nslphom: Implements nslphom algorithm

In lphom: Ecological Inference by Linear Programming under Homogeneity

Implements nslphom algorithm

Description

Estimates RxC vote transfer matrices (ecological contingency tables) with nslphom

Usage

nslphom(
  votes_election1,
  votes_election2,
  new_and_exit_voters = c("raw", "regular", "simultaneous", "full", "gold"),
  structural_zeros = NULL,
  iter.max = 10,
  min.first = FALSE,
  uniform = TRUE,
  distance.local = c("abs", "max", "none"),
  integers = FALSE,
  solver = "lp_solve",
  integers.solver = "symphony",
  burnin = 0,
  verbose = FALSE,
  tol = 10^-5,
  ...
)

Arguments

votes_election1	data.frame (or matrix) of order IxJ (likely of final order Ix(J-1) in regular and raw scenarios when net entries are estimated by the function) with the votes gained by the J political options competing on election 1 (or origin) in the I territorial units considered. In general, the row marginals of the I tables.
votes_election2	data.frame (or matrix) of order IxK (likely of final order Ix(K-1) in regular and raw scenarios when net exits are estimated by the function) with the votes gained by the K political options competing on election 2 (or destination) in the I territorial units considered. In general, the column marginals of the I tables.
new_and_exit_voters	A character string indicating the level of information available regarding new entries and exits of the election censuses between the two elections. This argument captures the different options discussed on Section 3 of Romero et al. (2020). This argument admits five values: raw, regular, simultaneous, full and gold. Default, raw. The argument simultaneous should be used in a typical ecological inference problem.
structural_zeros	Default, NULL. A list of vectors of length two, indicating the election options for which no transfer of votes are allowed between election 1 and election 2. For instance, when new_and_exit_voters is set to "regular", lphom implicitly states structural_zeros = list(c(J, K)) in case exits and/or entries are computed because the sum by rows of votes_election1 and votes_election2 does not coincide.
iter.max	Maximum number of iterations to be performed. The process ends when either the number of iterations reaches iter.max or when the maximum variation between two consecutive estimates of the probability transfer matrix is less than tol. By default, 10.
min.first	A TRUE/FALSE value. If FALSE, the matrix associated with the minimum HETe after performing iter.max iterations is taken as solution. If TRUE, the associated matrix to the instant in which the first decrease of HETe occurs is taken as solution. The process stops at that moment. In this last scenario (when min.first = TRUE), burnin = 0 is forced and iter.max is at least 100. Default, FALSE.
uniform	A TRUE/FALSE value that indicates if census exits affects all the electoral options in a (relatively) similar fashion in each voting unit: equation (13) of Pavia and Romero (2021). Default, TRUE.
distance.local	A string argument that indicates whether the second step of the lphom_local algorithm should be performed to solve potential indeterminacies of local solutions. Default, "abs". If distance.local = "abs" lphom_local selects in its second step the matrix closer to the temporary global solution under L_1 norm, among the first step compatible matrices. If distance.local = "max" lphom_local selects in its second step the matrix closer to the temporary global solution under L_Inf norm, among the first step compatible matrices. If distance.local = "none", the second step of lphom_local is not performed.
integers	A TRUE/FALSE value that indicates whether the problem is solved in integer values in each iteration, including iteration zero (lphom) and intermediate and final local solutions. If TRUE, the initial LP matrices are approximated in each iteration to the closest integer solution solving the corresponding Integer Linear Program. Default, FALSE.
solver	A character string indicating the linear programming solver to be used, only lp_solve and symphony are allowed. By default, lp_solve. The package Rsymphony needs to be installed for the option symphony to be used.
integers.solver	A character string indicating the linear programming solver to be used to approximate to the closest integer solution, only symphony and lp_solve are allowed. By default, symphony. The package Rsymphony needs to be installed for the option symphony to be used. Only used when integers = TRUE.
burnin	Number of initial solutions to be discarded before determining the final solution. By default, 0.
verbose	A TRUE/FALSE value that indicates if the main outputs of the function should be printed on the screen. Default, FALSE.
tol	Maximum deviation allowed between two consecutive iterations. The process ends when the maximum variation between two proportions for the estimation of the transfer matrix between two consecutive iterations is less than tol or the maximum number of iterations, iter.max, has been reached. By default, 0.00001.
...	Other arguments to be passed to the function. Not currently used.

Details

Description of the new_and_exit_voters argument in more detail.

• raw: The default value. This argument accounts for the most plausible scenario when estimating vote transfer matrices: A scenario with two elections elapsed at least some months where only the raw election data recorded in the I territorial units, in which the area under study is divided, are available. In this scenario, net exits (basically deaths) and net entries (basically new young voters) are estimated according to equation (7) of Romero et al. (2020). Constraints defined by equations (8) and (9) of Romero et al. (2020) and (13) of Pavia and Romero (2021a) are imposed. In this scenario, when net exits and/or net entries are negligible (such as between the first- and second-round of French Presidential elections), they are omitted in the outputs.

• regular: For estimating vote transfer matrices, this value accounts for a scenario with two elections elapsed at least some months where (i) the column J of votes_election1 corresponds to new young electors who have the right to vote for the first time, (ii) net exits (basically a consequence of mortality), and maybe other additional net entries, are computed according equation (7) of Romero et al. (2020), and (iii), when uniform = TRUE, within each unit it is assummed that net exits affect equally all the first J-1 options of election 1, i.e., equation (13) of Pavia and Romero (2021a) is applied. Constraints (8) and (9) of Romero et al. (2020) are imposed to start the process.

• simultaneous: This is the value to be used in a classical ecological inference problems, such as for racial voting, and in a scenario with two simultaneous elections. In this scenario, the sum by rows of votes_election1 and votes_election2 must coincide. Constraints defined by equations (8) and (9) of Romero et al. (2020) and (13) of Pavia and Romero (2021a) are not included in the model.

• full: This value accounts for a scenario with two elections elapsed at least some months, where: (i) the column J-1 of votes_election1 totals new young electors that have the right to vote for the first time; (ii) the column J of votes_election1 measures new immigrants that have the right to vote; and (iii) the column K of votes_election2 corresponds to total exits of the census lists (due to death or emigration). In this scenario, the sum by rows of votes_election1 and votes_election2 must agree and constraints (8) and (9) of Romero et al. (2020) are imposed.

• gold: This value accounts for a scenario similar to full, where total exits are separated out between exits due to emigration (column K-1 of votes_election2) and death (column K of votes_election2). In this scenario, the sum by rows of votes_election1 and votes_election2 must agree. The same restrictions as in the above scenario apply but for both columns K-1 and K of the vote transition probability matrix

Value

A list with the following components

VTM	A matrix of order JxK with the estimated percentages of row-standardized vote transitions from election 1 to election 2.
VTM.votes	A matrix of order JxK with the estimated vote transitions from election 1 to election 2.
OTM	A matrix of order KxJ with the estimated percentages of the origin of the votes obtained for the different options of election 2.
HETe	The estimated heterogeneity index as defined in equation (15) of Pavia and Romero (2021).
VTM.complete	A matrix of order J'xK' with the estimated proportions of row-standardized vote transitions from election 1 to election 2, including in regular and raw scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units.
VTM.complete.votes	A matrix of order J'xK' with the estimated vote transitions from election 1 to election 2, including in regular and raw scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units.
VTM.sequence	Array of order J'xK'x(iter+1) (where iter is the efective number of iterations performed) of the estimated matrices corresponding to each iteration.
HETe.sequence	Numeric vector of length iter+1 with the HETe coefficients corresponding to the matrices in VTM.sequence.
VTM.prop.units	An array of order J'xK'xI with the estimated proportions of vote transitions from election 1 to election 2 attained for each unit in the selected iteration.
VTM.votes.units	An array of order J'xK'xI with the estimated matrix of vote transitions from election 1 to election 2 attained for for each unit in the selected iteration.
zeros	A list of vectors of length two, indicating the election options for which no transfer of votes are allowed between election 1 and election 2.
iter	The real final number of iterations performed before ending the process.
iter.min	Number of the iteration associated to the selected VTM solution.
inputs	A list containing all the objects with the values used as arguments by the function.
origin	A matrix with the final data used as votes of the origin election after taking into account the level of information available regarding to new entries and exits of the election censuses between the two elections.
destination	A matrix with the final data used as votes of the origin election after taking into account the level of information available regarding to new entries and exits of the election censuses between the two elections.
EHet	A matrix of order IxK measuring in each spatial unit a distance to the homogeneity hypothesis, that is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results with the solution in each territorial unit for each option of election 2.
solution_init	A list with the main outputs produced by lphom().

• VTM_init: A matrix of order JxK with the estimated percentages of vote transitions from election 1 to election 2 initially obtained by lphom().

• VTM.votes_init: A matrix of order JxK with the estimated vote transitions from election 1 to election 2 initially obtained by lphom().

• OTM_init: A matrix of order KxJ with the estimated percentages of the origin of the votes obtained for the different options of election 2 initially obtained by lphom().

• HETe_init: The estimated heterogeneity index defined in equation (10) of Romero et al. (2020).

• EHet_init: A matrix of order IxK measuring in each spatial unit the distance to the homogeneity hypothesis, that is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results, using the lphom() solution, in each territorial unit for each option of election 2.

• VTM.complete_init: A matrix of order J'xK' with the estimated proportions of vote transitions from election 1 to election 2 initially obtained by lphom(), including in regular and raw scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units.

• VTM.complete.votes_init: A matrix of order J'xK' with the estimated vote transitions from election 1 to election 2 initially obtained by lphom(), including in regular and raw scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units.

Author(s)

Jose M. Pavia, [e-mail]

Rafael Romero [e-mail]

References

Pavia, JM, and Romero, R (2021). Improving estimates accuracy of voter transitions. Two new algorithms for ecological inference based on linear programming. doi: 10.31124/advance.14716638.v1.

See Also

lphom tslphom lclphom

Other linear programing ecological inference functions: lclphom(), lp_apriori(), lphom_dual(), lphom_joint(), lphom(), nslphom_dual(), nslphom_joint(), tslphom_dual(), tslphom_joint(), tslphom()

Examples

mt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw")
mt.ns$VTM
mt.ns$HETe
mt.ns$solution_init$HETe_init

lphom documentation built on March 21, 2022, 9:09 a.m.