Package 'affinitymatrix'

Estimate Dupuy and Galichon's model

Description

This function estimates the affinity matrix of the matching model of Dupuy and Galichon (2014), performs the saliency analysis and the rank tests. The user must supply a matched sample that is treated as the equilibrium matching of a bipartite one-to-one matching model without frictions and with Transferable Utility. For the sake of clarity, in the documentation we take the example of the marriage market and refer to "men" as the observations on one side of the market and to "women" as the observations on the other side. Other applications may include matching between CEOs and firms, firms and workers, buyers and sellers, etc.

Usage

estimate.affinity.matrix(
  X,
  Y,
  w = rep(1, N),
  A0 = matrix(0, nrow = Kx, ncol = Ky),
  lb = matrix(-Inf, nrow = Kx, ncol = Ky),
  ub = matrix(Inf, nrow = Kx, ncol = Ky),
  pr = 0.05,
  max_iter = 10000,
  tol_level = 1e-06,
  scale = 1,
  nB = 2000,
  verbose = TRUE
)

Arguments

X	The matrix of men's traits. Its rows must be ordered so that the i-th man is matched with the i-th woman: this means that nrow(X) must be equal to nrow(Y). Its columns correspond to the different matching variables: ncol(X) can be different from ncol(Y). For the sake of clarity of exposition when using descriptive tools such as show.correlations, it is recommended assigning the same matching variable to the k-th column of X and to the k-th column of Y, whenever possible. If X has more matching variables than Y, then those variables that appear in X but no in Y should be found in the last columns of X (and vice versa). The matrix is demeaned and rescaled before the start of the estimation algorithm.
Y	The matrix of women's traits. Its rows must be ordered so that the i-th woman is matched with the i-th man: this means that nrow(Y) must be equal to nrow(X). Its columns correspond to the different matching variables: ncol(Y) can be different from ncol(X). The matrix is demeaned and rescaled before the start of the estimation algorithm.
w	A vector of sample weights with length nrow(X). Defaults to uniform weights.
A0	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the initial values of the affinity matrix to be fed to the estimation algorithm. Optional. Defaults to matrix of zeros.
lb	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the lower bounds of the elements of the affinity matrix. Defaults to -Inf for all parameters.
ub	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the upper bounds of the elements of the affinity matrix. Defaults to Inf for all parameters.
pr	A probability indicating the significance level used to compute bootstrap two-sided confidence intervals for U, V and lambda. Defaults to 0.05.
max_iter	An integer indicating the maximum number of iterations in the Maximum Likelihood Estimation. See optim for the "L-BFGS-B" method. Defaults to 10000.
tol_level	A positive real number indicating the tolerance level in the Maximum Likelihood Estimation. See optim for the "L-BFGS-B" method. Defaults to 1e-6.
scale	A positive real number indicating the scale of the model. Defaults to 1.
nB	An integer indicating the number of bootstrap replications used to compute the confidence intervals of U, V and lambda. Defaults to 2000.
verbose	If TRUE, the function displays messages to keep track of its progress. Defaults to TRUE.

Value

The function returns a list with elements: X, the demeaned and rescaled matrix of men's traits; Y, the demeaned and rescaled matrix of men's traits; fx, the empirical marginal distribution of men; fy, the empirical marginal distribution of women; Aopt, the estimated affinity matrix; sdA, the standard errors of Aopt; tA, the Z-test statistics of Aopt; VarCovA, the full variance-covariance matrix of Aopt; rank.tests, a list with all the summaries of the rank tests on Aopt; U, whose columns are the left-singular vectors of Aopt; V, whose columns are the right-singular vectors of Aopt; lambda, whose elements are the singular values of Aopt; UCI, whose columns are the lower and the upper bounds of the confidence intervals of U; VCI, whose columns are the lower and the upper bounds of the confidence intervals of V; lambdaCI, whose columns are the lower and the upper bounds of the confidence intervals of lambda; df.bootstrap, a data frame resulting from the nB bootstrap replications and used to infer the empirical distribution of the estimated objects.

See Also

Dupuy, Arnaud, and Alfred Galichon. "Personality traits and the marriage market." Journal of Political Economy 122, no. 6 (2014): 1271-1319.

Examples

# Parameters
Kx = 4; Ky = 4; # number of matching variables on both sides of the market
N = 200 # sample size
mu = rep(0, Kx+Ky) # means of the data generating process
Sigma = matrix(c(1, 0.326, 0.1446, -0.0668, 0.5712, 0.4277, 0.1847, -0.2883,
                 0.326, 1, -0.0372, 0.0215, 0.2795, 0.8471, 0.1211, -0.0902,
                 0.1446, -0.0372, 1, -0.0244, 0.2186, 0.0636, 0.1489,
                 -0.1301, -0.0668, 0.0215, -0.0244, 1, 0.0192, 0.0452,
                 -0.0553, 0.2717, 0.5712, 0.2795, 0.2186, 0.0192, 1, 0.3309,
                 0.1324, -0.1896, 0.4277, 0.8471, 0.0636, 0.0452, 0.3309, 1,
                 0.0915, -0.1299, 0.1847, 0.1211, 0.1489, -0.0553, 0.1324,
                 0.0915, 1, -0.1959, -0.2883, -0.0902, -0.1301, 0.2717,
                 -0.1896, -0.1299, -0.1959, 1),
               nrow=Kx+Ky) # (normalized) variance-covariance matrix of the
               # data generating process
labels_x = c("Educ.", "Age", "Height", "BMI") # labels for men's matching variables
labels_y = c("Educ.", "Age", "Height", "BMI") # labels for women's matching variables

# Sample
data = MASS::mvrnorm(N, mu, Sigma) # generating sample
X = data[,1:Kx]; Y = data[,Kx+1:Ky] # men's and women's sample data
w = sort(runif(N-1)); w = c(w,1) - c(0,w) # sample weights

# Main estimation
res = estimate.affinity.matrix(X, Y, w = w, nB = 500)

# Summarize results
show.affinity.matrix(res, labels_x = labels_x, labels_y = labels_y)
show.diagonal(res, labels = labels_x)
show.test(res)
show.saliency(res, labels_x = labels_x, labels_y = labels_y,
              ncol_x = 2, ncol_y = 2)
show.correlations(res, labels_x = labels_x, labels_y = labels_y,
                  label_x_axis = "Husband", label_y_axis = "Wife", ndims = 2)

---

Estimate Dupuy and Galichon's model

Description

This function estimates the affinity matrix of the matching model of Dupuy and Galichon (2014) under a rank restriction on the affinity matrix, as suggested by Dupuy, Galichon and Sun (2019). In their own words, "to accommodate high dimensionality of the data, they propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix." This function also performs the saliency analysis and the rank tests. The user must supply a matched sample that is treated as the equilibrium matching of a bipartite one-to-one matching model without frictions and with Transferable Utility. For the sake of clarity, in the documentation we take the example of the marriage market and refer to "men" as the observations on one side of the market and to "women" as the observations on the other side. Other applications may include matching between CEOs and firms, firms and workers, buyers and sellers, etc.

Usage

estimate.affinity.matrix.lowrank(
  X,
  Y,
  w = rep(1, N),
  A0 = matrix(0, nrow = Kx, ncol = Ky),
  lb = matrix(-Inf, nrow = Kx, ncol = Ky),
  ub = matrix(Inf, nrow = Kx, ncol = Ky),
  pr = 0.05,
  max_iter = 10000,
  tol_level = 1e-08,
  tau = 1,
  scale = 1,
  cross_validation = TRUE,
  manual_lambda = 0,
  lambda_min = 0,
  Nfolds = 5,
  nB = 2000,
  verbose = TRUE
)

Arguments

X	The matrix of men's traits. Its rows must be ordered so that the i-th man is matched with the i-th woman: this means that nrow(X) must be equal to nrow(Y). Its columns correspond to the different matching variables: ncol(X) can be different from ncol(Y). For the sake of clarity of exposition when using descriptive tools such as show.correlations, it is recommended assigning the same matching variable to the k-th column of X and to the k-th column of Y, whenever possible. If X has more matching variables than Y, then those variables that appear in X but no in Y should be found in the last columns of X (and vice versa). The matrix is demeaned and rescaled before the start of the estimation algorithm.
Y	The matrix of women's traits. Its rows must be ordered so that the i-th woman is matched with the i-th man: this means that nrow(Y) must be equal to nrow(X). Its columns correspond to the different matching variables: ncol(Y) can be different from ncol(X). The matrix is demeaned and rescaled before the start of the estimation algorithm.
w	A vector of sample weights with length nrow(X). Defaults to uniform weights.
A0	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the initial values of the affinity matrix to be fed to the estimation algorithm. Optional. Defaults to matrix of zeros.
lb	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the lower bounds of the elements of the affinity matrix. Defaults to -Inf for all parameters.
ub	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the upper bounds of the elements of the affinity matrix. Defaults to Inf for all parameters.
pr	A probability indicating the significance level used to compute bootstrap two-sided confidence intervals for U, V and lambda. Defaults to 0.05.
max_iter	An integer indicating the maximum number of iterations in the proximal gradient descent algorithm. Defaults to 10000.
tol_level	A positive real number indicating the tolerance level in the proximal gradient descent algorithm. Defaults to 1e-8.
tau	A positive real number indicating a sensitivity parameter in the proximal gradient descent algorithm. Defaults to 1 and should not be changed unless computational problems arise.
scale	A positive real number indicating the scale of the model. Defaults to 1.
cross_validation	If TRUE, the function looks for a rank restriction through cross validation. The cross validation exercise aims to minimize the covariance mismatch: in other words, it avoids overfitting without excessively reducing the number of free parameters. Defaults to TRUE.
manual_lambda	A positive real number indicating the user-supply lambda when cross_validation==FALSE. The higher lambda, the tighter the rank restriction. Defaults to 0.
lambda_min	A positive real number indicating minimum value for lambda considered during the cross validation. We recommend using 0, but with a high number of matching variables relatively to the sample size it is reasonable to set lambda_min to a higher value. Defaults to 0.
Nfolds	An integer indicating the number of folds in the cross validation. Defaults to 5 and can be increased with a large sample size.
nB	An integer indicating the number of bootstrap replications used to compute the confidence intervals of Aopt, U, V and lambda. Defaults to 2000.
verbose	If TRUE, the function displays messages to keep track of its progress. Defaults to TRUE.

Value

The function returns a list with elements: X, the demeaned and rescaled matrix of men's traits; Y, the demeaned and rescaled matrix of men's traits; fx, the empirical marginal distribution of men; fy, the empirical marginal distribution of women; Aopt, the estimated affinity matrix; sdA, the standard errors of Aopt; tA, the Z-test statistics of Aopt; VarCovA, the full variance-covariance matrix of Aopt; rank.tests, a list with all the summaries of the rank tests on Aopt; U, whose columns are the left-singular vectors of Aopt; V, whose columns are the right-singular vectors of Aopt; lambda, whose elements are the singular values of Aopt; UCI, whose columns are the lower and the upper bounds of the confidence intervals of U; VCI, whose columns are the lower and the upper bounds of the confidence intervals of V; lambdaCI, whose columns are the lower and the upper bounds of the confidence intervals of lambda; df.bootstrap, a data frame resulting from the nB bootstrap replications and used to infer the empirical distribution of the estimated objects; lambda.rank.restriction, a positive real number indicating the value of the Lagrange multiplier of the nuclear norm constraint of the affinity matrix, either chosen by the user or through Cross Validation; df.cross.validation, a data frame containing the detailed results of the cross validation exercise.

See Also

Dupuy, Arnaud, Alfred Galichon, and Yifei Sun. "Estimating matching affinity matrices under low-rank constraints." Information and Inference: A Journal of the IMA 8, no. 4 (2019): 677-689. Dupuy, Arnaud, and Alfred Galichon. "Personality traits and the marriage market." Journal of Political Economy 122, no. 6 (2014): 1271-1319.

Examples

# Parameters
Kx = 2; Ky = 2; # number of matching variables on both sides of the market
N = 100 # sample size
mu = rep(0, Kx+Ky) # means of the data generating process
Sigma = matrix(c(1, -0.0244, 0.1489, -0.1301, -0.0244, 1, -0.0553, 0.2717,
                 0.1489, -0.0553, 1, -0.1959, -0.1301, 0.2717, -0.1959, 1),
                 nrow=Kx+Ky)
    # (normalized) variance-covariance matrix of the data generating process
labels_x = c("Height", "BMI") # labels for men's matching variables
labels_y = c("Height", "BMI") # labels for women's matching variables

# Sample
data = MASS::mvrnorm(N, mu, Sigma) # generating sample
X = data[,1:Kx]; Y = data[,Kx+1:Ky] # men's and women's sample data
w = sort(runif(N-1)); w = c(w,1) - c(0,w) # sample weights

# Main estimation
res = estimate.affinity.matrix.lowrank(X, Y, w = w, tol_level = 1e-03,
                                       nB = 50, Nfolds = 2)

# Summarize results
show.affinity.matrix(res, labels_x = labels_x, labels_y = labels_y)
show.diagonal(res, labels = labels_x)
show.test(res)
show.saliency(res, labels_x = labels_x, labels_y = labels_y,
              ncol_x = 2, ncol_y = 2)
show.cross.validation(res)
show.correlations(res, labels_x = labels_x, labels_y = labels_y,
                  label_x_axis = "Husband", label_y_axis = "Wife", ndims = 2)

---

Estimate Ciscato, Galichon and Gousse's model

Description

This function estimates the affinity matrix of the matching model of Ciscato Gousse and Galichon (2020), performs the saliency analysis and the rank tests. The user must supply a matched sample that is treated as the equilibrium matching of a bipartite one-to-one matching model without frictions and with Transferable Utility. The model differs from the original Dupuy and Galichon (2014) since all agents are pooled in one group and can match within the group. For the sake of clarity, in the documentation we take the example of the same-sex marriage market and refer to "first partner" and "second partner" in order to distinguish between the arbitrary partner order in a database (e.g., survey respondent and partner of the respondent). Note that in this case the variable "sex" is treated as a matching variable rather than a criterion to assign partners to one side of the market as in the bipartite case. Other applications may include matching between coworkers, roommates or teammates.

Usage

estimate.affinity.matrix.unipartite(
  X,
  Y,
  w = rep(1, N),
  A0 = matrix(0, nrow = K, ncol = K),
  lb = matrix(-Inf, nrow = K, ncol = K),
  ub = matrix(Inf, nrow = K, ncol = K),
  pr = 0.05,
  max_iter = 10000,
  tol_level = 1e-06,
  scale = 1,
  nB = 2000,
  verbose = TRUE
)

Arguments

X	The matrix of traits of the first partner. Its rows must be ordered so that the i-th individual in X is matched with the i-th partner in Y: this means that nrow(X) must be equal to nrow(Y). Its columns correspond to the different matching variables: ncol(X) must be equal to ncol(Y) and the variables must be sorted in the same way in both matrices. The matrix is demeaned and rescaled before the start of the estimation algorithm.
Y	The matrix of traits of the second partner. Its rows must be ordered so that the i-th individual in Y is matched with the i-th partner in X: this means that nrow(Y) must be equal to nrow(X). Its columns correspond to the different matching variables: ncol(Y) must be equal to ncol(X) and the variables must be sorted in the same way in both matrices. The matrix is demeaned and rescaled before the start of the estimation algorithm.
w	A vector of sample weights with length nrow(X). Defaults to uniform weights.
A0	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the initial values of the affinity matrix to be fed to the estimation algorithm. Optional. Defaults to a matrix of zeros.
lb	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the lower bounds of the elements of the affinity matrix. Defaults to -Inf for all parameters.
ub	A vector or matrix with ncol(X)*ncol(Y) elements corresponding to the upper bounds of the elements of the affinity matrix. Defaults to Inf for all parameters.
pr	A probability indicating the significance level used to compute bootstrap two-sided confidence intervals for U, V and lambda. Defaults to 0.05.
max_iter	An integer indicating the maximum number of iterations in the Maximum Likelihood Estimation. See optim for the "L-BFGS-B" method. Defaults to 10000.
tol_level	A positive real number indicating the tolerance level in the Maximum Likelihood Estimation. See optim for the "L-BFGS-B" method. Defaults to 1e-6.
scale	A positive real number indicating the scale of the model. Defaults to 1.
nB	An integer indicating the number of bootstrap replications used to compute the confidence intervals of U, V and lambda. Defaults to 2000.
verbose	If TRUE, the function displays messages to keep track of its progress. Defaults to TRUE.

Value

The function returns a list with elements: X, the demeaned and rescaled matrix of traits of the first partner; Y, the demeaned and rescaled matrix of traits of the second partner; fx, the empirical marginal distribution of first partners; fy, the empirical marginal distribution of second partners; Aopt, the estimated affinity matrix; sdA, the standard errors of Aopt; tA, the Z-test statistics of Aopt; VarCovA, the full variance-covariance matrix of Aopt; rank.tests, a list with all the summaries of the rank tests on Aopt; U, whose columns are the left-singular vectors of Aopt; V, whose columns are the right-singular vectors of Aopt; lambda, whose elements are the singular values of Aopt; UCI, whose columns are the lower and the upper bounds of the confidence intervals of U; VCI, whose columns are the lower and the upper bounds of the confidence intervals of V; lambdaCI, whose columns are the lower and the upper bounds of the confidence intervals of lambda; df.bootstrap, a data frame resulting from the nB bootstrap replications and used to infer the empirical distribution of the estimated objects.

See Also

Ciscato, Edoardo, Alfred Galichon, and Marion Gousse. "Like attract like? a structural comparison of homogamy across same-sex and different-sex households." Journal of Political Economy 128, no. 2 (2020): 740-781. Dupuy, Arnaud, and Alfred Galichon. "Personality traits and the marriage market." Journal of Political Economy 122, no. 6 (2014): 1271-1319.

Examples

# Parameters
K = 4 # number of matching variables
N = 100 # sample size
mu = rep(0, 2*K) # means of the data generating process
Sigma = matrix(c(1, -0.0992, 0.0443, -0.0246, -0.8145, 0.083, -0.0438,
    0.0357, -0.0992, 1, 0.0699, -0.0043, 0.083, 0.8463, 0.0699, -0.0129, 0.0443,
    0.0699, 1, -0.0434, -0.0438, 0.0699, 0.5127, -0.0383, -0.0246, -0.0043,
    -0.0434, 1, 0.0357, -0.0129, -0.0383, 0.6259, -0.8145, 0.083, -0.0438,
    0.0357, 1, -0.0992, 0.0443, -0.0246, 0.083, 0.8463, 0.0699, -0.0129, -0.0992,
    1, 0.0699, -0.0043, -0.0438, 0.0699, 0.5127, -0.0383, 0.0443, 0.0699, 1,
    -0.0434, 0.0357, -0.0129, -0.0383, 0.6259, -0.0246, -0.0043, -0.0434, 1),
               nrow=K+K) # (normalized) variance-covariance matrix of the
               # data generating process with a block symmetric structure
labels = c("Sex", "Age", "Educ.", "Black") # labels for matching variables

# Sample
data = MASS::mvrnorm(N, mu, Sigma) # generating sample
X = data[,1:K]; Y = data[,K+1:K] # men's and women's sample data
w = sort(runif(N-1)); w = c(w,1) - c(0,w) # sample weights

# Main estimation
res = estimate.affinity.matrix.unipartite(X, Y, w = w, nB = 500)

# Summarize results
show.affinity.matrix(res, labels_x = labels, labels_y = labels)
show.diagonal(res, labels = labels)
show.test(res)
show.saliency(res, labels_x = labels, labels_y = labels,
              ncol_x = 2, ncol_y = 2)
show.correlations(res, labels_x = labels, labels_y = labels,
                  label_x_axis = "First partner",
                  label_y_axis = "Second partner", ndims = 2)

---

Export an affinitymatrix table

Description

The function stores a LaTeX style table in a txt file.

Usage

export.table(tabular, name = "table", path = getwd())

Arguments

tabular	A long string corresponding to the output of show.affinity.matrix, show.diagonal or show.test, or one of the two elements of show.saliency (U.table or V.table).
name	A string indicating the name of the txt file. Defaults to "affinity_matrix".
path	A string indicating the path where to save the txt file. Defaults to current path.

Value

The function stores a long string in LaTeX style that can be processed in the standard LaTeX tabular environment in a txt file in located in path.

---

Print affinity matrix

Description

This function prints the estimated affinity matrix in LaTeX style. Standard errors are printed below the elements of the affinity matrix. Estimates that are significant at the pr level are printed in boldface: this format feature can be avoided by setting pr to 0.

Usage

show.affinity.matrix(
  res,
  labels_x = paste0("Trait ", 1:Kx),
  labels_y = paste0("Trait ", 1:Ky),
  pr = 0.05
)

Arguments

res	A list corresponding to the output of estimate.affinity.matrix, estimate.affinity.matrix.lowrank or estimate.affinity.matrix.unipartite.
labels_x	A vector of strings indicating the names of men's matching variables. Defaults to "Trait k" for every k matching variable.
labels_y	A vector of strings indicating the names of women's matching variables. Defaults to "Trait k" for every k matching variable.
pr	A probability indicating the two-tailed significance level required for an estimated parameter to be printed in boldface. Defaults to 0.05 and can be set to 0 to avoid printing any estimate in boldface.

Value

The function returns a long string in LaTeX style that can be processed in the standard LaTeX tabular environment in order to display the estimates of the affinity matrix Aopt.

---

Print correlations of matching factors with matching and outcome variables

Description

This function returns a list of plots, one for each of the first ndims orthogonal sorting dimension. In the k-th plot, the correlation between a man's observed matching variable and the man's k-th matching factor is plotted on the x-axis; the correlation between a woman's observed matching variable and the woman's k-th matching factor is plotted on the y-axis. In addition, the user can supply additional variables stored in the matrix Z that were not previously used in the estimation ("outcome variables"). The function prints the correlation between the outcome variable and the man's k-th matching factor on the x-axis, while the correlation between the outcome variable and the woman's k-th matching factor is on the y-axis.

Usage

show.correlations(
  res,
  Z = matrix(0, nrow = N, ncol = 0),
  labels_x = paste0("Trait ", 1:Kx),
  labels_y = paste0("Trait ", 1:Ky),
  labels_z = if (Kz > 0) paste0("Outcome ", 1:Kz) else c(),
  ndims = min(Kx, Ky, 10),
  pr = 0.02,
  color_arrows = c("black", "red"),
  size_arrows = 0.5,
  font_labels = c("bold", "italic"),
  label_x_axis = "First partner",
  label_y_axis = "Second partner"
)

Arguments

res	A list corresponding to the output of estimate.affinity.matrix, estimate.affinity.matrix.lowrank or estimate.affinity.matrix.unipartite.
Z	A matrix Z with additional variables that were not previously used in the estimation. The i-th row of Z must contain information on the couple formed by the i-th row of X and the i-th row of Y, so that nrow(Z)=nrow(X). Defaults to an empty matrix: Z is optional.
labels_x	A vector of strings indicating the names of men's matching variables. Defaults to "Trait k" for every k matching variable.
labels_y	A vector of strings indicating the names of women's matching variables. Defaults to "Trait k" for every k matching variable.
labels_z	A vector of strings indicating the names of the outcome variables. Defaults to "Outcome k" for every k outcome variable.
ndims	An integer indicating the number of orthogonal matching dimensions that will be plotted. The function plots the first \ codendims dimensions. Defaults to all dimensions unless the latter are more than 10, in which case only the first 10 are plotted.
pr	A probability indicating the two-tailed significance level required for a matching or outcome variable to be displayed in a plot. In order to avoid having too many variables plotted at the same time, the function only selects those whose correlation with the matching factor is significantly different from zero (in a two-tailed test) at the pr level. Defaults to 0.02 and can be set to 1 to print all variables.
color_arrows	A string or a vector of strings containing color names for the arrows. All matching variables are assigned the first color given in the vector, while all outcome variables are assigned the second color. See ggplot. Defaults to "black" and "red" respectively.
size_arrows	A positive real number or a vector containing the size of the arrows. All matching variables are assigned the first size given in the vector, while all outcome variables are assigned the second size. See ggplot. Defaults to 0.5 for both.
font_labels	A string or a vector of strings containing font types for the labels. All matching variables are assigned the first font type given in the vector, while all outcome variables are assigned the second font type. See ggplot. Defaults to "bold" and "italic" respectively.
label_x_axis	A string containing a root for all x-axis names in different plots. Defaults to "First partner".
label_y_axis	A string containing a root for all y-axis names in different plots. Defaults to "Second partner".

Value

The function returns a list of ndims plots created with ggplot.

See Also

Chiappori, Pierre-Andre, Edoardo Ciscato, and Carla Guerriero. "Analyzing matching patterns in marriage: theory and application to Italian data." HCEO Working Paper no. 2020-080 (2020).

---

Print cross validation summary

Description

This function returns a plot reporting the estimated covariance mismatch as a function of the rank restriction parameter lambda. This is the result of the cross validation exercise. The function is expected to be convex in lambda and the chosen lambda is the unique minimum.

Usage

show.cross.validation(res)

Arguments

res	A list corresponding to the output of estimate.affinity.matrix, estimate.affinity.matrix.lowrank or estimate.affinity.matrix.unipartite.

Value

The function returns a plot created with ggplot.

---

Print the diagonal of the affinity matrix

Description

This function prints the estimates of the diagonal of the affinity matrix in LaTeX style. Standard errors are printed below the elements of the affinity matrix. Estimates that are significant at the pr level are printed in boldface: this format feature can be avoided by setting pr to 0.

Usage

show.diagonal(res, labels = paste0("Trait ", 1:K), pr = 0.05)

Arguments

res	A list corresponding to the output of estimate.affinity.matrix, estimate.affinity.matrix.lowrank or estimate.affinity.matrix.unipartite.
labels	A vector of strings indicating the names of the matching variables. Defaults to "Trait k" for every k matching variable.
pr	A probability indicating the two-tailed significance level required for an estimated parameter to be printed in boldface. Defaults to 0.05 and can be set to 0 to avoid printing any estimate in boldface.

Value

The function returns a long string in LaTeX style that can be processed in the standard LaTeX tabular environment in order to display the estimates of diagonal of the affinity matrix Aopt.

---

Print summary of saliency analysis

Description

This function prints the results from the saliency analysis in LaTeX style. The function returns a list of two elements: U.table contains the first ncol_x vectors of loadings that map men's Kx observed traits into the first ncol_x matching factors; V.table contains the first ncol_y vectors of loadings that map women's Ky observed traits into the first ncol_y matching factors. In both tables, the last line reports the normalized singular values of the affinity matrix in descending order.

Usage

show.saliency(
  res,
  ncol_x = Kx,
  ncol_y = Ky,
  labels_x = paste0("Trait ", 1:Kx),
  labels_y = paste0("Trait ", 1:Ky),
  pr = 0.05
)

Arguments

res	A list corresponding to the output of estimate.affinity.matrix, estimate.affinity.matrix.lowrank or estimate.affinity.matrix.unipartite.
ncol_x	An integer indicating the number of singular vector to print for men. The function prints the first ncol_x singular vectors. Defaults to ncol(U).
ncol_y	An integer indicating the number of singular vector to print for women. The function prints the first ncol_y singular vectors. Defaults to ncol(V).
labels_x	A vector of strings indicating the names of men's matching variables. Defaults to "Trait k" for every k matching variable.
labels_y	A vector of strings indicating the names of women's matching variables. Defaults to "Trait k" for every k matching variable.
pr	A probability indicating the two-tailed significance level required for an estimated parameter to be printed in boldface. Defaults to 0.05 and can be set to 0 to avoid printing any estimate in boldface.

Value

The function returns a long string in LaTeX style that can be processed in the standard LaTeX tabular environment in order to display the estimates of the vectors of loadings for the first ncol_x men's matching factors and the first ncol_y women's matching factors.

---

Print summaries of rank tests

Description

This function prints the summaries of the first n_tests rank tests in in LaTeX. The first row specifies the null hypothesis, the second row gives the test statistic, the third the degrees of freedom and the fourth says whether the null hypothesis passes the test at the pr level.

Usage

show.test(res, pr = 0.05, n_tests = K - 1)

Arguments

res	A list corresponding to the output of estimate.affinity.matrix, estimate.affinity.matrix.lowrank or estimate.affinity.matrix.unipartite.
pr	A probability indicating the significance level required to pass a rank test. Defaults to 0.05.
n_tests	An integer indicating the number of tests to show. The function prints the first n_tests rank tests. Defaults to min(nrow(Y),nrow(X))-1.

Value

The function returns a long string in LaTeX style that can be processed in the standard LaTeX tabular environment in order to display the results from the first n_tests rank tests of the affinity matrix.

---