summary_rpm {rpm}

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")