Package 'rpm'

Title: Modeling of Revealed Preferences Matchings
Description: Statistical estimation of revealed preference models from data collected on bipartite matchings. The models are for matchings within a bipartite population where individuals have utility for people based on known and unknown characteristics. People can form a partnership or remain unpartnered. The model represents both the availability of potential partners of different types and preferences of individuals for such people. The software estimates preference parameters based on sample survey data on partnerships and population composition. The simulation of matchings and goodness-of-fit are considered. See Goyal, Handcock, Jackson, Rendall and Yeung (2022) <doi:10.1093/jrsssa/qnad031>.
Authors: Mark S. Handcock [aut, cre] , Ryan M. Admiraal [ctb], Fiona C. Yeung [ctb], Heide M. Jackson [ctb], Michael S. Rendall [ctb], Shuchi Goyal [ctb]
Maintainer: Mark S. Handcock <[email protected]>
License: GPL-3 + file LICENSE
Version: 0.7-3
Built: 2024-11-15 06:54:05 UTC
Source: CRAN

Help Index

Modeling of Revealed Preferences Matchings

Description

An integrated set of tools to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

Details

For a complete list of the functions, use library(help="rpm") or read the rest of the manual.

When publishing results obtained using this package the original authors are to be cited as:

Mark S. Handcock, Ryan M. Admiraal, Fiona C. Yeung, Heide M. Jackson, Michael S. Rendall and Shuchi Goyal (2022) rpm: Modeling of Revealed Preferences Matchings R package, Los Angeles, CA. Version 0.70, https://github.com/handcock/rpm.

All programs derived from this package must cite it. For complete citation information, use
citation(package="rpm").

For details on how to construct data for input to rpm() see the documentation:

help(fauxmatching)

For information on the current terms that can be used in formulas for rpm() see the documentation:

help("rpm-terms")

Value

No return value, called for side effects.

Author(s)

Mark S. Handcock <[email protected]>

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets, International Economic Review, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems, Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

Useful links:

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled",sampling_design="stock-flow")
summary(fit)

# For details on how to construct data for input:
help(fauxmatching)
# For information on the current terms that can be used in formulas:
help("rpm-terms")

ANOVA for rpm Fits

Description

Compute an analysis of variance table for one or more rpm fits.

Usage

## S3 method for class 'rpm'
anova(object, ...)

anova_rpmlist(object, ...)

Arguments

object, ...

objects of class rpm, usually, a result of a call to rpm.

Details

Specifying a single object gives a sequential analysis of variance table for that fit. That is, the reductions in the residual sum of squares as each term of the formula is added in turn are given in the rows of a table, plus the residual sum of squares.

The table will contain F statistics (and P values) comparing the mean square for the row to the residual mean square.

If more than one object is specified, the table has a row for the residual degrees of freedom and sum of squares for each model. For all but the first model, the change in degrees of freedom and sum of squares is also given. (This only make statistical sense if the models are nested.) It is conventional to list the models from smallest to largest, but this is up to the user.

Optionally the table can include test statistics. Normally the F statistic is most appropriate, which compares the mean square for a row to the residual sum of squares for the largest model considered. If scale is specified chi-squared tests can be used. Mallows' CpC_p statistic is the residual sum of squares plus twice the estimate of σ2\sigma^2 times the residual degrees of freedom.

If any of the objects do not have estimated log-likelihoods, produces an error, unless eval.loglik=TRUE.

Value

An object of class "anova" inheriting from class "data.frame".

Warning

The comparison between two or more models will only be valid if they are fitted to the same dataset. This may be a problem if there are missing values.

See Also

The model fitting function rpm, anova, logLik.rpm for adding the log-likelihood to an existing rpm object.

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled",sampling_design="stock-flow")
anova(fit)

Auxiliary for Controlling rpm

Description

Auxiliary function as user interface for fine-tuning RPM model fitting algorithm, which computes the MLPLE of the Revealed Preferences Model via optimization.

Usage

control.rpm(
  init_theta = NULL,
  algorithm = "NLOPT_LD_SLSQP",
  print_level = 0,
  xtol_rel = 1e-08,
  ftol_rel = 1e-08,
  ftol_abs = 1e-06,
  lower.bound = -10,
  upper.bound = 10,
  maxeval = 2000,
  bs.maxeval = 2000,
  bs.xtol_rel = 1e-08,
  bs.save.data = FALSE,
  check_derivatives = FALSE,
  bootstrap = TRUE,
  hessian = FALSE,
  seed = NULL,
  parallel.type = "PSOCK",
  parallel.ncores = 1,
  ncores = 1,
  constraints = c("none", "M_single"),
  logodds_single = FALSE,
  save.data = TRUE,
  robust.cov = FALSE,
  local_opts = list(algorithm = "NLOPT_LD_SLSQP", xtol_rel = 1e-07, maxeval = maxeval),
  nbootstrap = 50,
  nbootstrap.SD = 20,
  large.population.bootstrap = 5000,
  alpha = 0.05
)

Arguments

init_theta

vector; numeric vector of starting parameter values. This value and other possible starting values are applied to find a good optimizer. This can either have length the number of parameters corresponding to the terms in the formula or in addition the equilibrium constraints.
algorithm

string; The optimization algorithm to use. See nloptr::nloptr.print.options() and the NLopt website for a description of the algorithms.
print_level

integer; possible values: 0, 1, 2, or 3. This controls how much output is shown during the optimization process. Possible values: 0 (default): no output; 1: show iteration number and value of objective function; 2: 1 + show value of equalities/constraints; 3: 2 + show value of controls.
xtol_rel

scalar; Stop when an optimization step (or an estimate of the optimum) changes every parameter by less than xtol_rel multiplied by the absolute value of the parameter. If there is any chance that an optimal parameter is close to zero, you might want to set an absolute tolerance with xtol_abs as well. Criterion is disabled if xtol_rel is non-positive. Possible values: xtol_rel > 0. Default value: 1.0e-08.
ftol_rel

scalar; Stop when an optimization step (or an estimate of the optimum) changes the log-likelihood by less than ftol_rel multiplied by the absolute value of the log-likelihood.
ftol_abs

scalar; Stop when an optimization step (or an estimate of the optimum) changes the log-likelihood by less than ftol_abs. tolerance with xtol_abs as well. Criterion is disabled if ftol_abs is non-positive. Possible values: ftol_abs > 0. Default value: 1.0e-06.
lower.bound

numeric; lower bounds on the parameter estimates (that is, the beta and gamma parameters in the model). Can be a vector of the same size as the coefficient vector or a single number which is used for all bounds.
upper.bound

numeric; upper bounds on the parameter estimates (that is, the beta and gamma parameters in the model). Can be a vector of the same size as the coefficient vector or a single number which is used for all bounds.
maxeval

integer; Stop when the number of function evaluations exceeds maxeval. This is not a strict maximum: the number of function evaluations may exceed maxeval slightly, depending upon the algorithm. Criterion is disabled if maxeval is non-positive. Default value: 1000.
bs.maxeval

integer; Stop the bootstrap optimization when the number of function evaluations exceeds bs.maxeval. This is not a strict maximum: the number of function evaluations may exceed bs.maxeval slightly, depending upon the algorithm. Criterion is disabled if bs.maxeval is non-positive. Default value:50
bs.xtol_rel

scalar; Stop the bootstrap optimization when an optimization step (or an estimate of the optimum) changes every parameter by less than bs.xtol_rel multiplied by the absolute value of the parameter. See the parameter xtol_rel for details.
bs.save.data

logical; Should the bootstrapped data be saved in the bootstrap return list (as components Xdata and Zdata).
check_derivatives

logical; Compare the user-supplied analytic gradients with the finite difference approximations.
bootstrap

logical; If 'TRUE' use a bootstrap to compute the standard errors and associated covariance matrices. If 'FALSE' base the standard errors and associated covariance matrices on the Hessian of the (constrained) log-likelihood. In all cases the extended covariance matrix is returned in ext.covar.hessian. This is the matrix of parameters, log-odds of being single and the Lagrange multipliers.
hessian

logical; Depreciated. The negation of the 'bootstrap' argument.
seed

Seed value (integer) for the random number generator. See set.seed
parallel.type

The type of cluster to run. The typical choices are "MPI" and "PSOCK", where you must have "MPI" installed to use the former. The default is "PSOCK".
parallel.ncores

count; Depreciated. The renamed 'ncores' argument.
ncores

Number of processors to use in the bootstrap computations. The default is 1, that is no parallel processing.
constraints

string; Additional constraints to force the proportions of singles to match the (weighted) population estimates? This should not be required, but does stabilize the estimates in cases where there is much uncertainty. The possible values are "none" and "M_single" (the numbers of male singles of each type are reproduced). Note that adding constraints leads to over-constrained optimization which may fail.
logodds_single

logical; Should the log-odds ratio of being single relative to a randomly chosen person of the same sex from the the population be returned. If FALSE the log-odds of being single relative is returned. This is a pure preference parameter.
save.data

logical; Should the data be saved in the return list (as components Xdata and Zdata).
robust.cov

logical; Should the covariance matrix of the estimates be computed using a robust method (MASS::cov.mcd)? Only use if the bootstrap is unstable.
local_opts

list; list of options for nloptr sub-algorithm. See the nloptr package, but these are rarely changed.
nbootstrap

integer; Number of bootstrap resamples to take in the estimation of the covariance matrix of the parameter estimates.
nbootstrap.SD

integer; Number of bootstrap resamples to take in the estimation of the variances used in the studentized bootstrap. This is run for each nbootstrap sample and so is expensive.
large.population.bootstrap

integer; If the population size exceeds large.population.bootstrap then the large population approximation is used to simulate the matchings in the bootstrap. Otherwise the small population simulation is used (including the Gale-Shapley algorithm). The small population method is more accurate in smaller populations, with the default cutoff being 5000 people.
alpha

proportion; Type I error rate for the confidence intervals produced by the bootstrap.

Details

This function is only used within a call to the rpm function.

Some of the arguments are not yet fully implemented. It will evolve slower to incorporate more arguments as the package develops.

Value

A list with arguments as components.

See Also

rpm

Faux Data on Heterosexual Matching

Description

This data set represents a simulation of a bipartite matching. The data set is named fauxmatching. Its primary use is to illustrate the fitting of a Revealed Preference Matchings Model (rpm). The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. This provides such data for a matching between men and women of certain characteristics (or shared characteristics) of people of the opposite sex.

Usage

data(fauxmatching)

Format

fauxmatching is a list containing a pair of data.frame objects: Xdata and Zdata.

Xdata is for women. Each row is a woman, each column is a variable on that women or her partnerships. The women's ID variable s called pid and the variable with the ID of the women's partner is called pair_id. If the women is single the men's ID is NA. Zdata is for men. Each row is a man, each column is a variable on that men The men's ID variable is called pid.

pair_id

The ID of the person's partner. This is in both Xdata and Zdata.

sampled

The indicator that the person was sampled directly (as distinct from being included as the match of a directly sampled person. All single people are directly sampled. This is in both Xdata and Zdata.

Details

The pairings are determined by the pair_id variable in Xdata. If that variable is NA then the women is assumed to be single. If men are listed in Zdata and are not partnered then they are assumed single. Weights are specified by three optional variables in Xdata.

X_w

The weight variable for women. The sum of the weights of the sampled women is the number of women in the population.

Z_w

The weight variable for men. The sum of the weights of the sampled men is the number of men in the population.

pair_w

The weight variable for pairs.

Value

No return value, called for side effects.

Source

The data set is simulation based upon an rpm model fit to data from the 2008 SIPP.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
summary(fit)

This is the version of Gale-Shapley stable matching algorithm (translated from the Matlab code in Menzel (2015)).

Description

This code allows the self-matched option

Usage

Gale_Shapley(U, V, return.data.frame = FALSE, cpp = TRUE, nmax = 10 * nrow(U))

Arguments

U

The utility matrix for the women's side. Each row is a woman, each column is a man. The matrix entry (i,j) is the utility that woman i gains from pairing with man j. In other words, the utility is computed from woman i's perspective.
V

The utility matrix for the men's side. Each column is a man, each row is a woman. The matrix entry (i,j) is the utility that man j gains from pairing with woman i. In other words, the utility is computed from man j's perspective.
return.data.frame

logical Should a data.frame of the matching be returned instead of the paring matrix mu?
cpp

logical Should the Rcpp version of the code be used. This is much faster and uses a lot less memory.
nmax

count The maximum number of iterations of the inner loop within the Gale-Shapley algorithm. This can be reduced to speed up the algorithm at the potential cost of many partnerships being non-equilibruim.

Value

The function return depends on the return.data.frame value. If TRUE, it returns

data.frame

a two-column data.frame with the first column a women's index and the second column the men's index of their partner. It has as many rows as there are partnerships.

If FALSE, it returns the following matrix:

mu

If cpp=TRUE, a vector of length the number of women (nrow(U)) with the index of the matching man (i.e., the index is the row in V of the man). If there is no matching man, the index is 0. This can be used to reconstruct the matching matrix. If cpp=FALSE, the matching matrix, where 1 represents a pairing, 0 otherwise. Each row is a woman, each column is a man. The order of the rows is the same as the rows in U. The order of the columns is the same as the columns in V.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

rpm

Calculate goodness-of-fit statistics for Revealed Preference Matchings Model based on observed data

Description

gof.rpm ... It is typically based on the estimate from a rpm() call.

Usage

gof(object, ...)

## S3 method for class 'rpm'
gof(
  object,
  ...,
  empirical_p = TRUE,
  compare_sim = "sim-est",
  control = object$control,
  reboot = FALSE,
  verbose = FALSE
)

## S3 method for class 'gofrpm'
plot(x, ..., cex.axis = 0.7, main = "Goodness-of-fit diagnostics")

Arguments

object

list; an object of classrpm that is typically the result of a call to rpm().
...

Additional arguments, to be passed to lower-level functions.
empirical_p

logical; (Optional) If TRUE the function returns the empirical p-value of the sample statistic based on nsim simulations
compare_sim

string; describes which two objects are compared to compute simulated goodness-of-fit statistics; valid values are "sim-est": compares the marginal distribution of pairings in a simulated sample to the rpm model estimate of the marginal distribution based on that same simulated sample; mod-est: compares the marginal distribution of pairings in a simulated sample to the rpm model estimate used to generate the sample
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.
reboot

logical; if this is TRUE, the program will rerun the bootstrap at the coefficient values, rather than expect the object to contain a bs.results component with the bootstrap results run at the solution values. The latter is the default for rpm fits.
verbose

logical; if this is TRUE, the program will print out additional information, including data summary statistics.
x

a list, usually an object of class gofrpm
cex.axis

the magnification of the text used in axis notation;
main

Title for the goodness-of-fit plots.

Details

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This function simulates from such a model.

Value

gof.rpm returns a list consisting of the following elements:

observed_pmf

numeric matrix giving observed probability mass distribution over different household types
model_pmf

numeric matrix giving expected probability mass distribution from rpm model
obs_chi_sq

the count-based observed chi-square statistic comparing marginal distributions of the population the data and the model estimate
obs_chi_sq_cell

the contribution to the observed chi-squared statistic by household type
obs_kl

the Kullback-Leibler (KL) divergence computed by comparing the observed marginal distributions to the expected marginal distribution based on the rpm model estimate
obs_kl_cell

the contribution to the observed KL divergence by household type
empirical_p_chi_sq

the proportion of simulated chi-square statistics that are greater than or equal to the observed chi-square statistic
empirical_p_kl

the proportion of simulated KL divergences that are greater than or equal to the observed KL divergence
chi_sq_simulated

vector of size nsim storing all simulated chi-square statistics
kl_simulated

vector of size nsim storing all simulated KL divergences
chi_sq_cell_mean

Mean contributions of each household type to the simulated chi_sq statistic
chi_sq_cell_sd

Standard deviation of the contributions of each household type to the simulated chi_sq statistics
chi_sq_cell_median

Median contributions of each household type to the simulated chi_sq statistic
chi_sq_cell_iqr

Interquartile range of the contributions of each household type to the simulated chi_sq statistics
kl_cell_mean

Mean contributions of each household type to the simulated KL divergences
kl_cell_sd

Standard deviation of the contributions of each household type to the simulated KL divergencesc
kl_cell_median

Median contributions of each household type to the simulated KL divergences
kl_cell_iqr

Interquartile range of the contributions of each household type to the simulated KL divergences

Methods (by class)

  • gof(rpm): Calculate goodness-of-fit statistics for Revealed Preference Matchings Model based on observed data

Functions

  • plot(gofrpm): plot.gofrpm plots diagnostics such empirical p-value based on chi-square statistics and KL divergences. See rpm for more information on these models.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

Examples

library(rpm)

data(fauxmatching)
fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
a <- gof(fit)

Returns a list containing the terms in a given formula

Description

Returns a list containing the terms in a given formula

Usage

list_rhs.formula(object)

Arguments

object

formula A formula having a right-hand-side that can be interpretated as a rpm specification. returns a list containing terms in a given formula, handling + and - operators and parentheses, and keeping track of whether a term has a plus or a minus sign.

Value

list_rhs.formula returns a list of formula terms, with an additional numerical vector attribute "sign" with of the same length, giving the corresponding term's sign as +1 or -1.

A logLik method for ['rpm'] fits.

Description

A function to return the log-likelihood associated with an rpm fit

Usage

## S3 method for class 'rpm'
logLik(object, ...)

Arguments

object

An rpm fit, returned by rpm.
...

Other arguments to the likelihood functions.

Value

a logLik object.

See Also

logLik, logLikNull

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled",sampling_design="stock-flow")
logLik(fit)

Calculate the null model likelihood

Description

Calculate the null model likelihood

Usage

logLikNull(object, ...)

## S3 method for class 'rpm'
logLikNull(object, ...)

Arguments

object

a fitted model.
...

further arguments to lower-level functions.

logLikNull computes, when possible the log-probability of the data under the null model (reference distribution).

Value

logLikNull returns an object of type logLik if it is able to compute the null model probability, and NA otherwise.

Methods (by class)

  • logLikNull(rpm): A method for ['rpm'] fits to compute the null likelihood (that is, relative to the constant only model).

['print'] objects to the ['message'] output.

Description

A thin wrapper around ['print'] that captures its output and prints it as a ['message'], usually to STDERR. Tis is part of ['statnet.common'].

Usage

message_print(..., messageArgs = NULL)

Arguments

...

arguments to ['print'].
messageArgs

a list of arguments to be passed directly to ['message'].

Value

No return value, called for side effects.

Examples

cat(1:5)

print(1:5)
message_print(1:5) # Looks the same (though may be in a different color on some frontends).

suppressMessages(print(1:5)) # Still prints
suppressMessages(message_print(1:5)) # Silenced

Micro simulate a population from a Revealed Preference Matchings Model

Description

microsimulate simulates a population of the pairs and singles from a Revealed Preference Matchings Model. It is typically based on the estimate from a rpm() call.

Usage

microsimulate(
  object,
  nsim = 1,
  seed = NULL,
  pmfW_N = NULL,
  pmfM_N = NULL,
  large.population = TRUE,
  bootstrap = FALSE,
  control = control.rpm(),
  counts.only = FALSE,
  verbose = FALSE
)

Arguments

object

list; an object of classrpm that is typically the result of a call to rpm().
nsim

Number of matchings to be randomly drawn from the given model on the set of all matchings / singles.
seed

integer; (Optional) random number seed.
pmfW_N

vector; The population count of the number of women of each type. This should be compatible with the type in the object.
pmfM_N

vector; The population count of the number of men of each type. This should be compatible with the type in the object.
large.population

logical; If TRUE a large population approximation is used to generate the matchings (rather than the individual level generation of utilities). This is much faster and uses a lot less memory. It is TRUE by default. If used, a sample is drawn rather than the population being returned. The sample size is controlled by pmfW_N and pmfM_N.
bootstrap

logical; If TRUE the original population is sampled from. If FALSE the population underlying the fitted model is sampled from.
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.
counts.only

logical; If TRUE only the matrices of counts and the PMF of the population of households is returned. If FALSE It is FALSE by default.
verbose

logical; Should verbose messages be printed out.

Details

The function requites the numbers of women of each type and the number of men of each type to be specified.

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This function simulates a population from such a model.

Value

A list of lists, each a simulation from the population. Each of the simulation lists contains components population being a list with components Xdata and Zdata (for use with rpm()).

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

Examples

library(rpm)

data(fauxmatching)
fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
num_women = fit$N*exp(fit$gw)
num_men   = fit$N*exp(fit$gm)
pmfW_N <- round(fit$pmfW * num_women)
pmfM_N <- round(fit$pmfM * num_men)
a <- microsimulate(fit, pmfW_N=pmfW_N, pmfM_N=pmfM_N)

Fit a Revealed Preference Matchings Model

Description

rpm estimates the parameters of a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

Usage

rpm(
  formula,
  Xdata,
  Zdata,
  Xid = NULL,
  Zid = NULL,
  pair_id = NULL,
  X_w = NULL,
  Z_w = NULL,
  pair_w = NULL,
  sampled = NULL,
  sampling_design = "stock-flow",
  fixed.margins = NULL,
  control = control.rpm(),
  verbose = FALSE
)

Arguments

formula

formula; an formula object, of the form ~ <model terms>. For the details on the possible <model terms>, see rpm-terms.
Xdata

data.frame for women. Each row is a woman, each column is a variable on that women or her partnerships. It must contain the women's ID variable (see Xid) and a variable with the ID of the women's partner. If the women is single the men's ID should be NA.
Zdata

data.frame for men. Each row is a man, each column is a variable on that men It must contain the men's ID variable (see Zid).
Xid

string The name of the variable in Xdata containing the IDs of the women.
Zid

string The name of the variable in Zdata containing the IDs of the men.
pair_id

string The name of the variable in Xdata containing the ID of the men paired with the women in Xid. If the women is not paired it must be NA.
X_w

string The name of the variable in Xdata containing the individual weight of the women. If this is NULL then it is assumed the sample is unweighted from a population with 2000 women in it.
Z_w

string The name of the variable in Zdata containing the individual weight of the man If this is NULL then it is assumed the sample is unweighted from a population with 2000 men in it.
pair_w

string The name of the variable in Xdata containing the pair weight of that women. If the women is not paired it should be NA. If this is NULL then it is computed from the individual weights using the sampling_design. Note that the pair weights currently do not play a role in the estimation. They do in the quasi-likelihood version of the code. If this is NULL then it is assumed the sample is unweighted from a population with 2000 men in it.
sampled

string The name of the logical variable in Xdata and Zdata containing the indicator that the person was sampled directly (as distinct from being included as the match of a directly sampled person. All single people are directly sampled.
sampling_design

string; The name of the sampling protocol used to select the survey data. Valid values are "stock-flow" (default) (individuals are sampled, data contains both singles and couples); "stock-stock" (households are sampled, each household can be a single or a couple); "census" (the sample is a census of the population of people).
fixed.margins

list If not NULL the numbers of men and women (i.e, in pmfW and pmfM) are assumed determined by outside information and are hence fixed. In this case fixed.margins should be a list with two elements. The first is a vector of women's margins for each type and the second is the men's margins for each type. The default, NULL, means these are estimated from sample data.
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.
verbose

logical; if this is TRUE, the program will print out additional information, including data summary statistics.

Details

The pairings are determined by the pair_id variable in Xdata. If that variable is NA then the women is assumed to be single. If men are listed in Zdata and are not partnered then they are assumed single. Weights are specified by three optional variables in Xdata.

X_w

: This is character string of the name of the weight variable for women. The sum of the weights should be the number of women in the population.

Z_w

: This is character string of the name of the weight variable for men. The sum of the weights should be the number of men in the population.

pair_w

: This is character string of the name of the weight variable for pairs.

Value

rpm returns an object of class rpm.object that is a list consisting of the following elements:

coef

The maximum psuedo-likelihood estimate of θ\theta, the vector of coefficients for the model parameters. This includes the model β\beta and the model Γ\Gamma.
coefficients

The bias-corrected bootstrap estimate of θ\theta, the vector of coefficients for the model parameters. This includes the model β\beta and the model Γ\Gamma.
loglik

The value of the maximized log-likelihood.
exitflag

integer value with the status of the optimization (4 is success as xtol_rel or xtol_abs was reached). Other codes are 1 = generic success; 2 = optimization stopped because ftol_rel or ftol_abs was reached; 3 = optimization stopped because stopval was reached; 4 = optimization stopped because xtol_rel or xtol_abs was reached; 5 = optimization stopped because maxeval was reached; 6 = optimization stopped because maxtime was reached.
call

the call that was made to nloptr.
x0

vector with starting values for the optimization.
message

more informative message with the status of the optimization.
iterations

number of iterations that were executed.
objective

value if the objective function in the solution.
solution

optimal value of the controls.
version

version of NLopt that was used.
covar

Approximate covariance matrix of the estimates.
eq

Values from the equality constraints. Larger values indicate non-convergence.
sample

A matrix with the number of rows the MCMC sample size and the number of rows the number of parameters.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

control.rpm, summary.rpm, print.rpm

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled",sampling_design="stock-flow")
summary(fit)

Fit a Revealed Preference Matchings Model

Description

rpm_MLPLE estimates the parameters of a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

Usage

rpm_MLPLE(
  formula,
  Xdata,
  Zdata,
  Xid = NULL,
  Zid = NULL,
  pair_id = NULL,
  X_w = NULL,
  Z_w = NULL,
  pair_w = NULL,
  sampled = NULL,
  sampling_design = "stock-flow",
  fixed.margins = fixed.margins,
  control = control.rpm(),
  verbose = FALSE
)

Arguments

formula

formula; an formula object, of the form ~ <model terms>. For the details on the possible <model terms>, see rpm-terms.
Xdata

data.frame for women. Each row is a woman, each column is a variable on that women or her partnerships. It must contain the women's ID variable (see Xid) and a variable with the ID of the women's partner. If the women is single the men's ID should be NA.
Zdata

data.frame for men. Each row is a man, each column is a variable on that men It must contain the men's ID variable (see Zid).
Xid

string The name of the variable in Xdata containing the IDs of the women.
Zid

string The name of the variable in Zdata containing the IDs of the men.
pair_id

string The name of the variable in Xdata containing the ID of the men paired with the women in Xid. If the women is not paired it must be NA.
X_w

string The name of the variable in Xdata containing the individual weight of the women. If this is NULL then it is assumed the sample is unweighted from a population with 2000 women in it.
Z_w

string The name of the variable in Zdata containing the individual weight of the man If this is NULL then it is assumed the sample is unweighted from a population with 2000 men in it.
pair_w

string The name of the variable in Xdata containing the pair weight of that women. If the women is not paired it should be NA. If this is NULL then it is computed from the individual weights using the sampling_design. Note that the pair weights currently do not play a role in the estimation. They do in the quasi-likelihood version of the code. If this is NULL then it is assumed the sample is unweighted from a population with 2000 men in it.
sampled

string The name of the logical variable in Xdata and Zdata containing the indicator that the person was sampled directly (as distinct from being included as the match of a directly sampled person. All single people are directly sampled.
sampling_design

string; The name of the sampling protocol used to select the survey data. Valid values are "stock-flow" (default) (individuals are sampled, data contains both singles and couples); "stock-stock" (households are sampled, each household can be a single or a couple); "census" (the sample is a census of the population of people).
fixed.margins

list If not NULL the numbers of men and women (i.e, in pmfW and pmfM) are assumed determined by outside information and are hence fixed. In this case fixed.margins should be a list with two elements. The first is a vector of women's margins for each type and the second is the men's margins for each type. The default, NULL, means these are estimated from sample data.
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.
verbose

logical; if this is TRUE, the program will print out additional information, including data summary statistics.

Details

It is usually called via the rpm function.

The pairings are determined by the pair_id variable in Xdata. If that variable is NA then the women is assumed to be single. If men are listed in Zdata and are not partnered then they are assumed single. Weights are specified by three optional variables in Xdata.

X_w

: This is character string of the name of the weight variable for women. The sum of the weights should be the number of women in the population.

Z_w

: This is character string of the name of the weight variable for men. The sum of the weights should be the number of men in the population.

pair_w

: This is character string of the name of the weight variable for pairs.

Value

rpm returns an object of class rpm.object that is a list consisting of the following elements:

coefficients

The bias-corrected bootstrap estimate of θ\theta, the vector of coefficients for the model parameters. This includes the model β\beta and the model Γ\Gamma.
loglik

The value of the maximized log-likelihood.
exitflag

integer value with the status of the optimization (4 is success as xtol_rel or xtol_abs was reached). Other codes are 1 = generic success; 2 = optimization stopped because ftol_rel or ftol_abs was reached; 3 = optimization stopped because stopval was reached; 4 = optimization stopped because xtol_rel or xtol_abs was reached; 5 = optimization stopped because maxeval was reached; 6 = optimization stopped because maxtime was reached.
call

the call that was made to nloptr.
x0

vector with starting values for the optimization.
message

more informative message with the status of the optimization.
iterations

number of iterations that were executed.
objective

value if the objective function in the solution.
solution

optimal value of the controls.
version

version of NLopt that was used.
covar

Approximate covariance matrix of the estimates.
eq

Values from the equality constraints. Larger values indicate non-convergence.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

control.rpm, summary.rpm, print.rpm

Examples

library(rpm)

data(fauxmatching)
fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled",sampling_design="stock-flow")
summary(fit)

Terms used in a Revealed Preference Matchings Model

Description

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

Details

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This page describes the possible terms (and hence linear utility functions) included in rpm package.

Value

No return value, called for side effects.

Specifying models

Terms to rpm are specified by a formula to represent the pairings and covariates This is done via a formula, that is, an formula object, of the form ~ <term 1> + <term 2> ..., where <term 1>, <term 2>, etc, are each terms chosen from the list given below.

absdiff(attr) (quantitative attribute), absdiff(attr) (quantitative attribute)

Absolute difference: The attr argument specifies a quantitative attribute This term adds one statistic to the model equaling abs(attr[i]-attr[j]) for all women-man dyad (i,j).

W_greaterthan(attr)

Women's value greater than the men's value Adds one statistic indicating if the women's value exceeds the men's value.

M_greaterthan(attr)

Men's value greater than the women's value Adds one statistic indicating if the men's value exceeds the women's value.

W_atleast(attr,threshold=0)

Values greater than or equal to a threshold Adds one statistic indicating if the women's value of the attribute equals or exceeds threshold.

W_atmost(threshold=0)

Values less than or equal to a threshold Adds one statistic indicating if the women's value equals or is exceeded by threshold.

W_cov(attr) (quantitative attribute), W_cov(attr) (quantitative attribute)

Main effect of a covariate for women: The attr argument specifies a quantitative attribute This term adds a single statistic equaling the value of attr(i) for women ii in the dyad. For categorical attributes, see W_factor.

diff(attr) (quantitative attribute), diff(attr) (quantitative attribute)

Woman's Gap: The attr argument specifies a quantitative attribute This term adds one statistic to the model being attr[i]-attr[j] for women ii and man jj. Specifically, it is the excess of the woman's value over the man's value.

WtoM_diff(attr, diff) (ordinal categorical attribute), WtoM_diff(attr) (ordinal categorical discrete attribute)

Woman's Gap: The attr argument specifies a ordinal categorical attribute This term adds one statistic to the model being an indicator that attr[i]=attr[j]+diff for women ii and man jj. Specifically, it indicates if the woman's value is diff higher than the man's value.

MtoW_diff(attr, diff) (ordinal categorical attribute), MtoW_diff(attr) (ordinal categorical discrete attribute)

Man's Gap: The attr argument specifies a ordinal categorical attribute This term adds one statistic to the model being an indicator that attr[j]=attr[i]+diff for women ii and man jj. Specifically, it indicates if the man's value is diff higher than the woman's value.

MtoW_diff(attr) (quantitative attribute), MtoW_diff(attr) (quantitative attribute)

Difference: The attr argument specifies a quantitative attribute This term adds one statistic to the model attr[j]-attr[i] for women ii and man jj.

W_factor(attr, base=1, levels=-1) (categorical attribute), W_factor(attr, base=1, levels=-1) (categorical attribute)

Factor attribute effect for women: The attr argument specifies a categorical attribute This term adds multiple statistics to the model, one for each of (a subset of) the unique values of the attr attribute. Each of these statistics indicates if the women's has that attribute.

homophily(attr)

Uniform homophily effect: The attr argument specifies a categorical attribute This term adds one statistic to the model indicating that the dyad matches on that attribute.

match(attr, diff=FALSE, collapse=NULL)

Attribute-based homophily effect: The attr argument specifies a categorical attribute This term adds one statistic to the model for each categorical level, unless diff is set to TRUE, in which case the term adds multiple statistics to the model, one for each of (a subset of) the unique values of the attr attribute. If diff is set to TRUE, the optional argument collapse control what dyads are collapsed (or pooled). Specifically, it is a list of indices of attribute values which are to be collapsed into a single term. For example, collapse=list(c(1,4)) will collapse the (1,1) and the (4,4) dyads into a single term (and group). Multiple lists can be included with arbitrary numbers of dyads in a group.

mix(attr, base=NULL, collapse=NULL)

Attribute mixing: The attr argument specifies a categorical attributes By default, this term adds one statistic to the model for each possible pairing of attribute values. The statistic indicates if the dyad has that pairing of values. In other words, this term produces one statistic for every entry in the mixing matrix for the attribute(s). The ordering of the attribute values is lexicographic: alphabetical (for nominal categories) or numerical (for ordered categories). The optional argument base control what statistics are included in the model, specifically it lists the index of the omitted terms (in order). For example, base=2 omits the second term. The optional argument collapse control what dyads are collapsed (or pooled). Specifically, it is a list of lists. Each element of the list is a list of dyads which are to be collapsed into a single term. For example, collapse=list(list(c(1,4),c(2,4))) will collapse the (1,4) and the (2,4) dyads into a single term (and group). Multiple lists can be included with arbitrary numbers of dyads in a group.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

rpm package, rpm

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
summary(fit)

Creates a model function list for the continuous terms in a Revealed Preference Matchings Model

Description

rpm.model.matrix assumes a bipartite network (i.e. two-sided matching market) It creates a model matrix according to the formula passed in. See rpm-terms for a description of the possible terms.

Usage

rpm.model.functions(model.terms, control)

Arguments

model.terms

For the details on the possible countinuous <model terms>, see rpm-terms. This includes the covariates used to construct the model matrix. They are used in conjunction with the model terms.
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.

Value

A list of model terms as bivariate functions.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

rpm

Examples

# nothing yet

Creates a model matrix to estimate the parameters of a Revealed Preference Matchings Model

Description

rpm.model.matrix assumes a bipartite network (i.e. two-sided matching market) It creates a model matrix according to the formula passed in. See rpm-terms for a description of the possible terms.

Usage

rpm.model.matrix(model.terms, Xall, Zall, intercept = TRUE)

Arguments

model.terms

For the details on the possible <model terms>, see rpm-terms. This includes the covariates used to construct the model matrix. They are used in conjunction with the model terms.
Xall

the unique types of women
Zall

the unique types of men
intercept

logical; If TRUE, the default, an intercept term is prepended.

Value

A list consists of the following elements:

X

the model matrix for women.
Z

the model matrix for men.
Xnames

the names of the covariates for women.
Znames

the names of the covariates for men.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

rpm

Examples

# nothing yet

Compute the population distribution of pairs and singles from a Revealed Preference Matchings Model

Description

rpmpopulationpmf computes the probability mass function for a population of the pairs and singles from a Revealed Preference Matchings Model based on arbitary availability distribution and preferences. It is typically based on the estimate from a rpm() call.

Usage

rpmpopulationpmf(
  object,
  N = 2000,
  num_women = NULL,
  num_men = NULL,
  pmfW = NULL,
  pmfM = NULL,
  verbose = FALSE
)

Arguments

object

list; an object of classrpm that is typically the result of a call to rpm().
N

integer; The total population size. This must be set. The number of women and men are derived from the (weighted) data.
num_women

integer; (Optional) The number of women in the population.
num_men

integer; (Optional) The number of men in the population.
pmfW

vector; (Optional) The population proportions of the numbers of women of each type. This should be compatible with the type in the object.
pmfM

vector; (Optional) The population proportions of the numbers of men of each type. This should be compatible with the type in the object.
verbose

logical; Should verbose messages be printed out.

Details

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This function simulates from such a model.

Value

A list of data.frame, each a simulation from the population.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
a <- rpmpopulationpmf(fit)

Simulate a sample of pairs and singles from a Revealed Preference Matchings Model

Description

simulate.rpm simulates a population of the pairs and singles from a Revealed Preference Matchings Model. It is typically based on the estimate from a rpm() call.

Usage

## S3 method for class 'rpm'
simulate(
  object,
  nsim = 1,
  seed = NULL,
  ...,
  N = NULL,
  num_women = NULL,
  num_men = NULL,
  pmfW = NULL,
  pmfM = NULL,
  large.population = TRUE,
  num_sampled = NULL,
  bootstrap = FALSE,
  sampling_design = NULL,
  control = control.rpm(),
  verbose = FALSE
)

Arguments

object

list; an object of classrpm that is typically the result of a call to rpm().
nsim

Number of matchings to be randomly drawn from the given model on the set of all matchings / singles.
seed

integer; (Optional) random number seed.
...

Additional arguments, to be passed to lower-level functions.
N

integer; The total population size. This must be set. The number of women and men are derived from the (weighted) data.
num_women

integer; (Optional) The number of women in the population.
num_men

integer; (Optional) The number of men in the population.
pmfW

vector; (Optional) The population proportions of the numbers of women of each type. This should be compatible with the type in the object.
pmfM

vector; (Optional) The population proportions of the numbers of men of each type. This should be compatible with the type in the object.
large.population

logical; If TRUE a large population approximation is used to generate the matchings (rather than the individual level generation of utilities). This is much faster and uses a lot less memory. It is TRUE by default. If used, a sample is drawn rather than the population being returned. The sample size is controlled by num_sampled.
num_sampled

integer; The size of the sample to be drawn. For "stock-stock" sampling this is the number of sampled households. For "stock-flow" it is the number of sampled people. For "census" it is the total population size, N. If NULL the size is the same as the passed fitted object (that is, the original data), although this is only a guess and it should be explicitly set.
bootstrap

logical; If TRUE the original population is sampled from. If FALSE the population underlying the fitted model is sampled from.
sampling_design

string; The name of the sampling protocol used to select the survey data. Valid values are "stock-flow" (individuals are sampled, data contains both singles and couples); "stock-stock" (households are sampled, each household can be a single or a couple); "census" (the sample is a census of the population of people). The final option, the default, is NULL whereby the design is taken from the passed object.
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.
verbose

logical; Should verbose messages be printed out.

Details

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This function simulates from such a model.

Value

A list of data.frame, each a simulation from the population.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

Examples

library(rpm)

data(fauxmatching)
fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
a <- simulate(fit)

Summarize Revealed Preference Matchings data via a Model Specification

Description

summary_rpm produces tabular summaries of data revealed preference matchings based on a formula specifying a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities.

Usage

summary_rpm(
  formula,
  Xdata,
  Zdata,
  Xid = NULL,
  Zid = NULL,
  pair_id = NULL,
  X_w = NULL,
  Z_w = NULL,
  pair_w = NULL,
  sampled = NULL,
  sampling_design = "stock-flow",
  control = control.rpm(),
  verbose = FALSE
)

Arguments

formula

formula; an formula object, of the form ~ <model terms>. For the details on the possible <model terms>, see rpm-terms.
Xdata

data.frame for women. Each row is a woman, each column is a variable on that women or her partnerships. It must contain the women's ID variable (see Xid) and a variable with the ID of the women's partner. If the women is single the men's ID should be NA.
Zdata

data.frame for men. Each row is a man, each column is a variable on that men It must contain the men's ID variable (see Zid).
Xid

string The name of the variable in Xdata containing the IDs of the women.
Zid

string The name of the variable in Zdata containing the IDs of the men.
pair_id

string The name of the variable in Xdata containing the ID of the men paired with the women in Xid. If the women is not paired it must be NA.
X_w

string The name of the variable in Xdata containing the individual weight of the women. If this is NULL then it is assumed the sample is unweighted from a population with 2000 women in it.
Z_w

string The name of the variable in Zdata containing the individual weight of the man If this is NULL then it is assumed the sample is unweighted from a population with 2000 men in it.
pair_w

string The name of the variable in Xdata containing the pair weight of that women. If the women is not paired it should be NA. If this is NULL then it is computed from the individual weights using the sampling_design. Note that the pair weights currently do not play a role in the estimation. They do in the quasi-likelihood version of the code. If this is NULL then it is assumed the sample is unweighted from a population with 2000 men in it.
sampled

string The name of the logical variable in Xdata and Zdata containing the indicator that the person was sampled directly (as distinct from being included as the match of a directly sampled person. All single people are directly sampled.
sampling_design

string; The name of the sampling protocol used to select the survey data. Valid values are "stock-flow" (default) (individuals are sampled, data contains both singles and couples); "stock-stock" (households are sampled, each household can be a single or a couple); "census" (the sample is a census of the population of people).
control

A list of control parameters for algorithm tuning. Constructed using control.rpm, which should be consulted for specifics.
verbose

logical; if this is TRUE, the program will print out additional information, including data summary statistics.

Details

The pairings are determined by the pair_id variable in Xdata. If that variable is NA then the women is assumed to be single. If men are listed in Zdata and are not partnered then they are assumed single. Weights are specified by three optional variables in Xdata.

X_w

: This is character string of the name of the weight variable for women. The sum of the weights should be the number of women in the population.

Z_w

: This is character string of the name of the weight variable for men. The sum of the weights should be the number of men in the population.

pair_w

: This is character string of the name of the weight variable for pairs.

Value

summary returns a list with many components, like rpm object without the model estimates. In particular it includes stats and popstats. stats is the named vector of sample statistics from the model. while popstats is the named vector of population statistics from the model. It alos includes counts and pmf. Each of these is a contingency table in array representation of S3 class c("xtabs", "table"), with a "call"

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

See Also

control.rpm, summary.rpm, rpm

Examples

library(rpm)
data(fauxmatching)
summary_rpm(~match("edu") + WtoM_diff("edu",3),
        Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
        X_w="X_w", Z_w="Z_w",
        pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
        sampled="sampled",sampling_design="stock-flow")

Summarizing rpm Model Fits

Description

[base::summary()] method for [rpm()] fits.

Usage

## S3 method for class 'rpm'
summary(
  object,
  ...,
  digits = max(3, getOption("digits") - 3),
  correlation = FALSE,
  covariance = FALSE,
  include.single = TRUE
)

## S3 method for class 'summary.rpm'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  correlation = FALSE,
  covariance = FALSE,
  signif.stars = getOption("show.signif.stars"),
  eps.Pvalue = 1e-04,
  print.header = TRUE,
  print.formula = FALSE,
  print.fitinfo = TRUE,
  print.coefmat = TRUE,
  print.message = TRUE,
  print.deviances = TRUE,
  print.drop = TRUE,
  ...
)

Arguments

object

an object of class rpm, usually, a result of a call to [rpm()].
...

For [summary.rpm()] additional arguments are passed to [logLik.rpm()]. For [print.summary.rpm()], to [stats::printCoefmat()].
digits

significant digits for coefficients. The default is max(3, getOption("digits")-3).
correlation

logical whether the correlation matrix of the estimated parameters should be printed (T or F); default=FALSE
covariance

logical whether the covariance matrix of the estimated parameters should be printed (T or F); default=FALSE
include.single

logical; if 'TRUE', include in the summary table the coefficients of the log-odds of being single for each category of women and men.
x

object of class 'summary.rpm' returned by [summary.rpm()].
signif.stars

whether to print dots and stars to signify statistical significance. See [print.summary.lm()].
eps.Pvalue

pp-values below this level will be printed as "<'eps.Pvalue'".
print.formula, print.fitinfo, print.coefmat, print.message, print.deviances, print.drop, print.header

which components of the fit summary to print.

Details

[summary.rpm()] tries to be smart about formatting the coefficients, standard errors, etc.

The default printout of the summary object contains the call, number of iterations used, null and residual deviances, and the values of AIC and BIC. The coefficient table contains the following columns:

- 'Estimate', 'Std. Error' - parameter estimates and their standard errors - 'z value', 'Pr(>|z|)' - z-test and p-values

Value

The function [summary.rpm()] computes and returns a list of summary statistics of the fitted [rpm()] model given in 'object'. Note that for backwards compatibility, it returns the coefficient table.

The returned object is a list of class "summary.rpm" with the following elements:

formula

ERGM model formula
digits

the 'digits' inputted to <summary.rpm> or the default value (despite the fact the digits will be 5)
correlation, covariance

whether to print correlation/covariance matrices of the estimated parameters
iterations

object$iterations
control

the [control.rpm()] object used
samplesize

MCMC sample size
message

optional message on the validity of the standard error estimates
aic.null, bic.null

values of AIC and BIC for the null model
aic, bic

values of AIC and BIC
coefficients

data frames with model parameters and associated statistics
asycov

asymptotic covariance matrix
asyse

asymptotic standard error matrix
offset, drop, estimate, iterations, mle.lik, null.lik

see documentation of the object returned by [rpm()]

See Also

The model fitting function [rpm()], [print.rpm()], and [base::summary()]. Function [stats::coef()] will extract the data frame of coefficients with standard errors, t-statistics and p-values.

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled",sampling_design="stock-flow")
summary(fit)

Extract or replace the *ult*imate (last) element of a vector or a list, or an element counting from the end.

Description

Extract or replace the *ult*imate (last) element of a vector or a list, or an element counting from the end.

Usage

ult(x, i = 1L) <- value

ult(x, i = 1L)

Arguments

x

a vector or a list.
i

index from the end of the list to extract or replace (where 1 is the last element, 2 is the penultimate element, etc.).
value

Replacement value for the 'i'th element from the end.

Value

An element of 'x'.

Note

Due to the way in which assigning to a function is implemented in R, 'ult(x) <- e' may be less efficient than 'x[[length(x)]] <- e'.

Examples

(x <- c(1:5))
(ult(x) <- 6)
(ult(x, 2) <- 7) # 2nd last.
x



x <- 1:5
(last <- ult(x))
(penultimate <- ult(x, 2)) # 2nd last.