`redist.mcmc.mpi`

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

```
redist.mcmc.mpi(
adj,
total_pop,
nsims,
ndists = NA,
init_plan = NULL,
loopscompleted = 0,
nloop = 1,
nthin = 1,
eprob = 0.05,
lambda = 0,
pop_tol = NA,
group_pop = NA,
areasvec = NA,
counties = 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,
verbose = FALSE,
cities = NULL
)
```

- adj
An adjacency matrix, list, or object of class "SpatialPolygonsDataFrame."

- total_pop
A vector containing the populations of each geographic unit.

- nsims
The number of simulations run before a save point.

- ndists
The number of congressional districts. The default is

`NULL`

.- init_plan
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`

.- loopscompleted
Number of save points reached by the algorithm. The default is

`0`

.- nloop
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`

.- nthin
The amount by which to thin the Markov Chain. The default is

`1`

.- eprob
The probability of keeping an edge connected. The default is

`0.05`

.- lambda
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`

.- pop_tol
The strength of the hard population constraint.

`pop_tol`

= 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`

.- group_pop
A vector of populations for some sub-group of interest. The default is

`NULL`

.- areasvec
A vector of precinct areas for discrete Polsby-Popper. The default is

`NULL`

.- counties
A vector of county membership assignments. The default is

`NULL`

.- borderlength_mat
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`

.- ssdmat
A matrix of squared distances between geographic units. The default is

`NULL`

.- compactness_metric
The compactness metric to use when constraining on compactness. Default is

`fryer-holden`

, the other implemented option is`polsby-popper`

.- rngseed
Allows the user to set the seed for the simulations. Default is

`NULL`

.- constraint
Which constraint to apply. Accepts any combination of

`compact`

,`vra`

,`population`

,`similarity`

, or`none`

(no constraint applied). The default is NULL.- constraintweights
The weights to apply to each constraint. Should be a vector the same length as constraint. Default is NULL.

- betaseq
Sequence of beta values for tempering. The default is

`powerlaw`

(see Fifield et. al (2015) for details).- betaseqlength
Length of beta sequence desired for tempering. The default is

`10`

.- adjswaps
Flag to restrict swaps of beta so that only values adjacent to current constraint are proposed. The default is

`TRUE`

.- freq
Frequency of between-chain swaps. Default to once every 100 iterations

- savename
Filename to save simulations. Default is

`NULL`

.- maxiterrsg
Maximum number of iterations for random seed-and-grow algorithm to generate starting values. Default is 5000.

- verbose
Whether to print initialization statement. Default is

`TRUE`

.- cities
integer vector of cities for QPS constraint.

`redist.mcmc.mpi`

returns an object of class "redist". The object
`redist`

is a list that contains the following 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_vra
A vector containing the value of the vra 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.

This function allows users to simulate redistricting plans using Markov Chain Monte Carlo methods. Several constraints corresponding 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.

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.

```
if (FALSE) {
# Cannot run on machines without Rmpi
data(fl25)
data(fl25_enum)
data(fl25_adj)
## Code to run the simulations in Figure 4 in Fifield, Higgins, Imai and
## Tarr (2015)
## Get an initial partition
init_plan <- fl25_enum$plans[, 5118]
## Run the algorithm
redist.mcmc.mpi(adj = fl25_adj, total_pop = fl25$pop,
init_plan = init_plan, nsims = 10000, savename = "test")
}
```