`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.

```
redist.ipw(
plans,
resampleconstraint = c("pop_dev", "edges_removed", "segregation", "status_quo"),
targetbeta,
targetpop = NULL,
temper = 0
)
```

- plans
An object of class `redist_plans` from `redist_flip()`.

- 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`

.

`redist.ipw`

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

`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.

- constraint_vra
A vector containing the value of the vra 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.

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.

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.

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.

```
# \donttest{
data(iowa)
map_ia <- redist_map(iowa, existing_plan = cd_2010, pop_tol = 0.01)
cons <- redist_constr(map_ia)
cons <- add_constr_pop_dev(cons, strength = 5.4)
alg <- redist_flip(map_ia, nsims = 500, constraints = cons)
#>
#> ── redist_flip() ────────────────────────────────────────────────────────────────────────────────────────────────────────
#>
#> ── Automated Redistricting Simulation Using Markov Chain Monte Carlo ──
#> ℹ Preprocessing data.
#> ℹ Starting swMH().
#>
■ 0% | ETA: 1s
#>
■■■■■■■ 19% | ETA: 1s | MH Acceptance: 0.98
#>
■■■■■■■■■■■ 33% | ETA: 1s | MH Acceptance: 0.95
#>
■■■■■■■■■■■■■■■■■■■ 60% | ETA: 0s | MH Acceptance: 0.95
#>
■■■■■■■■■■■■■■■■■■■■■■■■■■■ 86% | ETA: 0s | MH Acceptance: 0.96
#>
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 100% | ETA: 0s | MH Acceptance: 0.96
#>
alg_ipw <- redist.ipw(plans = alg,
resampleconstraint = "pop_dev",
targetbeta = 1,
targetpop = 0.05)
# }
```