redist (version 1.0)

redist.ipw: Inverse probability reweighting for MCMC Redistricting

Description

redist.ipw properly weights and resamples simulated redistricting plans so that the set of simulated plans resemble a random sample from the underlying distribution. redist.ipw is used to correct the sample when population parity, geographic compactness, or other constraints are implemented.

Usage

redist.ipw(algout,
           resampleconstraint = c("pop", "compact", "segregation", "similar"),
           targetbeta,
           targetpop = NULL,
           temper = 0)

Arguments

algout

An object of class "redist".

resampleconstraint

The constraint implemented in the simulations: one of "pop", "compact", "segregation", or "similar".

targetbeta

The target value of the constraint.

targetpop

The desired level of population parity. targetpop = 0.01 means that the desired distance from population parity is 1%. The default is NULL.

temper

A flag for whether simulated tempering was used to improve the mixing of the Markov Chain. The default is 1.

Value

• redist.ipw 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 resample redistricting plans using inverse probability weighting techniques described in Rubin (1987). This techniques reweights and resamples redistricting plans so that the resulting sample is representative of a random sample from the uniform distribution.

References

Fifield, Benjamin, Michael Higgins, Kosuke Imai and Alexander Tarr. (2015) "A New Automated Redistricting Simulator Using Markov Chain Monte Carlo." Working Paper. Available at http://imai.princeton.edu/research/files/redist.pdf.

Rubin, Donald. (1987) "Comment: A Noniterative Sampling/Importance Resampling Alternative to the Data Augmentation Algorithm for Creating a Few Imputations when Fractions of Missing Information are Modest: the SIR Algorithm." Journal of the American Statistical Association.

See Also

redist.mcmc to simulate redistricting plans using Markov Chain Monte Carlo techniques.

Examples

data(algdat.p20)

## Code to run the simulations in Figure 4 of Fifield, Higgins, 
## Imai and Tarr (2015)

## Get an initial partition
set.seed(1)
initcds <- algdat.p20$cdmat[,sample(1:ncol(algdat.p20$cdmat), 1)]

## Vector of beta weights
betaweights <- rep(NA, 10); for(i in 1:10){betaweights[i] <- 4^i}

## Run simulations - tempering population constraint
alg_253_20_st <- redist.mcmc(adjobj = algdat.p20$adjlist,
                             popvec = algdat.p20$precinct.data$pop,
                             initcds = initcds,
                             nsims = 10000,
                             betapop = -5.4,
                             betaweights = betaweights,
                             temperbetapop = 1)

## Resample using inverse probability weighting. 
## Target distance from parity is 20alg_253_20_st <- redist.ipw(alg_253_20_st,
                            resampleconstraint = "pop",
                            targetbeta = -5.4,
                            targetpop = .2,
                            temper = 1)