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",
...
)A list with the following components
A matrix of order J'xK' (where J'=J-1 or J and K'=K-1 or K) with the estimated percentages of row-standardized vote transitions from election 1 to election 2.
In raw, regular, ordinary and enriched scenarios when the percentage of net entries is small, less than 1% of the census in all units,
net entries are omitted (i.e., the number of rows of VTM is equal to J1) even when estimates for net entries different from zero are obtained. Likewise, in the same scenarios when the percentage of net exits is small, less than 1%
of the census in all units, net exits are omitted (i.e., the number of rows of VTM is equal to K2) even when estimates for net exits different from zero are obtained.
A matrix of order J'xK' (where J'=J-1 or J and K'=K-1 or K) with the estimated vote transitions from election 1 to election 2.
In raw, regular, ordinary and enriched scenarios when the percentage of net entries is small, less than 1% of the census,
net entries are omitted (i.e., J = J1) even when estimates for net entries different from zero are obtained. Likewise, in the same scenarios when the percentage of net exits is small, less than 1%
of the census, net exits are omitted (i.e., K = K2) even when estimates for net exits different from zero are obtained.
A matrix of order KxJ with the estimated percentages of the origin of the votes obtained for the different options of election 2.
The estimated heterogeneity index as defined in equation (15) of Pavia and Romero (2022).
A matrix of order JxK with the estimated proportions of row-standardized vote transitions from election 1 to election 2, including in raw, regular, ordinary and enriched scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units.
A matrix of order JxK with the estimated vote transitions from election 1 to election 2, including in raw, regular, ordinary and enriched scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units.
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.
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.
A matrix of order JxK with the estimated proportions of vote transitions from election 1 to election 2, including in raw, regular, ordinary and enriched scenarios the row and the column corresponding to net_entries and net_exits even when they are really small, less than 1% in all units, corresponding to the final iteration.
Array of order JxKx(iter+1) (where iter is the efective number of iterations performed) of the intermediate estimated matrices corresponding to each iteration.
Numeric vector of length iter+1 with the HETe coefficients corresponding to the matrices in VTM.sequence.
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.
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.
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.
The real final number of iterations performed before ending the process.
A matrix of order Ix(iter+1) with the number of iteration corresponding to the solution selected for each unit in each iteration.
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 VTM.prop.units or VTM.votes.units.
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.
A list containing all the objects with the values used as arguments by the function.
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.
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.
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.
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.
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.
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.
A character string indicating the level of information available
in votes_election1 and votes_election2 regarding new entries
and exits of the election censuses between the two elections.
This argument allows, in addition to the options discussed in Pavia
(2023), three more options. This argument admits eleven different values:
raw, regular, ordinary, enriched, adjust1, adjust2,
simultaneous, semifull, full, fullreverse and gold.
Default, raw.
data.frame (or matrix) of order J0xK0 with an initial estimate of the
(row-standarized) global voter transition proportions/fractions, pjk0, between
the first J0 (election) options of election 1 and the first K0 (election) options
of election 2. This matrix can contain some missing values. When no a priori
information is available apriori is a null object. Default, NULL.
A number between 0 and 1, informing the relative weight the user assigns to the
apriori information. Setting lambda = 0 is equivalent to not having a priori
information (i.e., apriori = NULL). Default, 0.5.
A TRUE/FALSE value that informs whether census exits impact all the electoral options
in a (relatively) similar fashion in all iterations, including iteration 0 and
when deriving units tables. If uniform = TRUE typically at least one of the equations
among equations (6) to (11) of Pavia (2023) is included in the underlying model.
This parameter has no effect in simultaneous scenarios. It also has not impact
in raw and regular scenarios when no net exits are estimated by the function
from the provided information. Default, TRUE.
Default NULL. A list of vectors of length two, indicating the election options
for which no transfer of votes are allowed between election 1 and election 2.
For instance, when new_and_exit_voters is set to "semifull",
lphom implicitly states structural_zeros = list(c(J1, K2)).
A TRUE/FALSE value that indicates whether the problem is solved in integer values
in both iterations, including iteration zero (lphom) and the rest of iterations,
when deriving unit tables solutions. If integers = TRUE, the LP matrices are
approximated to the closest integer solution solving
the corresponding Integer Linear Program. Default, FALSE.
Maximum number of iterations to be performed. The process ends when either the
number of iterations reaches iter.max or when there is no error reduction in any
local unit between two consecutive iterations. By default, 1000.
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: previous and posterior.
Default, posterior.
A string argument that indicates whether the second step of the lphom_local algorithm
should be performed to solve potential indeterminacies of local solutions.
Default, "abs".
If distance.local = "abs" lphom_local selects in its second step the matrix
closer to the temporary global solution under L_1 norm, among the first step compatible matrices.
If distance.local = "max" lphom_local selects in its second step the matrix
closer to the temporary global solution under L_Inf norm, among the first step compatible matrices.
If distance.local = "none", the second step of lphom_local is not performed.
A TRUE/FALSE value that indicates if a summary of the results of the computations performed
to estimate net entries and exits should be printed on the screen. Default, TRUE.
A character string indicating the linear programming solver to be used, only
lp_solve and symphony are allowed. By default, lp_solve. The package Rsymphony
needs to be installed for the option symphony to be used.
A character string indicating the linear programming solver to be used for
approximating the LP solution to the closest integer solution.
Only symphony and lp_solve are allowed. By default, symphony.
The package Rsymphony needs to be installed for the
option symphony to be used. Only used when integers = TRUE.
Other arguments to be passed to the function. Not currently used.
Jose M. Pavia, pavia@uv.es
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.
Pavia, JM, and Romero, R (2024). Improving estimates accuracy of voter transitions. Two new algorithms for ecological inference based on linear programming, Sociological Methods & Research, 53(4), 1491–1533. tools:::Rd_expr_doi("10.1177/00491241221092725").
Pavia, JM. (2024). A local convergent ecological inference algorithm for RxC tables. The Journal of Mathematical Sociology, 49(1), 25-46. tools:::Rd_expr_doi("10.1080/0022250X.2024.2423943").
Pavia, JM (2024). Integer estimation of inner-cell values in RxC ecological tables. Bulletin of Sociological Methodology, 164(1), 97-121. tools:::Rd_expr_doi("10.1177/07591063241277064").
lphom tslphom nslphom rslphom
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_init
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