lp_apriori {lphom}

Implements lp_apriori models

Description

Adjusts an initial J0xK0 vote transfer matrix (ecological contingency table) to guarantee (i) congruency with aggregate results and (ii) completeness.

Usage

lp_apriori(
  votes_election1,
  votes_election2,
  apriori,
  weights = "constant",
  new_and_exit_voters = "raw",
  uniform = TRUE,
  solver = "lp_solve",
  integers = TRUE,
  integers.solver = "symphony",
  ...
)

Arguments

votes_election1

data.frame (or matrix) of order IxJ1 (or vector of length J1) with the votes gained by (or the numbers corresponding to) the J1 political options competing on election 1 (or origin) in the I territorial units considered.

votes_election2

data.frame (or matrix) of order IxK2 (or vector of length K2) with the votes gained by (or the numbers corresponding to) the K2 political options competing on election 2 (or destination) in the I territorial units considered.

apriori

data.frame (or matrix) of order J0xK0 with an initial estimate of the (row-standarized) voter transition proportions/fractions, pjk0, between the first J0 election options of election 1 and the first K0 election options of election 2. It could be also a data.frame (matrix) of counts. This matrix can contain some missing values.

weights

Either a numeric matrix (or data.frame) of order J0xK0 of weights, wjk, or a character string indicating the structure of weights to be used. As character string this argument admits seven different values: constant, x, xy, expected, counts, sqrt, or sd. Default, constant (i.e., wjk = 1). The wjk coefficients measure the (relative) degree of confidence we have in the a priori values pjk0. Everything else constant, the greater a weight wjk the closer the estimated pjk and the pjk0 proportions will be. As numeric matrix, this matrix can contain some missing values, usually located in the same cells than the missing values of apriori.

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.

uniform

A TRUE/FALSE value that indicates if census exits affect all the electoral options in a (relatively) similar fashion; depending on the scenario any equation(s) among equations (6) to (11) of Pavia (2023) could be used in the underlying model. 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

A TRUE/FALSE value that indicates whether the LP solution of counts (votes) must be approximate to the closest integer solution using ILP to generate the final solution. Default, TRUE.

integers.solver

A character string indicating the linear programming solver to be used for approximating 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 JxK 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, 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.

VTM.votes

A matrix of order JxK 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.

weights

A matrix of order JxK with the weights used to adjust the a priori 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.

VTM.complete

A matrix of order JxK with the estimated proportions of row-standardized vote transitions from election 1 to election 2. In raw, regular, ordinary and enriched scenarios, this matrix includes the row and the column corresponding to net entries and net exits (when they are present) even when they are really small.

VTM.complete.votes

A matrix of order JxK with the estimated vote transitions from election 1 to election 2. In raw, regular, ordinary and enriched scenarios, this matrix includes the row and the column corresponding to net entries and net exits (when they are present) even when they are really small.

inputs

A list containing all the objects with the values used as arguments by the function.

origin

A vector 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 vector 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.

Author(s)

Jose M. Pavia, [e-mail]

References

Pavia, JM (2023). Adjustment of initial estimates of voter transition probabilities to guarantee consistency and completeness, SN Social Sciences, 3, 75. doi:10.1007/s43545-023-00658-y.

See Also

lphom tslphom nslphom lclphom

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

Examples

P0 <- matrix(c(.75, .02, .15, .08, .01, .01, .97, .01,
               .01, .01, .01, .97, .01, .10, .80, .09,
               .20, .30, .30, .20, .10, .10, .50, .30,
               .10, .30, NA, NA, .25, .20, NA, NA), 
             byrow = TRUE, 8, 4)
mt <- lp_apriori(France2017P[, 1:8], France2017P[, 9:12], P0, integers = FALSE)