rslphom {lphom}

Implements rslphom algorithm

Description

Estimates RxC (JxK) vote transfer matrices (ecological contingency tables) with rslphom

Usage

rslphom(
  votes_election1,
  votes_election2,
  emphasis = 0.995,
  new_and_exit_voters = c("raw", "regular", "ordinary", "enriched", "adjust1", "adjust2",
    "simultaneous", "semifull", "full", "fullreverse", "gold"),
  apriori = NULL,
  lambda = 0.5,
  uniform = TRUE,
  structural_zeros = NULL,
  integers = FALSE,
  distance.local = c("abs", "max", "none"),
  save.local.by.emphasis = FALSE,
  verbose = TRUE,
  solver = "lp_solve",
  integers.solver = "symphony",
  ...
)

Arguments

votes_election1

data.frame (or matrix) of order IxJ1 with the votes gained by (or the counts corresponding to) the J1 political options competing (available) on election 1 (or origin) in the I units considered. In general, the row marginals of the I tables corresponding to the units.

votes_election2

data.frame (or matrix) of order IxK2 with the votes gained by (or the counts corresponding to) the K2 political options competing (available) on election 2 (or destination) in the I (territorial) units considered. In general, the column marginals of the I tables corresponding to the units.

emphasis

A numerical vector of values between 0 and 1 informing of the weights/emphasis to be used to promote each unit when estimating its transfer matrix. Default, 0.995. When the length of emphasis is one, only a weight (a level of emphasis) is analyzed. When the length of emphasis is higher than one, as many as different weights/emphasis as the length of emphasis are tried in the estimation of the transfer matrix of each unit. In each unit, the local solution selected corresponds to the transfer matrix with lower expected error.

new_and_exit_voters

A character string indicating the level of information available in votes_election1 and votes_election2 regarding new entries and exits of the election censuses between the two elections. This argument allows, in addition to the options discussed in Pavia (2023), three more options. This argument admits eleven different values: raw, regular, ordinary, enriched, adjust1, adjust2, simultaneous, semifull, full, fullreverse and gold. Default, raw.

apriori

data.frame (or matrix) of order J0xK0 with an initial estimate of the (row-standarized) global voter transition proportions/fractions, pjk0, between the first J0 (election) options of election 1 and the first K0 (election) options of election 2. This matrix can contain some missing values. When no a priori information is available apriori is a null object. Default, NULL.

lambda

A number between 0 and 1 informing the relative weight the user assigns to the apriori information. Setting lambda = 0 is equivalent to not having a priori information (i.e., apriori = NULL). Default, 0.5.

uniform

A TRUE/FALSE value that informs whether census exits impact all the electoral options in a (relatively) similar fashion in all iterations, including iteration 0 and when deriving units tables. If uniform = TRUE typically at least one of the equations among equations (6) to (11) of Pavia (2023) is included in the underlying model. This parameter has no effect in simultaneous scenarios. It also has not impact in raw and regular scenarios when no net exits are estimated by the function from the provided information. Default, TRUE.

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 "semifull", lphom implicitly states structural_zeros = list(c(J1, K2)).

integers

A TRUE/FALSE value that indicates whether the problem is solved in integer values in all the steps, including lphom intermediate solutions and unit solutions. If integers = TRUE, the LP matrices are approximated to the closest integer solution solving the corresponding Integer Linear Program. Default, FALSE.

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.

save.local.by.emphasis

A TRUE/FALSE value that indicates if the estimated matrices obtained in each unit for each value of emphasis should be saved. Default, FALSE.

verbose

A TRUE/FALSE value that indicates if a summary of the results of the computations performed to estimate net entries and exits should be printed on the screen. Default, TRUE.

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 for approximating the LP solution 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.

...

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 electoral space under study is divided, are available. In this scenario, net exits and net entries are estimated according to equation (7) of Romero et al. (2020). When both net entries and exits are no null, constraint (15) of Pavia (2023) applies. If there are net exits and uniform = TRUE either constraints (6) or (8) and (15) of Pavia (2023) are imposed. In this scenario, J could be equal to J1 or J1 + 1 and K equal to K2 or K2 + 1.

• regular: This value accounts for a scenario with two elections elapsed at least some months where (i) the column J1 of votes_election1 corresponds to new young electors who have the right to vote for the first time, (ii) net exits and maybe other additional net entries are computed according to equation (7) of Romero et al. (2020), and (iii) we can (or not) assume that net exits impact equally all the first J1 - 1 options of election 1. When both net entries and exits are no null, constraints (13) and (15) of Pavia (2023) apply. If uniform = TRUE and there are net exits either constraints (8) or (11) of Pavia (2023), depending on whether there are or not net entries, are also imposed. In this scenario, J could be equal to J1 or J1 + 1 and K equal to K2 or K2 + 1. Note that this scenario could be also used if column J1 of votes_election1 would correspond to immigrants instead of new young electors.

• ordinary: This value accounts for a scenario with two elections elapsed at least some months where (i) the column K1 of votes_election2 corresponds to electors who died in the period between elections, (ii) net entries and maybe other additional net exits are computed according to equation (7) of Romero et al. (2020), and (iii) we can assume (or not) that exits impact equally all the J1 options of election 1. When both net entries and exits are no null, constraints (14) and (15) of Pavia (2023) apply and if uniform = TRUE either constraints (8) and (9) or, without net entries, (6) and (7) of Pavia (2023) are also imposed. In this scenario, J could be equal to J1 or J1 + 1 and K equal to K2 or K2 + 1. Note that this scenario could be also used if column K1 of votes_election2 would correspond to emigrants instead of deaths.

• enriched: This value accounts for a scenario that somehow combine regular and ordinary scenarios. We consider two elections elapsed at least some months where (i) the column J1 of votes_election1 corresponds to new young electors who have the right to vote for the first time, (ii) the column K2 of votes_election2 corresponds to electors who died in the interperiod election, (iii) other (net) entries and (net) exits are computed according to equation (7) of Romero et al. (2020), and (iv) we can assume (or not) that exits impact equally all the J1 - 1 options of election 1. When both net entries and exits are no null, constraints (12) to (15) of Pavia (2023) apply and if uniform = TRUE constraints (10) and (11) of Pavia (2023) are also imposed. In this scenario, J could be equal to J1 or J1 + 1 and K equal to K2 or K2 + 1. Note that this scenario could be also used if the column J1 of votes_election1 would correspond to immigrants instead of new young electors and/or if column K1 of votes_election2 would correspond to emigrants instead of deaths.

• adjust1: This value accounts for a scenario with two elections elapsed at least some months where the census in each of the I polling units of the first election (the row-sums of votes_election1) are proportionally adjusted to match the corresponding census of the polling units in the second election (the row-sums of votes_election2). If integers = TRUE, each row in votes_election1 is proportionally adjusted to the closest integer vector whose sum is equal to the sum of the corresponding row in votes_election2.

• adjust2: This value accounts for a scenario with two elections elapsed at least some months where the census in each of the I polling units of the second election (the row-sums of votes_election2) are proportionally adjusted to match the corresponding census of the polling units in the first election (the row-sums of votes_election1). If integers = TRUE, each row in votes_election2 is adjusted to the closest integer vector whose sum is equal to the sum of the corresponding row in votes_election1.

• simultaneous: This is the value to be used in classical ecological inference problems, such as in ecological studies of racial voting, and in scenarios 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) are not included in the model. In this case, the lphom function just implements the basic model defined, for instance, by equations (1) to (5) of Pavia (2024).

• semifull: This value accounts for a scenario with two elections elapsed at least some months, where: (i) the column J1 = J of votes_election1 totals new electors (young and immigrants) that have the right to vote for the first time and (ii) the column K2 = 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 constraint (15) of Pavia (2023) apply. Additionally, if uniform = TRUE constraints (8) of Pavia (2023) are also imposed.

• 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 (=J1) of votes_election1 measures new immigrants that have the right to vote and (iii) the column K (=K2) 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 (13) and (15) of Pavia (2023) apply. Additionally, if uniform = TRUE constraints (11) of Pavia (2023) are also imposed.

• fullreverse: This value is somehow the mirror version of full. It accounts for a scenario with two elections elapsed at least some months, where (i) the column J1 = J of votes_election1 totals new electors (young and immigrants) that have the right to vote for the first time and (ii) 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 and constraints (14) and (15) of Pavia (2023) apply. Additionally, if uniform = TRUE constraints (8) and (9) of Pavia (2023) are also 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. Constraints (12) to (15) of Pavia (2023) apply and if uniform = TRUE constraints (10) and (11) of Pavia (2023) are also imposed.

Value

A list with the following components

VTM

A matrix of order J'xK' (where J'=J-1 or J and K'= K-1 or K) with the estimated percentages of row-standardized vote transitions from election 1 to election 2. In raw, regular, ordinary and enriched scenarios when the percentage of net entries is small, less than 1% of the census in all units, net entries are omitted (i.e., the number of rows of VTM is equal to J1) even when estimates for net entries different from zero are obtained. Likewise, in the same scenarios when the percentage of net exits is small, less than 1% of the census in all units, net exits are omitted (i.e., the number of rows of VTM is equal to K2) even when estimates for net exits different from zero are obtained.

VTM.votes

A matrix of order J'xK' (where J'=J-1 or J and K'= K-1 or K) with the estimated vote transitions from election 1 to election 2. In raw, regular, ordinary and enriched scenarios when the percentage of net entries is small, less than 1% of the census, net entries are omitted (i.e., J = J1) even when estimates for net entries different from zero are obtained. Likewise, in the same scenarios when the percentage of net exits is small, less than 1% of the census, net exits are omitted (i.e., K = K2) even when estimates for net exits different from zero are obtained.

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 (2022).

VTM.complete

A matrix of order JxK with the estimated proportions of row-standardized vote transitions from election 1 to election 2, including in raw, regular, ordinary and enriched 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 JxK with the estimated vote transitions from election 1 to election 2, including in raw, regular, ordinary and enriched 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.prop.units

An array of order JxKxI with the estimated proportions of vote transitions from election 1 to election 2 attained for each unit after adjusting the lphom() initial estimate.

VTM.votes.units

An array of order JxKxI with the estimated matrix of vote transitions from election 1 to election 2 attained for each unit after adjusting the lphom() initial estimate.

VTM.sequence

Array of order JxKxlength(emphasis) with the global estimated matrices corresponding to each weight.

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.

errors

A matrix of order Ixlength(emphasis) with the expected errors for each unit and weight. The solution determined by VTM.prop.units or VTM.votes.units is the one obtained combining the unit solutions corresponding to the minimum observed errors.

VTM.prop.units.by.emphasis

An array of order JxKxIxlength(emphasis) with the estimated proportions of vote transitions from election 1 to election 2 attained in each unit for each weight. This is a NULL array if save.local.by.emphasis = FALSE.

deterministic.bounds

A list of two matrices of order JxK and two arrays of order JxKxI containing for each vote transition the lower and upper allowed proportions given the observed aggregates.

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 J'xK' with the estimated percentages of vote transitions from election 1 to election 2 initially obtained by lphom() with the raw data, without promoting any unit.

• VTM.votes_init: A matrix of order J'xK' with the estimated vote transitions from election 1 to election 2 initially obtained by lphom() with the raw data, without promoting any unit.

• 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() with the raw data, without promoting any unit.

• 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 with the raw data, without promoting any unit, in each territorial unit for each option of election 2.

• VTM.complete_init: A matrix of order JxK with the estimated proportions of vote transitions from election 1 to election 2 initially obtained by lphom(), including in raw, regular, ordinary and enriched 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 JxK with the estimated vote transitions from election 1 to election 2 initially obtained by lphom(), including in raw, regular, ordinary and enriched 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]

References

Pavia, JM, and Romero, R (2022). Improving estimates accuracy of voter transitions. Two new algorithms for ecological inference based on linear programming, Sociological Methods & Research. doi:10.1177/00491241221092725.

Pavia, JM, and Penades, A (2024). A bottom-up approach for ecological inference.

See Also

lphom tslphom nslphom lclphom

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

Examples

mt.rs <- rslphom(France2017P[, 1:8] , France2017P[, 9:12], emphasis = 0.5)
mt.rs$VTM