, Rafael Romero [aut]| Title: | Ecological Inference by Linear Programming under Homogeneity |
|---|---|
| Description: | Provides a bunch of algorithms based on linear programming for estimating, under the homogeneity hypothesis, RxC ecological contingency tables (or vote transition matrices) using mainly aggregate data (from voting units). References: Pavía and Romero (2022) <doi:10.1177/00491241221092725>. Pavía (2023) <doi:10.1007/s43545-023-00658-y>. Pavía and Romero (2024) <doi:10.1093/jrsssa/qnae013>. Pavía (2024) A local convergent ecological inference algorithm for RxC tables. Pavía and Penadés (2024). A bottom-up approach for ecological inference. Romero, Pavía, Martín and Romero (2020) <doi:10.1080/02664763.2020.1804842>. Acknowledgements: The authors wish to thank Consellería de Educación, Universidades y Empleo, Generalitat Valenciana (grant AICO/2021/257) and Ministerio de Economía e Innovación (grant PID2021-128228NB-I00) for supporting this research. |
| Authors: | Jose M. Pavía [aut, cre]
, Rafael Romero [aut] |
| Maintainer: | Jose M. Pavía <[email protected]> |
| License: | EPL | file LICENSE |
| Version: | 0.3.5-5 |
| Built: | 2024-10-30 06:46:28 UTC |
| Source: | CRAN |
Takes as input an object generated with an algorithm of the lphom-family (lphom, tslphom, nslphom, tslphom_dual, nslphom_joint, ....) and returns as output an object of the same class as the input object with all their relevant estimated (local and global) transfer matrices of counts updated to their closest integer matrices. The rest of main components of the object are also accordingly updated.
adjust2integers(x, solver = "symphony", ...)adjust2integers(x, solver = "symphony", ...)
x |
An object output of a lphom family algorithm |
solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
... |
Other arguments passed on the method. Not currently used. |
The updating of the matrices is performed using integer linear programming after imposing all the row- and column-constraints.
An object of the same class and components as x with its components properly updated after adjusting the estimated count matrices in x using integer linear programming
Jose M. Pavia, [email protected]
...
mt.ts <- tslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") mt.ts <- adjust2integers(mt.ts, solver = "lp_solve")mt.ts <- tslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") mt.ts <- adjust2integers(mt.ts, solver = "lp_solve")
Estimates confidence intervals for the (vote) transfer probabilities obtained with lphom()
confidence_intervals_pjk(lphom.object, level = 0.9, num.d = 11, B = 30)confidence_intervals_pjk(lphom.object, level = 0.9, num.d = 11, B = 30)
lphom.object |
An object output of the lphom() function. |
level |
A number between 0 and 1 to be used as level of confidence for the intervals. By default 0.90 |
num.d |
Number maximum of different disturbances, |
B |
Integer that determines the number of simulations to be performed for each disturbance value. By default, 30. |
A list with the following components
TM.estimation |
Transfer matrix of probability point estimates. |
TM.lower |
Transfer matrix of lower values for the probability estimates. |
TM.upper |
Transfer matrix of upper values for the probability estimates. |
level |
Confidence level used when computing the confidence intervals. |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Romero, R, Pavia, JM, Martin, J and Romero G (2020). Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election. Journal of Applied Statistics, 47(13-15), 2711-2736. doi:10.1080/02664763.2020.1804842
Martin, J (2020). Analisis de la incertidumbre en la estimacion de la movilidad electoral mediante el procedimiento plhom. PhD Dissertation.
# Do not run # mt.lphom <- lphom(France2017P[, 1:8], France2017P[, 9:12], "raw", NULL, FALSE) # set.seed(533423) # confidence_intervals_pjk(mt.lphom, level = 0.90, num.d = 5, B = 8)# Do not run # mt.lphom <- lphom(France2017P[, 1:8], France2017P[, 9:12], "raw", NULL, FALSE) # set.seed(533423) # confidence_intervals_pjk(mt.lphom, level = 0.90, num.d = 5, B = 8)
Estimation of the error index (EI) of a RxC vote transfer matrix obtained with lphom()
error_lphom( lphom.object, upper.alfa = 0.1, show.plot = TRUE, num.d = 11, B = 30 )error_lphom( lphom.object, upper.alfa = 0.1, show.plot = TRUE, num.d = 11, B = 30 )
lphom.object |
An object output of the lphom() function. |
upper.alfa |
Upper bound that will not be exceed by the EI estimate with a confidence 1 - alpha. By default, 0.10. |
show.plot |
TRUE/FALSE. Indicates whether the plot showing the relationship between EI and HETe estimated by simulation for the election under study should be displayed as a side-effect. By default, TRUE. |
num.d |
Number maximum of different disturbances, |
B |
Integer that determines the number of simulations to be performed for each disturbance value. By default, 30. |
A list with the following components
EI.estimate |
Point estimate for EI. |
EI.upper |
Upper bound with confidence 1 - alpha of the EI estimate |
figure |
ggplot2 object describing the graphical representation of the relationship between EI and HETe. |
equation |
lm object of the adjustment between EI and HETe. |
statistics |
A four column matrix with the values of HET, HETe, EI and d associated with each simulated scenario. |
TMs.real |
Array with the simulated real transfer matrices associated with each scenario. |
TMs.estimate |
Array with the estimated transfer matrices associated with each scenario. |
ggplot2 is needed to be installed for this function to work.
See equation (12) in Romero et al. (2020) for a definition of the EI index.
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Romero, R, Pavia, JM, Martin, J and Romero G (2020). Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election. Journal of Applied Statistics, 47(13-15), 2711-2736. doi:10.1080/02664763.2020.1804842
lphom confidence_intervals_pjk
mt.lphom <- lphom(France2017P[, 1:8], France2017P[, 9:12], new_and_exit_voters = "raw", verbose = FALSE) set.seed(253443) example <- error_lphom(mt.lphom, upper.alfa = 0.10, show.plot = FALSE, num.d = 5, B = 8) example$EI.estimatemt.lphom <- lphom(France2017P[, 1:8], France2017P[, 9:12], new_and_exit_voters = "raw", verbose = FALSE) set.seed(253443) example <- error_lphom(mt.lphom, upper.alfa = 0.10, show.plot = FALSE, num.d = 5, B = 8) example$EI.estimate
Data frame containing the official results recorded in the first and second rounds of the 2017 French presidential election in the 107 territorial French departments and in an artificial department that groups the French electors living abroad.
data(France2017D)data(France2017D)
A table containing 108 observations and 13 variables:
Number of people abstaining (NonVoters) in the first-round of 2017 Presidential Election.
Number of people voting either blank or null in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Emmanuel Macron in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Marine Le Pen in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Francois Fillon in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Jean-Luc Melenchon in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Benoit Hamon in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Nicolas Dupont-Aignan in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by the rest of candidates in the first-round of 2017 Presidential Election.
Number of people abstaining (NonVoters) in the second-round of 2017 Presidential Election.
Number of people voting either blank or null in the second-round of 2017 Presidential Election.
Number of votes gained at a national level by Emmanuel Macron in the second-round of 2017 Presidential Election
Number of votes gained at a national level by Marine Le Pen in the second-round of 2017 Presidential Election
Own elaboration from data available in https://www.conseil-constitutionnel.fr/, retrieved 3 March 2020.
Data frame containing the provisional results of the first and second rounds of the 2017 French presidential election in the 12 French continental regions (Auvergne-Rhone-Alpes, Bourgogne-Franche-Comte, Brittany, Centre-Val de Loire, Grand Est, Hauts-de-France, Ile-de-France, Normandy, Nouvelle-Aquitaine, Occitanie, Pays de la Loire, Provence-Alpes-Cote d'Azur) plus an additional region that covers Corsica and the rest of French overseas regions.
data(France2017P)data(France2017P)
A table containing 13 observations and 12 variables:
Number of people abstaining (NonVoters) and voting either blank or null in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Emmanuel Macron in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Marine Le Pen in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Francois Fillon in the first-round of 2017 Presidential Election.
Number of votes gained at a national level bu Jean-Luc Melenchon in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Benoit Hamon in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by Nicolas Dupont-Aignan in the first-round of 2017 Presidential Election.
Number of votes gained at a national level by the rest of candidates in the first-round of 2017 Presidential Election.
Number of people abstaining (NonVoters) in the second-round of 2017 Presidential Election.
Number of people voting either blank or null in the second-round of 2017 Presidential Election.
Number of votes gained at a national level by Emmanuel Macron in the second-round of 2017 Presidential Election
Number of votes gained at a national level by Marine Le Pen in the second-round of 2017 Presidential Election
Own elaboration from data available in https://www.francetvinfo.fr/elections/resultats/, retrieved 7 May 2017.
Estimates RxC (JxK) vote transfer matrices (ecological contingency tables) with lclphom
lclphom( votes_election1, votes_election2, 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, iter.max = 1000, type.errors = "posterior", distance.local = c("abs", "max", "none"), verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", ... )lclphom( votes_election1, votes_election2, 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, iter.max = 1000, type.errors = "posterior", distance.local = c("abs", "max", "none"), verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", ... )
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. |
new_and_exit_voters |
A character string indicating the level of information available
in |
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 |
lambda |
A number between 0 and 1, informing the relative weight the user assigns to the
|
uniform |
A |
structural_zeros |
Default |
integers |
A |
iter.max |
Maximum number of iterations to be performed. The process ends when either the
number of iterations reaches |
type.errors |
A string argument that indicates whether the errors (distance to homogeneity) to be
computed for the temporary local solutions are calculated taking as reference the
previous global matrix (the one that is used to derive the temporary local solution)
or taking as reference the posterior global matrix (the one in which the temporary
local solution is integrated). This argument admits two values: |
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, |
verbose |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used for
approximating the LP solution to the closest integer solution.
Only |
... |
Other arguments to be passed to the function. Not currently used. |
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.
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 |
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 |
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 |
VTM.complete.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2, including in |
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 in the solution. |
VTM.votes.units |
An array of order JxKxI with the estimated matrix of vote transitions from election 1 to election 2 attained for for each unit in the solution. |
VTM.complete.last.iter |
A matrix of order JxK with the estimated proportions of vote transitions from election 1 to election 2, including in |
VTM.sequence |
Array of order JxKx(iter+1) (where |
HETe.sequence |
Numeric vector of length |
VTM.prop.units.last.iter |
An array of order JxKxI with the estimated proportions of vote transitions from election 1 to election 2 attained for each unit in the final iteration. |
VTM.votes.units.last.iter |
An array of order JxKxI with the estimated matrix of vote transitions from election 1 to election 2 attained for each unit in the final 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.units |
A matrix of order Ix(iter+1) with the number of iteration corresponding to the solution selected for each unit in each iteration. |
errors |
A vector of length I with the minimal error observed in the sequence for each unit. It corresponds to
the unit-error associated with the solution linked with either |
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().
VTM.votes_init: A matrix of order J'xK' 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 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.
Jose M. Pavia, [email protected]
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. (2024). A local convergent ecological inference algorithm for RxC tables.
Other linear programing ecological inference functions:
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
mt.lc <- lclphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") mt.lc$VTM mt.lc$HETe mt.lc$solution_init$HETe_initmt.lc <- lclphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") mt.lc$VTM mt.lc$HETe mt.lc$solution_init$HETe_init
Adjusts an initial J0xK0 vote transfer matrix (ecological contingency table) to guarantee (i) congruency with aggregate results and (ii) completeness.
lp_apriori( votes_election1, votes_election2, apriori, weights = "constant", new_and_exit_voters = "raw", uniform = TRUE, solver = "lp_solve", integers = TRUE, integers.solver = "symphony", ... )lp_apriori( votes_election1, votes_election2, apriori, weights = "constant", new_and_exit_voters = "raw", uniform = TRUE, solver = "lp_solve", integers = TRUE, integers.solver = "symphony", ... )
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: |
new_and_exit_voters |
A character string indicating the level of information available
in |
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, |
solver |
A character string indicating the linear programming solver to be used, only
|
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 |
... |
Other arguments to be passed to the function. Not currently used. |
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.
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 |
VTM.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2.
In |
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 |
VTM.complete.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2.
In |
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. |
Jose M. Pavia, [email protected]
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.
Other linear programing ecological inference functions:
lclphom(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
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)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)
Estimates RxC (JxK) vote transfer matrices (ecological contingency tables) with lphom
lphom( votes_election1, votes_election2, 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, verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", ... )lphom( votes_election1, votes_election2, 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, verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", ... )
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. |
new_and_exit_voters |
A character string indicating the level of information available
in |
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 |
lambda |
A number between 0 and 1, informing the relative weight the user assigns to the
|
uniform |
A |
structural_zeros |
Default |
integers |
A |
verbose |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used for
approximating the LP solution to the closest integer solution.
Only |
... |
Other arguments to be passed to the function. Not currently used. |
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.
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 |
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 |
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 defined in equation (11) of Romero et al. (2020). |
VTM.complete |
A matrix of order JxK with the estimated proportions of row-standardized vote transitions from election 1 to election 2.
In |
VTM.complete.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2.
In |
deterministic.bounds |
A list of two matrices of order JxK containing for each vote transition the lower and upper proportions allowed 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 in each territorial unit for each option of election 2. |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Romero, R, Pavia, JM, Martin, J and Romero G (2020). Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election. Journal of Applied Statistics, 47(13-15), 2711-2736. doi:10.1080/02664763.2020.1804842
tslphom nslphom lclphom rslphom
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
lphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw")lphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw")
Estimates RxC vote transfer matrices (ecological contingency tables) with lphom_dual
lphom_dual( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )lphom_dual( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )
votes_election1 |
data.frame (or matrix) of order IxJ with the counts to be initially
mapped to rows. When estimating vote transfer matrices, the votes gained by
the J political options competing on election 1 (or origin) in the I
territorial units considered. The sum by rows of |
votes_election2 |
data.frame (or matrix) of order IxK with the counts to be initially mapped
to columns. When estimating vote transfer matrices, the votes gained by
the K political options competing on election 2 (or destination) in the I
territorial units considered. The sum by rows of |
integers |
A TRUE/FALSE value that indicates whether the LP solution of counts (votes) must be approximate to the closest integer solution using ILP. Default, FALSE. |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
... |
Other arguments to be passed to the function. Not currently used. |
A list with the following components
VTM.votes.w |
The matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
VTM.votes.a |
The matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2, attained simple averaging the two dual solutions. |
HETe.w |
Estimated heterogeneity index associated to the |
HETe.a |
Estimated heterogeneity index associated to the |
VTM12.w |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1 to election 2 associated to the |
VTM21.w |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2 to election 1 associated to the |
VTM12.a |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1 to election 2 associated to the |
VTM21.a |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2 to election 1 associated to the |
lphom.object.12 |
The output of the |
lphom.object.21 |
The output of the |
inputs |
A list containing all the objects with the values used as arguments by the function. |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Pavia, JM and Romero, R (2024). Symmetry estimating RxC vote transfer matrices from aggregate data. Journal of the Royal Statistical Society, Series A – Statistics in Society, forthcoming. doi:10.1093/jrsssa/qnae013
lphom tslphom_dual nslphom_dual lphom_joint tslphom_joint nslphom_joint
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
x <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- lphom_dual(x, y) mt$VTM.votes.w mt$HETe.wx <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- lphom_dual(x, y) mt$VTM.votes.w mt$HETe.w
Estimates RxC vote transfer matrices (ecological contingency tables) with lphom_joint
lphom_joint( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )lphom_joint( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )
votes_election1 |
data.frame (or matrix) of order IxJ with the counts to be initially
mapped to rows. When estimating vote transfer matrices, the votes gained by
the J political options competing on election 1 (or origin) in the I
territorial units considered. The sum by rows of |
votes_election2 |
data.frame (or matrix) of order IxK with the counts to be initially mapped
to columns. When estimating vote transfer matrices, the votes gained by
the K political options competing on election 2 (or destination) in the I
territorial units considered. The sum by rows of |
integers |
A TRUE/FALSE value that indicates whether the LP solution of counts (votes) must be approximate to the closest integer solution using ILP. Default, FALSE. |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
... |
Other arguments to be passed to the function. Not currently used. |
A list with the following components
VTM.votes |
A matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2. |
HETe |
The estimated heterogeneity index associated to the |
VTM12 |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1 to election 2 associated to the |
VTM21 |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2 to election 1 associated to the |
EHet12 |
A matrix of order IxK measuring in each unit a distance to the homogeneity hypothesis. That is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results in each territorial unit for each option of election two. The matrix Eik. |
EHet21 |
A matrix of order IxJ measuring in each unit a distance to the homogeneity hypothesis. That is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results in each territorial unit for each option of election one. The matrix Eij. |
deterministic.bounds |
A list of two matrices of order JxK containing for each vote transition the lower and upper proportions allowed given the observed aggregates. |
inputs |
A list containing all the objects with the values used as arguments by the function. |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Pavia, JM and Romero, R (2024). Symmetry estimating RxC vote transfer matrices from aggregate data. Journal of the Royal Statistical Society, Series A – Statistics in Society, forthcoming. doi:10.1093/jrsssa/qnae013
lphom lphom_dual tslphom_dual nslphom_dual tslphom_joint nslphom_joint
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
x <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- lphom_joint(x, y) mt$VTM.votes mt$HETex <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- lphom_joint(x, y) mt$VTM.votes mt$HETe
Estimates RxC (JxK) vote transfer matrices (ecological contingency tables) with nslphom
nslphom( votes_election1, votes_election2, new_and_exit_voters = c("raw", "regular", "ordinary", "enriched", "adjust1", "adjust2", "simultaneous", "semifull", "full", "fullreverse", "gold"), apriori = NULL, lambda = 0.5, uniform = TRUE, iter.max = 10, min.first = FALSE, structural_zeros = NULL, integers = FALSE, distance.local = c("abs", "max", "none"), verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", burnin = 0, tol = 10^-5, ... )nslphom( votes_election1, votes_election2, new_and_exit_voters = c("raw", "regular", "ordinary", "enriched", "adjust1", "adjust2", "simultaneous", "semifull", "full", "fullreverse", "gold"), apriori = NULL, lambda = 0.5, uniform = TRUE, iter.max = 10, min.first = FALSE, structural_zeros = NULL, integers = FALSE, distance.local = c("abs", "max", "none"), verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", burnin = 0, tol = 10^-5, ... )
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. |
new_and_exit_voters |
A character string indicating the level of information available
in |
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 |
lambda |
A number between 0 and 1, informing the relative weight the user assigns to the
|
uniform |
A |
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 |
min.first |
A |
structural_zeros |
Default |
integers |
A |
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, |
verbose |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
burnin |
Number of initial solutions to be discarded before determining the final solution. By default, 0. |
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 |
... |
Other arguments to be passed to the function. Not currently used. |
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.
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 |
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 |
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 |
VTM.complete.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2, including in |
VTM.sequence |
Array of order JxKx(iter+1) (where |
HETe.sequence |
Numeric vector of length |
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 in the selected iteration. |
VTM.votes.units |
An array of order JxKxI 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 |
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 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.
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
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.
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
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_initmt.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
Estimates RxC vote transfer matrices (ecological contingency tables) with nslphom_dual
nslphom_dual( votes_election1, votes_election2, iter.max = 10, min.first = FALSE, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", tol = 10^-5, ... )nslphom_dual( votes_election1, votes_election2, iter.max = 10, min.first = FALSE, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", tol = 10^-5, ... )
votes_election1 |
data.frame (or matrix) of order IxJ with the counts to be initially
mapped to rows. When estimating vote transfer matrices, the votes gained by
the J political options competing on election 1 (or origin) in the I
territorial units considered. The sum by rows of |
votes_election2 |
data.frame (or matrix) of order IxK with the counts to be initially mapped
to columns. When estimating vote transfer matrices, the votes gained by
the K political options competing on election 2 (or destination) in the I
territorial units considered. The sum by rows of |
iter.max |
Maximum number of iterations to be performed in each dual linear program.
The process ends independently in each system 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 |
min.first |
A |
integers |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
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 |
... |
Other arguments to be passed to the function. Not currently used. |
A list with the following components
VTM.votes.w |
The matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
VTM.votes.units.w |
The array of order JxKxI with the local estimated cross-distributions of votes of elections 1 and 2 by unit, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
VTM.votes.a |
The matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2, attained simple averaging the two dual solutions. |
VTM.votes.units.a |
The matrix of order JxKxI with the estimated cross-distributions of votes of elections 1 and 2 by unit, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
HETe.w |
Estimated heterogeneity index associated to the |
HETe.a |
Estimated heterogeneity index associated to the |
VTM12.w |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1
to election 2 associated to the |
VTM21.w |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2
to election 1 associated to the |
VTM12.a |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1
to election 2 associated to the |
VTM21.a |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2
to election 1 associated to the |
nslphom.object.12 |
The output of the |
nslphom.object.21 |
The output of the |
inputs |
A list containing all the objects with the values used as arguments by the function. |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Pavia, JM and Romero, R (2024). Symmetry estimating RxC vote transfer matrices from aggregate data. Journal of the Royal Statistical Society, Series A – Statistics in Society, forthcoming. doi:10.1093/jrsssa/qnae013
nslphom lphom_dual tslphom_dual lphom_joint tslphom_joint nslphom_joint
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
x <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- nslphom_dual(x, y) mt$VTM.votes.w mt$HETe.wx <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- nslphom_dual(x, y) mt$VTM.votes.w mt$HETe.w
Estimates RxC vote transfer matrices (ecological contingency tables) with nslphom_joint
nslphom_joint( votes_election1, votes_election2, iter.max = 10, min.first = FALSE, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", tol = 0.001, ... )nslphom_joint( votes_election1, votes_election2, iter.max = 10, min.first = FALSE, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", tol = 0.001, ... )
votes_election1 |
data.frame (or matrix) of order IxJ with the counts to be initially
mapped to rows. When estimating vote transfer matrices, the votes gained by
the J political options competing on election 1 (or origin) in the I
territorial units considered. The sum by rows of |
votes_election2 |
data.frame (or matrix) of order IxK with the counts to be initially mapped
to columns. When estimating vote transfer matrices, the votes gained by
the K political options competing on election 2 (or destination) in the I
territorial units considered. The sum by rows of |
iter.max |
Maximum number of iterations to be performed. The process ends independently when either
the number of iterations reaches iter.max or when the maximum variation between two
consecutive estimates of both ways probability transfer matrices are less than |
min.first |
A |
integers |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
tol |
Maximum deviation allowed between two consecutive iterations. The process ends when the maximum
variation between the estimated cross-distributions of votes between two consecutive
iterations is less than |
... |
Other arguments to be passed to the function. Not currently used. |
A list with the following components
VTM.votes |
A matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2. |
HETe |
The estimated heterogeneity index associated to the |
VTM12 |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1 to election 2 associated to the |
VTM21 |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2 to election 1 associated to the |
VTM.votes.units |
An array of order JxKxI with the estimated matrix of cross-distributions of votes of elections 1 and 2 attained for each unit in iteration of the solution. |
iter |
The real final number of iterations performed before ending the process. |
iter.min |
Number of the iteration associated to the selected |
EHet12 |
A matrix of order IxK measuring in each unit a distance to the homogeneity hypothesis. That is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results in each territorial unit for each option of election two. The matrix Eik. |
EHet21 |
A matrix of order IxJ measuring in each unit a distance to the homogeneity hypothesis. That is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results in each territorial unit for each option of election one. The matrix Eij. |
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. |
solution_init |
A list with the main outputs produced by lphom_joint(). |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Pavia, JM and Romero, R (2024). Symmetry estimating RxC vote transfer matrices from aggregate data. Journal of the Royal Statistical Society, Series A – Statistics in Society, forthcoming. doi:10.1093/jrsssa/qnae013
nslphom lphom_dual tslphom_dual nslphom_dual lphom_joint tslphom_joint
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
x <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- nslphom_joint(x, y, iter.max = 3) mt$VTM.votes mt$HETex <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- nslphom_joint(x, y, iter.max = 3) mt$VTM.votes mt$HETe
Plot method for objects obtained with an algorithm of the lphom-family (lphom, tslphom, nslphom, tslphom_dual, nslphom_joint, ....).
## S3 method for class 'lphom' plot( x, complete = FALSE, margins = TRUE, digits = 2, row.names = NULL, col.names = NULL, size.numbers = 6, size.labels = 4, size.margins = 4, colour.cells = "deeppink3", colour.grid = "blanchedalmond", alpha = 0.5, which = NULL, ..., type = "w", show.plot = TRUE )## S3 method for class 'lphom' plot( x, complete = FALSE, margins = TRUE, digits = 2, row.names = NULL, col.names = NULL, size.numbers = 6, size.labels = 4, size.margins = 4, colour.cells = "deeppink3", colour.grid = "blanchedalmond", alpha = 0.5, which = NULL, ..., type = "w", show.plot = TRUE )
x |
An object output of a |
complete |
A |
margins |
A |
digits |
Integer indicating the number of decimal places to be shown. Default, 2. |
row.names |
Names to be used for the rows of the matrix. |
col.names |
Names to be used for the columns of the matrix. |
size.numbers |
A reference number indicating the average font size to be used for the transfer numbers. Default, 6. |
size.labels |
A number indicating the font size to be used for labels. Default, 4. |
size.margins |
A number indicating the font size to be used for margin numbers. Default, 4. |
colour.cells |
Background base colour for cells. |
colour.grid |
Colour to be used for grid lines. |
alpha |
A [0,1] number of colour transparency. |
which |
A vector of integers informing the units for which the aggregate transfer matrix should be plotted. Default, |
... |
Other arguments passed on to methods. Not currently used. |
type |
A character string indicating the solution (transfer matrix) to be plotted. Only valid for _dual algorithms. |
show.plot |
A |
Invisibly returns the (ggplot) description of the plot, which is a list with components that contain the plot itself, the data, information about the scales, panels etc.
ggplot2 is needed to be installed for this function to work.
Jose M. Pavia, [email protected]
mt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") p <- plot(mt.ns, show.plot = FALSE) pmt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") p <- plot(mt.ns, show.plot = FALSE) p
Print method for objects obtained with an algorithm of the lphom-family (lphom, tslphom, nslphom, tslphom_dual, nslphom_joint, ....).
## S3 method for class 'lphom' print(x, ..., margins = TRUE, digits = 2)## S3 method for class 'lphom' print(x, ..., margins = TRUE, digits = 2)
x |
An object output of a |
... |
Other arguments passed on to methods. Not currently used. |
margins |
A |
digits |
Integer indicating the number of decimal places to be shown. Default, 2. |
Jose M. Pavia, [email protected]
mt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") print(mt.ns, digits = 2, margins = TRUE)mt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") print(mt.ns, digits = 2, margins = TRUE)
Print method for summary.lphom objects
## S3 method for class 'summary.lphom' print(x, ..., margins = TRUE, digits = 2)## S3 method for class 'summary.lphom' print(x, ..., margins = TRUE, digits = 2)
x |
An |
... |
Other arguments passed on to methods. Not currently used. |
margins |
A |
digits |
Integer indicating the number of decimal places to be shown. Default, 2. |
Estimates RxC (JxK) vote transfer matrices (ecological contingency tables) with rslphom
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", ... )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", ... )
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 |
new_and_exit_voters |
A character string indicating the level of information available
in |
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 |
lambda |
A number between 0 and 1 informing the relative weight the user assigns to the
|
uniform |
A |
structural_zeros |
Default |
integers |
A |
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, |
save.local.by.emphasis |
A |
verbose |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used for
approximating the LP solution to the closest integer solution.
Only |
... |
Other arguments to be passed to the function. Not currently used. |
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.
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 |
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 |
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 |
VTM.complete.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2, including in |
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.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 |
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.
Jose M. Pavia, [email protected]
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.
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
tslphom_dual(),
tslphom_joint(),
tslphom()
mt.rs <- rslphom(France2017P[, 1:8] , France2017P[, 9:12], emphasis = 0.5) mt.rs$VTMmt.rs <- rslphom(France2017P[, 1:8] , France2017P[, 9:12], emphasis = 0.5) mt.rs$VTM
Summary method for objects obtained with an algorithm of the lphom-family (lphom, tslphom, nslphom, tslphom_dual, nslphom_joint, ....).
## S3 method for class 'lphom' summary(object, ...)## S3 method for class 'lphom' summary(object, ...)
object |
An object output of a |
... |
Other arguments passed on to methods. Not currently used. |
An object of class "summary.lphom".
Jose M. Pavia, [email protected]
mt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") summary(mt.ns)mt.ns <- nslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") summary(mt.ns)
Estimates RxC (JxK) vote transfer matrices (ecological contingency tables) with tslphom
tslphom( votes_election1, votes_election2, 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"), verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", ... )tslphom( votes_election1, votes_election2, 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"), verbose = TRUE, solver = "lp_solve", integers.solver = "symphony", ... )
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. |
new_and_exit_voters |
A character string indicating the level of information available
in |
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 |
lambda |
A number between 0 and 1, informing the relative weight the user assigns to the
|
uniform |
A |
structural_zeros |
Default |
integers |
A |
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, |
verbose |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used for
approximating the LP solution to the closest integer solution.
Only |
... |
Other arguments to be passed to the function. Not currently used. |
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.
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 |
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 |
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 |
VTM.complete.votes |
A matrix of order JxK with the estimated vote transitions from election 1 to election 2, including in |
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. |
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. |
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().
VTM.votes_init: A matrix of order J'xK' 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: 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.
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
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.
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom_joint()
mt.ts <- tslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") mt.ts$VTM mt.ts$HETe mt.ts$solution_init$HETe_initmt.ts <- tslphom(France2017P[, 1:8] , France2017P[, 9:12], new_and_exit_voters= "raw") mt.ts$VTM mt.ts$HETe mt.ts$solution_init$HETe_init
Estimates RxC vote transfer matrices (ecological contingency tables) with tslphom_dual
tslphom_dual( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )tslphom_dual( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )
votes_election1 |
data.frame (or matrix) of order IxJ with the counts to be initially
mapped to rows. When estimating vote transfer matrices, the votes gained by
the J political options competing on election 1 (or origin) in the I
territorial units considered. The sum by rows of |
votes_election2 |
data.frame (or matrix) of order IxK with the counts to be initially mapped
to columns. When estimating vote transfer matrices, the votes gained by
the K political options competing on election 2 (or destination) in the I
territorial units considered. The sum by rows of |
integers |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
... |
Other arguments to be passed to the function. Not currently used. |
A list with the following components
VTM.votes.w |
The matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
VTM.votes.units.w |
The array of order JxKxI with the local estimated cross-distributions of votes of elections 1 and 2 by unit, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
VTM.votes.a |
The matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2, attained simple averaging the two dual solutions. |
VTM.votes.units.a |
The matrix of order JxKxI with the estimated cross-distributions of votes of elections 1 and 2 by unit, attained weighting the two dual solutions using as weights the corresponding HTEe estimates. |
HETe.w |
Estimated heterogeneity index associated to the |
HETe.a |
Estimated heterogeneity index associated to the |
VTM12.w |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1
to election 2 associated to the |
VTM21.w |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2
to election 1 associated to the |
VTM12.a |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1
to election 2 associated to the |
VTM21.a |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2
to election 1 associated to the |
tslphom.object.12 |
The output of the |
tslphom.object.21 |
The output of the |
inputs |
A list containing all the objects with the values used as arguments by the function. |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Pavia, JM and Romero, R (2024). Symmetry estimating RxC vote transfer matrices from aggregate data. Journal of the Royal Statistical Society, Series A – Statistics in Society, forthcoming. doi:10.1093/jrsssa/qnae013
tslphom lphom_dual nslphom_dual lphom_joint tslphom_joint nslphom_joint
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_joint(),
tslphom()
x <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- tslphom_dual(x, y) mt$VTM.votes.w mt$HETe.wx <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- tslphom_dual(x, y) mt$VTM.votes.w mt$HETe.w
Estimates RxC vote transfer matrices (ecological contingency tables) with tslphom_joint
tslphom_joint( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )tslphom_joint( votes_election1, votes_election2, integers = FALSE, solver = "lp_solve", integers.solver = "symphony", ... )
votes_election1 |
data.frame (or matrix) of order IxJ with the counts to be initially
mapped to rows. When estimating vote transfer matrices, the votes gained by
the J political options competing on election 1 (or origin) in the I
territorial units considered. The sum by rows of |
votes_election2 |
data.frame (or matrix) of order IxK with the counts to be initially mapped
to columns. When estimating vote transfer matrices, the votes gained by
the K political options competing on election 2 (or destination) in the I
territorial units considered. The sum by rows of |
integers |
A |
solver |
A character string indicating the linear programming solver to be used, only
|
integers.solver |
A character string indicating the linear programming solver to be used to approximate
to the closest integer solution, only |
... |
Other arguments to be passed to the function. Not currently used. |
A list with the following components
VTM.votes |
A matrix of order JxK with the estimated cross-distribution of votes of elections 1 and 2. |
HETe |
The estimated heterogeneity index associated to the |
VTM12 |
The matrix of order JxK with the estimated row-standardized proportions of vote transitions from election 1 to election 2 associated to the |
VTM21 |
The matrix of order KxJ with the estimated row-standardized proportions of vote transitions from election 2 to election 1 associated to the |
VTM.votes.units |
An array of order JxKxI with the estimated matrix of cross-distributions of votes of elections 1 and 2 attained for each unit after congruently adjusting the lphom_joint() initial estimate. |
EHet12 |
A matrix of order IxK measuring in each unit a distance to the homogeneity hypothesis. That is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results in each territorial unit for each option of election two. The matrix Eik. |
EHet21 |
A matrix of order IxJ measuring in each unit a distance to the homogeneity hypothesis. That is, the differences under the homogeneity hypothesis between the actual recorded results and the expected results in each territorial unit for each option of election one. The matrix Eij. |
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. |
solution_init |
A list with the main outputs produced by lphom_joint(). |
Jose M. Pavia, [email protected]
Rafael Romero [email protected]
Pavia, JM and Romero, R (2024). Symmetry estimating RxC vote transfer matrices from aggregate data. Journal of the Royal Statistical Society, Series A – Statistics in Society, forthcoming. doi:10.1093/jrsssa/qnae013
tslphom lphom_dual tslphom_dual nslphom_dual lphom_joint nslphom_joint
Other linear programing ecological inference functions:
lclphom(),
lp_apriori(),
lphom_dual(),
lphom_joint(),
lphom(),
nslphom_dual(),
nslphom_joint(),
nslphom(),
rslphom(),
tslphom_dual(),
tslphom()
x <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- tslphom_joint(x, y) mt$VTM.votes mt$HETex <- France2017P[, 1:8] y <- France2017P[, 9:12] y[,1] <- y[,1] - (rowSums(y) - rowSums(x)) mt <- tslphom_joint(x, y) mt$VTM.votes mt$HETe