint_similar

A vector containing the value of the similarity constraint for each accepted redistricting plan.

beta_sequence

A vector containing the value of beta for each iteration of the algorithm. Returned when tempering is being used.

mhdecisions_beta

A vector specifying whether a proposed beta value was accepted (1) or rejected (0) in a given iteration of the algorithm. Returned when tempering is being used.

mhprob_beta

A vector containing the Metropolis-Hastings acceptance probability for each iteration of the algorithm. Returned when tempering is being used.

## Details

This function allows users to simulate redistricting plans using Markov Chain Monte Carlo methods. Several constraints correspoding to substantive requirements in the redistricting process are implemented, including population parity and geographic compactness. In addition, the function includes multiple-swap and parallel tempering functionality in MPI to improve the mixing of the Markov Chain.

## References

Fifield, Benjamin, Michael Higgins, Kosuke Imai and Alexander Tarr. (2016) "A New Automated Redistricting Simulator Using Markov Chain Monte Carlo." Working Paper. Available at http://imai.princeton.edu/research/files/redist.pdf.

## Examples

if (FALSE) {
data(algdat.pfull)
## Code to run the simulations in Figure 4 in Fifield, Higgins,
## Imai and Tarr (2015)

## Get an initial partition
set.seed(1)
initcds <- algdat.pfull$cdmat[,sample(1:ncol(algdat.pfull$cdmat), 1)]

## Run the algorithm
redist.mcmc.mpi(adjobj = algdat.pfull$adjlist, popvec = algdat.pfull$precinct.data\$pop,
initcds = initcds,
nsims = 10000, savename = "test")
}