Calculate Projective Distributions, Averages, and Contrasts for a Summary Statistic

The projective distribution of a district-level summary statistic (McCartan 2024) is the distribution of values of that statistic across a set of plans for the district each precinct belongs to. The projective average of a statistic is the average value of the projective distribution in each precinct. A projective contrast is the difference between the projective average for a single plan and the projective average for an ensemble of sampled plans.

It is very important to properly account for variation in the projective distribution when looking at projective contrasts. The pfdr argument to proj_contr() will calculate q-values for each precinct that can be used to control the positive false discovery rate (pFDR) to avoid being misled by this variation. See redist.plot.contr_pfdr() for a way to automatically plot projective contrasts with this false discovery rate control.

Usage

proj_distr(plans, x, draws = NA)

proj_avg(plans, x, draws = NA)

proj_contr(plans, x, compare = NA, draws = NA, norm = FALSE, pfdr = FALSE)

Arguments

plans

A redist_plans object.

x

A district-level summary statistic calculated from the plans object. Tidy-evaluated in plans.

draws

which draws/samples to include in the projective distribution. NULL will include all draws, including reference plans. The special value NA will include all sampled (non-reference) draws. An integer, logical, or character vector indicating specific draws may also be provided.

compare

The plan to compare to the rest of the ensemble (which is controlled by draws). Defaults to the first reference plan, if any exists

norm

If TRUE, normalize the contrast by the standard deviation of the projective distribution, precinct-wise. This will make the projective contrast in terms of z-scores.

pfdr

If TRUE, calculate q-values for each precinct that can be used to control the positive false discovery rate (pFDR) at a given level by thresholding the q-values at that level. Q-values are stored as the "q" attribute on the returned vector. Requires the matrixStats package be installed.

Value

proj_distr: A matrix with a row for each precinct (row in the map object) and a column for every draw described by draws.

proj_avg: A numeric vector of length matching the number of precincts.

proj_contr: A numeric vector of length matching the number of precincts, optionally with a "q" attribute containing q-values.

References

McCartan, C. (2024). Projective Averages for Summarizing Redistricting Ensembles. arXiv preprint. Available at https://arxiv.org/pdf/2401.06381.

Examples

data(iowa)
map <- redist_map(iowa, existing_plan = cd_2010, pop_tol = 0.01)
plans <- redist_smc(map, 50, silent = TRUE)
plans$dem <- group_frac(map, dem_08, tot_08, plans)

proj_distr(plans, dem)[ ,1] # a 99-by-50 matrix, just showing first column
#>  [1] 0.4516652 0.4516652 0.5655551 0.5946792 0.4516652 0.5655551 0.5655551
#>  [8] 0.4516652 0.5655551 0.5655551 0.4516652 0.5655551 0.4516652 0.4516652
#> [15] 0.4516652 0.5946792 0.5655551 0.4516652 0.5655551 0.4516652 0.4516652
#> [22] 0.5655551 0.5655551 0.4516652 0.4516652 0.5946792 0.4516652 0.5655551
#> [29] 0.5946792 0.4516652 0.5655551 0.5655551 0.5655551 0.5655551 0.5655551
#> [36] 0.4516652 0.4516652 0.5655551 0.4516652 0.4516652 0.5655551 0.5420706
#> [43] 0.4516652 0.5946792 0.5655551 0.5655551 0.4516652 0.5420706 0.5655551
#> [50] 0.5420706 0.5946792 0.5946792 0.5655551 0.5420706 0.5655551 0.5946792
#> [57] 0.5946792 0.5946792 0.5420706 0.4516652 0.4516652 0.5420706 0.5420706
#> [64] 0.5420706 0.4516652 0.5655551 0.4516652 0.5420706 0.4516652 0.5946792
#> [71] 0.4516652 0.4516652 0.4516652 0.5655551 0.4516652 0.5655551 0.5420706
#> [78] 0.4516652 0.5420706 0.4516652 0.4516652 0.5946792 0.4516652 0.4516652
#> [85] 0.5420706 0.5655551 0.4516652 0.4516652 0.5946792 0.5946792 0.4516652
#> [92] 0.5420706 0.5946792 0.5655551 0.5655551 0.5655551 0.4516652 0.5655551
#> [99] 0.5655551
plot(map, proj_avg(plans, dem))

plot(map, proj_contr(plans, dem))

plot(map, proj_contr(plans, dem, compare="cd_2010"))