redist.flip | R Documentation |
redist.mcmc
is used to simulate Congressional redistricting
plans using Markov Chain Monte Carlo methods.
redist.flip(
adj,
total_pop,
nsims,
ndists = NULL,
init_plan = NULL,
constraints = redist_constr(),
loopscompleted = 0,
nloop = 1,
warmup = 0,
nthin = 1,
eprob = 0.05,
lambda = 0,
pop_tol = NULL,
temper = FALSE,
betaseq = "powerlaw",
betaseqlength = 10,
betaweights = NULL,
adjswaps = TRUE,
rngseed = NULL,
maxiterrsg = 5000,
adapt_lambda = FALSE,
adapt_eprob = FALSE,
exact_mh = FALSE,
savename = NULL,
verbose = TRUE
)
adj |
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
|
init_plan |
A vector containing the congressional district labels
of each geographic unit. If not provided, random and contiguous congressional
district assignments will be generated using |
constraints |
A |
loopscompleted |
Number of save points reached by the
algorithm. The default is |
nloop |
The total number of save points for the algorithm. The
default is |
warmup |
The number of warmup samples to discard. The default is 0. |
nthin |
The amount by which to thin the Markov Chain. The
default is |
eprob |
The probability of keeping an edge connected. The
default is |
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( |
pop_tol |
The strength of the hard population
constraint. |
temper |
Whether to use simulated tempering algorithm. Default is FALSE. |
betaseq |
Sequence of beta values for tempering. The default is
|
betaseqlength |
Length of beta sequence desired for
tempering. The default is |
betaweights |
Sequence of weights for different values of
beta. Allows the user to upweight certain values of beta over
others. The default is |
adjswaps |
Flag to restrict swaps of beta so that only
values adjacent to current constraint are proposed. The default is
|
rngseed |
Allows the user to set the seed for the
simulations. Default is |
maxiterrsg |
Maximum number of iterations for random seed-and-grow algorithm to generate starting values. Default is 5000. |
adapt_lambda |
Whether to adaptively tune the lambda parameter so that the Metropolis-Hastings acceptance probability falls between 20% and 40%. Default is FALSE. |
adapt_eprob |
Whether to adaptively tune the edgecut probability parameter so that the Metropolis-Hastings acceptance probability falls between 20% and 40%. Default is FALSE. |
exact_mh |
Whether to use the approximate (0) or exact (1) Metropolis-Hastings ratio calculation for accept-reject rule. Default is FALSE. |
savename |
Filename to save simulations. Default is |
verbose |
Whether to print initialization statement.
Default is |
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 simulated tempering functionality to improve the mixing of the Markov Chain.
redist.mcmc
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):
plans |
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 |
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_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. |
constraint_partisan |
A vector containing the value of the partisan constraint for each accepted redistricting plan. |
constraint_minority |
A vector containing the value of the minority constraint for each accepted redistricting plan. |
constraint_hinge |
A vector containing the value of the hinge constraint for each accepted redistricting plan. |
constraint_qps |
A vector containing the value of the QPS 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. |
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.
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$plans[, 5118]
## Run the algorithm
alg_253 <- redist.flip(adj = fl25_adj, total_pop = fl25$pop,
init_plan = init_plan, nsims = 10000)
## You can also let it find a plan on its own!
sims <- redist.flip(adj = fl25_adj, total_pop = fl25$pop,
ndists = 3, nsims = 10000)
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