R: 'Flip' Markov Chain Monte Carlo Redistricting Simulation...

redist_flip {redist}

R Documentation

'Flip' Markov Chain Monte Carlo Redistricting Simulation (Fifield et al. 2020)

Description

This function allows users to simulate redistricting plans using a Markov Chain Monte Carlo algorithm (Fifield, Higgins, Imai, and Tarr 2020). 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.

Usage

redist_flip(
  map,
  nsims,
  warmup = 0,
  init_plan,
  constraints = add_constr_edges_rem(redist_constr(map), 0.4),
  thin = 1,
  eprob = 0.05,
  lambda = 0,
  temper = FALSE,
  betaseq = "powerlaw",
  betaseqlength = 10,
  betaweights = NULL,
  adapt_lambda = FALSE,
  adapt_eprob = FALSE,
  exact_mh = FALSE,
  adjswaps = TRUE,
  init_name = NULL,
  verbose = TRUE,
  nthin
)

Arguments

`map`	A `redist_map` object.
`nsims`	The number of samples to draw, not including warmup.
`warmup`	The number of warmup samples to discard.
`init_plan`	A vector containing the congressional district labels of each geographic unit. The default is `NULL`. If not provided, a random initial plan will be generated using `redist_smc`. You can also request to initialize using `redist.rsg` by supplying 'rsg', though this is not recommended behavior.
`constraints`	A `redist_constr` object.
`thin`	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`	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`.
`temper`	Whether to use simulated tempering algorithm. Default is FALSE.
`betaseq`	Sequence of beta values for tempering. The default is `powerlaw` (see Fifield et. al (2020) for details).
`betaseqlength`	Length of beta sequence desired for tempering. The default is `10`.
`betaweights`	betaweights Sequence of weights for different values of beta. Allows the user to upweight certain values of beta over others. The default is `NULL` (equal weighting).
`adapt_lambda`	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`	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 (FALSE) or exact (TRUE) Metropolis-Hastings ratio calculation for accept-reject rule. Default is FALSE.
`adjswaps`	Flag to restrict swaps of beta so that only values adjacent to current constraint are proposed. The default is `TRUE`.
`init_name`	a name for the initial plan, or `FALSE` to not include the initial plan in the output. Defaults to the column name of the existing plan, or "`<init>`" if the initial plan is sampled.
`verbose`	Whether to print initialization statement. Default is `TRUE`.
`nthin`	Deprecated. Use `thin`.

Details

redist_flip allows for Gibbs constraints to be supplied via a list object passed to constraints. redist_flip uses a small compactness constraint by default, as this improves the realism of the maps greatly and also leads to large speed improvements. (One of the most time consuming aspects of the flip MCMC backend is checking for district shattering, which is slowed down even further by non-compact districts. As such, it is recommended that all flip simulations use at least a minimal compactness constraint, even if you weaken it from the default settings.) The default is a compact constraint using the edges-removed metric with a weight of 0.6. For very small maps (< 100 precincts), you will likely want to weaken (lower) this constraint, while for very large maps (> 5000 precincts), you will likely want to strengthen (increase) this constraint. Otherwise, for most maps, the default constraint should be a good starting place.

redist_flip samples from a known target distribution which can be described using the constraints. The following describes the constraints available. The general advice is to set weights in a way that gets between 20% and 40% acceptance on average, though more tuning advice is available in the vignette on using MCMC methods.Having too small of an acceptance rate indicates that the weights within constraints are too large and will impact sampling efficiency. If the Metropolis Hastings acceptance rate is too large, this may impact the target distribution, but may be fine for general exploration of possible maps.

There are currently 9 implemented constraint types, though 'compact and partisan have sub-types which are specified via a character metric within their respective list objects. The constraints are as follows:

compact - biases the algorithm towards drawing more compact districts.
weight - the coefficient to put on the Gibbs constraint
metric - which metric to use. Must be one of edges-removed (the default), polsby-popper, fryer-holden, or log-st. Using Polsby Popper is generally not recommended, as edges-removed is faster and highly correlated. log-st can be used to match the target distribution of redist_smc or redist_mergesplit.
areas - Only used with polsby-popper - A vector of precinct areas.
borderlength_mat - Only used with polsby-popper - A matrix of precinct border lengths.
ssdmat - Only used with fryer-holden - A matrix of squared distances between precinct centroids.
ssd_denom - Only used with fryer-holden - a positive integer to use as the normalizing constant for the Relative Proximity Index.
population - A Gibbs constraint to complement the hard population constraint set by pop_tol. This penalizes moves which move away from smaller population parity deviations. It is very useful when an init_plan sits outside of the desired pop_tol but there are substantive reasons to use that plan. This constraint uses the input to total_pop.
weight - the coefficient to put on the Gibbs constraint
countysplit This is a Gibbs constraint to minimize county splits. Unlike SMC's county constraint, this allows for more than ndists - 1 splits and does not require that counties are contiguous.
weight - the coefficient to put on the Gibbs constraint
hinge This uses the proportion of a group in a district and matches to the nearest target proportion, and then creates a penalty of \sqrt{max(0, nearest.target - group.pct)}.
weight - the coefficient to put on the Gibbs constraint
minorityprop - A numeric vector of minority proportions (between 0 and 1) which districts should aim to have
vra This takes two target proportions of the presence of a minority group within a district. (|target.min - group.pct||target.other - group.pct|)^{1.5})
weight - the coefficient to put on the Gibbs constraint
target_min - the target minority percentage. Often, this is set to 0.55 to encourage minority majority districts.
target_other - the target minority percentage for non majority minority districts.
minority This constraint sorts the districts by the proportion of a group in a district and compares the highest districts to the entries of minorityprop. This takes the form \sum_{i=1}^{n} \sqrt{|group.pct(i) - minorityprop(i)| } where n is the length of minorityprop input.
weight - the coefficient to put on the Gibbs constraint
minorityprop - A numeric vector of minority proportions (between 0 and 1) which districts should aim to have
similarity This is a status-quo constraint which penalizes plans which are very different from the starting place. It is useful for local exploration.
weight - the coefficient to put on the Gibbs constraint
partisan This is a constraint which minimizes partisan bias, either as measured as the difference from proportional representation or as the magnitude of the efficiency gap.
weight - the coefficient to put on the Gibbs constraint
rvote - An integer vector of votes for Republicans or other party
dvote - An integer vector of votes for Democrats or other party
metric - which metric to use. Must be one of proportional-representation or efficiency-gap.
segregation This constraint attempts to minimize the degree of dissimilarity between districts by group population.
weight - the coefficient to put on the Gibbs constraint

Value

A redist_plans object containing the simulated plans.

References

Fifield, B., Higgins, M., Imai, K., & Tarr, A. (2020). Automated redistricting simulation using Markov chain Monte Carlo. Journal of Computational and Graphical Statistics, 29(4), 715-728.

Examples

data(iowa)
iowa_map <- redist_map(iowa, ndists = 4, existing_plan = cd_2010, total_pop = pop,
    pop_tol = 0.05)
sims <- redist_flip(map = iowa_map, nsims = 100)

[Package redist version 4.2.0 Index]