Type:	Package
Title:	Quantile Peer Effect Models
Version:	0.0.1
Date:	2025-07-10
Description:	Simulating and estimating peer effect models including the quantile-based specification (Houndetoungan, 2025 <doi:10.48550/arXiv.2506.12920>), and the models with Constant Elasticity of Substitution (CES)-based social norm (Boucher et al., 2024 <doi:10.3982/ECTA21048>).
License:	GPL-3
Language:	en-US
Encoding:	UTF-8
BugReports:	https://github.com/ahoundetoungan/QuantilePeer/issues
URL:	https://github.com/ahoundetoungan/QuantilePeer
Depends:	R (≥ 3.5.0)
Imports:	Rcpp (≥ 1.0.0), formula.tools, Matrix, MASS
LinkingTo:	Rcpp, RcppArmadillo, RcppEigen, RcppNumerical
RoxygenNote:	7.3.2
Suggests:	knitr, rmarkdown, PartialNetwork,
VignetteBuilder:	knitr
NeedsCompilation:	yes
Packaged:	2025-06-18 12:23:44 UTC; haache
Author:	Aristide Houndetoungan [cre, aut]
Maintainer:	Aristide Houndetoungan <aristide.houndetoungan@ecn.ulaval.ca>
Repository:	CRAN
Date/Publication:	2025-06-19 15:10:02 UTC

The QuantilePeer package

Description

The QuantilePeer package simulates and estimates peer effect models including the quantile-based specification (Houndetoungan, 2025 doi:10.3982/ECTA21048), and the models with Constant Elasticity of Substitution (CES)-based social norm (Boucher et al., 2024 doi:10.3982/ECTA21048).

Author(s)

Maintainer: Aristide Houndetoungan aristide.houndetoungan@ecn.ulaval.ca (ORCID)

References

Boucher, V., Rendall, M., Ushchev, P., & Zenou, Y. (2024). Toward a general theory of peer effects. Econometrica, 92(2), 543-565, doi:10.3982/ECTA21048.

Houndetoungan, A. (2025). Quantile peer effect models. arXiv preprint arXiv:2405.17290, doi:10.48550/arXiv.2506.12920.

Hyndman, R. J., & Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361-365, doi:10.1080/00031305.1996.10473566.

See Also

Useful links:

• https://github.com/ahoundetoungan/QuantilePeer

• Report bugs at https://github.com/ahoundetoungan/QuantilePeer/issues

Estimation of CES-Based Peer Effects Models

Description

cespeer estimates the CES-based peer effects model introduced by Boucher et al. (2024). See Details.

Usage

cespeer(
  formula,
  instrument,
  Glist,
  structural = FALSE,
  fixed.effects = FALSE,
  set.rho = NULL,
  grid.rho = seq(-400, 400, radius),
  radius = 5,
  tol = 1e-08,
  drop = NULL,
  compute.cov = TRUE,
  HAC = "iid",
  data
)

Arguments

Details

Let \mathcal{N} be a set of n agents indexed by the integer i \in [1, n]. Agents are connected through a network characterized by an adjacency matrix \mathbf{G} = [g_{ij}] of dimension n \times n, where g_{ij} = 1 if agent j is a friend of agent i, and g_{ij} = 0 otherwise. In weighted networks, g_{ij} can be a nonnegative variable (not necessarily binary) that measures the intensity of the outgoing link from i to j. The model can also accommodate such networks. Note that the network generally consists of multiple independent subnets (e.g., schools). The Glist argument is the list of subnets. In the case of a single subnet, Glist should be a list containing one matrix.

The reduced-form specification of the CES-based peer effects model is given by:

y_i = \lambda\left(\sum_{j = 1}^n g_{ij}y_j^{\rho}\right)^{1/\rho} + \mathbf{x}_i^{\prime}\beta + \varepsilon_i,

where \varepsilon_i is an idiosyncratic error term, \lambda captures the effect of the social norm \left(\sum_{j = 1}^n g_{ij}y_j^{\rho}\right)^{1/\rho}, and \beta captures the effect of \mathbf{x}_i on y_i. The parameter \rho determines the form of the social norm in the model.

• When \rho > 1, individuals are more sensitive to peers with high outcomes.

• When \rho < 1, individuals are more sensitive to peers with low outcomes.

• When \rho = 1, peer effects are uniform across peer outcome values.
  

The structural specification of the model differs for isolated and non-isolated individuals. For an isolated i, the specification is similar to a standard linear-in-means model without social interactions, given by:

y_i = \mathbf{x}_i^{\prime}\beta + \varepsilon_i.

If node i is non-isolated, the specification is:

y_i = \lambda\left(\sum_{j = 1}^n g_{ij}y_j^{\rho}\right)^{1/\rho} + (1 - \lambda_2)\mathbf{x}_i^{\prime}\beta + \varepsilon_i,

where \lambda_2 determines whether preferences exhibit conformity or complementarity/substitution. Identification of \beta and \lambda_2 requires the network to include a sufficient number of isolated individuals.

Value

A list containing:

References

Boucher, V., Rendall, M., Ushchev, P., & Zenou, Y. (2024). Toward a general theory of peer effects. Econometrica, 92(2), 543-565, doi:10.3982/ECTA21048.

See Also

qpeer, linpeer

Examples

set.seed(123)
ngr  <- 50  # Number of subnets
nvec <- rep(30, ngr)  # Size of subnets
n    <- sum(nvec)

### Simulating Data
## Network matrix
G <- lapply(1:ngr, function(z) {
  Gz <- matrix(rbinom(nvec[z]^2, 1, 0.3), nvec[z], nvec[z])
  diag(Gz) <- 0
  # Adding isolated nodes (important for the structural model)
  niso <- sample(0:nvec[z], 1, prob = (nvec[z] + 1):1 / sum((nvec[z] + 1):1))
  if (niso > 0) {
    Gz[sample(1:nvec[z], niso), ] <- 0
  }
  # Row-normalization
  rs   <- rowSums(Gz); rs[rs == 0] <- 1
  Gz/rs
})

X   <- cbind(rnorm(n), rpois(n, 2))
l   <- 0.55
b   <- c(2, -0.5, 1)
rho <- -2
eps <- rnorm(n, 0, 0.4)

## Generating `y`
y <- cespeer.sim(formula = ~ X, Glist = G, rho = rho, lambda = l,
                 beta = b, epsilon = eps)$y

### Estimation
## Computing instruments
z <- fitted.values(lm(y ~ X))

## Reduced-form model
rest <- cespeer(formula = y ~ X, instrument = ~ z, Glist = G, fixed.effects = "yes",
                radius = 5, grid.rho = seq(-10, 10, 1))
summary(rest)

## Structural model
sest <- cespeer(formula = y ~ X, instrument = ~ z, Glist = G, fixed.effects = "yes",
                radius = 5, structural = TRUE, grid.rho = seq(-10, 10, 1))
summary(sest)

## Quantile model
z    <- qpeer.inst(formula = ~ X, Glist = G, tau = seq(0, 1, 0.1), max.distance = 2, 
                   checkrank = TRUE)$instruments
qest <- qpeer(formula = y ~ X, excluded.instruments  = ~ z, Glist = G, 
              fixed.effects = "yes", tau = seq(0, 1, 1/3), structural = TRUE)
summary(qest)

Compute the CES Social Norm

Description

cespeer.data computes the CES social norm, along with the first and second derivatives of the CES social norm with respect to the substitution parameter \rho.

Usage

cespeer.data(y, Glist, rho)

Arguments

Value

A four-column matrix with the following columns:

Simulating Peer Effect Models with a CES Social Norm

Description

cespeer.sim simulates peer effect models with a Constant Elasticity of Substitution (CES) based social norm (Boucher et al., 2024).

Usage

cespeer.sim(
  formula,
  Glist,
  parms,
  rho,
  lambda,
  beta,
  epsilon,
  structural = FALSE,
  init,
  tol = 1e-10,
  maxit = 500,
  data
)

Arguments

Value

A list containing:

References

Boucher, V., Rendall, M., Ushchev, P., & Zenou, Y. (2024). Toward a general theory of peer effects. Econometrica, 92(2), 543-565, doi:10.3982/ECTA21048.

See Also

cespeer, qpeer.sim

Examples

set.seed(123)
ngr  <- 50
nvec <- rep(30, ngr)
n    <- sum(nvec)
G    <- lapply(1:ngr, function(z){
  Gz <- matrix(rbinom(nvec[z]^2, 1, 0.3), nvec[z])
  diag(Gz) <- 0
  Gz/rowSums(Gz) # Row-normalized network
})
tau  <- seq(0, 1, 0.25)
X    <- cbind(rnorm(n), rpois(n, 2))
l    <- 0.55
rho  <- 3
b    <- c(4, -0.5, 1)

out  <- cespeer.sim(formula = ~ X, Glist = G, rho = rho, lambda = l, beta = b)
summary(out$y)
out$iteration

Demeaning Variables

Description

demean demeans variables by subtracting the within-subnetwork average. In each subnetwork, this transformation can be performed separately for isolated and non-isolated nodes.

Usage

demean(X, Glist, separate = FALSE, drop = NULL)

Arguments

Value

A matrix or vector with the same dimensions as X, containing the demeaned values.

Estimating Peer Effects Models

Description

qpeer estimates the quantile peer effect models introduced by Houndetoungan (2025). In the linpeer function, quantile peer variables are replaced with the average peer variable, and they can be replaced with other peer variables in the genpeer function.

Usage

genpeer(
  formula,
  excluded.instruments,
  endogenous.variables,
  Glist,
  data,
  estimator = "IV",
  structural = FALSE,
  drop = NULL,
  fixed.effects = FALSE,
  HAC = "iid",
  checkrank = FALSE,
  compute.cov = TRUE,
  tol = 1e-10
)

linpeer(
  formula,
  excluded.instruments,
  Glist,
  data,
  estimator = "IV",
  structural = FALSE,
  drop = NULL,
  fixed.effects = FALSE,
  HAC = "iid",
  checkrank = FALSE,
  compute.cov = TRUE,
  tol = 1e-10
)

qpeer(
  formula,
  excluded.instruments,
  Glist,
  tau,
  type = 7,
  data,
  estimator = "IV",
  structural = FALSE,
  fixed.effects = FALSE,
  HAC = "iid",
  checkrank = FALSE,
  drop = NULL,
  compute.cov = TRUE,
  tol = 1e-10
)

Arguments

Details

Let \mathcal{N} be a set of n agents indexed by the integer i \in [1, n]. Agents are connected through a network that is characterized by an adjacency matrix \mathbf{G} = [g_{ij}] of dimension n \times n, where g_{ij} = 1 if agent j is a friend of agent i, and g_{ij} = 0 otherwise. In weighted networks, g_{ij} can be a nonnegative variable (not necessarily binary) that measures the intensity of the outgoing link from i to j. The model can also accommodate such networks. Note that the network is generally constituted in many independent subnets (eg: schools). The Glist argument is the list of subnets. In the case of a single subnet, Glist will be a list containing one matrix.

Let \mathcal{T} be a set of quantile levels. The reduced-form specification of quantile peer effect models is given by:

y_i = \sum_{\tau \in \mathcal{T}} \lambda_{\tau} q_{\tau,i}(\mathbf{y}_{-i}) + \mathbf{x}_i^{\prime}\beta + \varepsilon_i,

where \mathbf{y}_{-i} = (y_1, \ldots, y_{i-1}, y_{i+1}, \ldots, y_n)^{\prime} is the vector of outcomes for other units, and q_{\tau,i}(\mathbf{y}_{-i}) is the sample \tau-quantile of peer outcomes. The term \varepsilon_i is an idiosyncratic error term, \lambda_{\tau} captures the effect of the \tau-quantile of peer outcomes on y_i, and \beta captures the effect of \mathbf{x}_i on y_i. For the definition of the sample \tau-quantile, see Hyndman and Fan (1996). If the network matrix is weighted, the sample weighted quantile can be used, where the outcome for friend j of i is weighted by g_{ij}. It can be shown that the sample \tau-quantile is a weighted average of two peer outcomes. For more details, see the quantile and qpeer.instruments functions.

The quantile q_{\tau,i}(\mathbf{y}_{-i}) can be replaced with the average peer variable in linpeer or with other measures in genpeer through the endogenous.variables argument. In genpeer, it is possible to specify multiple peer variables, such as male peer averages and female peer averages. Additionally, both quantiles and averages can be included (genpeer is general and encompasses qpeer and linpeer). See examples.

One issue in linear peer effect models is that individual preferences with conformity and complementarity/substitution lead to the same reduced form. However, it is possible to disentangle both types of preferences using isolated individuals (individuals without friends). The structural specification of the model differs between isolated and nonisolated individuals. For isolated i, the specification is similar to a standard linear-in-means model without social interactions, given by:

y_i = \mathbf{x}_i^{\prime}\beta + \varepsilon_i.

If node i is non-isolated, the specification is given by:

y_i = \sum_{\tau \in \mathcal{T}} \lambda_{\tau} q_{\tau,i}(\mathbf{y}_{-i}) + (1 - \lambda_2)(\mathbf{x}_i^{\prime}\beta + \varepsilon_i),

where \lambda_2 determines whether preferences exhibit conformity or complementarity/substitution. In general, \lambda_2 > 0 and this means that that preferences are conformist (anti-conformity may be possible in some models when \lambda_2 < 0). In contrast, when \lambda_2 = 0, there is complementarity/substitution between individuals depending on the signs of the \lambda_{\tau} parameters. It is obvious that \beta and \lambda_2 can be identified only if the network includes enough isolated individuals.

Value

A list containing:

References

Houndetoungan, A. (2025). Quantile peer effect models. arXiv preprint arXiv:2405.17290, doi:10.48550/arXiv.2506.12920.

Hyndman, R. J., & Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361-365, doi:10.1080/00031305.1996.10473566.

See Also

qpeer.sim, qpeer.instruments

Examples

set.seed(123)
ngr  <- 50  # Number of subnets
nvec <- rep(30, ngr)  # Size of subnets
n    <- sum(nvec)

### Simulating Data
## Network matrix
G <- lapply(1:ngr, function(z) {
  Gz <- matrix(rbinom(nvec[z]^2, 1, 0.3), nvec[z], nvec[z])
  diag(Gz) <- 0
  # Adding isolated nodes (important for the structural model)
  niso <- sample(0:nvec[z], 1, prob = (nvec[z] + 1):1 / sum((nvec[z] + 1):1))
  if (niso > 0) {
    Gz[sample(1:nvec[z], niso), ] <- 0
  }
  Gz
})

tau <- seq(0, 1, 1/3)
X   <- cbind(rnorm(n), rpois(n, 2))
l   <- c(0.2, 0.15, 0.1, 0.2)
b   <- c(2, -0.5, 1)
eps <- rnorm(n, 0, 0.4)

## Generating `y`
y <- qpeer.sim(formula = ~ X, Glist = G, tau = tau, lambda = l, 
               beta = b, epsilon = eps)$y

### Estimation
## Computing instruments
Z <- qpeer.inst(formula = ~ X, Glist = G, tau = seq(0, 1, 0.1), 
                max.distance = 2, checkrank = TRUE)
Z <- Z$instruments

## Reduced-form model 
rest <- qpeer(formula = y ~ X, excluded.instruments = ~ Z, Glist = G, tau = tau)
summary(rest)
summary(rest, diagnostic = TRUE)  # Summary with diagnostics

## Structural model
sest <- qpeer(formula = y ~ X, excluded.instruments = ~ Z, Glist = G, tau = tau,
              structural = TRUE)
summary(sest, diagnostic = TRUE)
# The lambda^* parameter is y_q (conformity) in the outputs.
# There is no conformity in the data, so the estimate will be approximately 0.

## Structural model with double fixed effects per subnet using optimal GMM 
## and controlling for heteroskedasticity
sesto <- qpeer(formula = y ~ X, excluded.instruments = ~ Z, Glist = G, tau = tau,
               structural = TRUE, fixed.effects = "separate", HAC = "hetero", 
               estimator = "gmm.optimal")
summary(sesto, diagnostic = TRUE)

## Average peer effect model
# Row-normalized network to compute instruments
Gnorm <- lapply(G, function(g) {
  d <- rowSums(g)
  d[d == 0] <- 1
  g / d
})

# GX and GGX
Gall <- Matrix::bdiag(Gnorm)
GX   <- as.matrix(Gall %*% X)
GGX  <- as.matrix(Gall %*% GX)

# Standard linear model
lpeer <- linpeer(formula = y ~ X + GX, excluded.instruments = ~ GGX, Glist = Gnorm)
summary(lpeer, diagnostic = TRUE)
# Note: The normalized network is used here by definition of the model.
# Contextual effects are also included (this is also possible for the quantile model).

# The standard model can also be structural
lpeers <- linpeer(formula = y ~ X + GX, excluded.instruments = ~ GGX, Glist = Gnorm,
                  structural = TRUE, fixed.effects = "separate")
summary(lpeers, diagnostic = TRUE)

## Estimation using `genpeer`
# Average peer variable computed manually and included as an endogenous variable
Gy     <- as.vector(Gall %*% y)
gpeer1 <- genpeer(formula = y ~ X + GX, excluded.instruments = ~ GGX, 
                  endogenous.variables = ~ Gy, Glist = Gnorm, structural = TRUE, 
                  fixed.effects = "separate")
summary(gpeer1, diagnostic = TRUE)

# Using both average peer variables and quantile peer variables as endogenous,
# or only the quantile peer variable
# Quantile peer `y`
qy <- qpeer.inst(formula = y ~ 1, Glist = G, tau = tau)
qy <- qy$qy

# Model estimation
gpeer2 <- genpeer(formula = y ~ X + GX, excluded.instruments = ~ GGX + Z, 
                  endogenous.variables = ~ Gy + qy, Glist = Gnorm, structural = TRUE, 
                  fixed.effects = "separate")
summary(gpeer2, diagnostic = TRUE)

Simulating Linear Peer Effect Models

Description

linpeer.sim simulates linear peer effect models.

Usage

linpeer.sim(
  formula,
  Glist,
  parms,
  lambda,
  beta,
  epsilon,
  structural = FALSE,
  data
)

Arguments

Value

A list containing:

See Also

qpeer, linpeer

Examples

set.seed(123)
ngr  <- 50
nvec <- rep(30, ngr)
n    <- sum(nvec)
G    <- lapply(1:ngr, function(z){
  Gz <- matrix(rbinom(nvec[z]^2, 1, 0.3), nvec[z])
  diag(Gz) <- 0
  Gz/rowSums(Gz) # Row-normalized network
})
X    <- cbind(rnorm(n), rpois(n, 2))
l    <- 0.5
b    <- c(2, -0.5, 1)

out  <- linpeer.sim(formula = ~ X, Glist = G, lambda = l, beta = b)
summary(out$y)

Printing Specification Tests for Peer Effects Models

Description

A print method for the class qpeer.test.

Usage

## S3 method for class 'qpeer.test'
print(x, ...)

Arguments

Value

No return value, called for side effects

Computing Instruments for Linear Models with Quantile Peer Effects

Description

qpeer.instruments computes quantile peer variables.

Usage

qpeer.instruments(
  formula,
  Glist,
  tau,
  type = 7,
  data,
  max.distance = 1,
  checkrank = FALSE,
  tol = 1e-10
)

qpeer.instrument(
  formula,
  Glist,
  tau,
  type = 7,
  data,
  max.distance = 1,
  checkrank = FALSE
)

qpeer.inst(
  formula,
  Glist,
  tau,
  type = 7,
  data,
  max.distance = 1,
  checkrank = FALSE
)

qpeer.insts(
  formula,
  Glist,
  tau,
  type = 7,
  data,
  max.distance = 1,
  checkrank = FALSE
)

Arguments

Details

The sample quantile is computed as a weighted average of two peer outcomes (see Hyndman and Fan, 1996). Specifically:

q_{\tau,i}(x_{-i}) = (1 - \omega_i)x_{i,(\pi_i)} + \omega_ix_{i,(\pi_i+1)},

where x_{i,(1)}, x_{i,(2)}, x_{i,(3)}, \ldots are the order statistics of the outcome within i's peers, and q_{\tau,i}(x_{-i}) represents the sample \tau-quantile of the outcome within i's peer group. If y is specified, then the ranks \pi_i and the weights \omega_i for the variables in X are determined based on y. The network matrices in Glist can be weighted or unweighted. If weighted, the sample weighted quantile is computed, where the outcome for friend j of i is weighted by g_{ij}, the (i, j) entry of the network matrix.

Value

A matrix including quantile peer variables

A list containing:

References

Hyndman, R. J., & Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361-365, doi:10.1080/00031305.1996.10473566.

See Also

qpeer, qpeer.sim, linpeer

Examples

ngr  <- 50
nvec <- rep(30, ngr)
n    <- sum(nvec)
G    <- lapply(1:ngr, function(z){
  Gz <- matrix(rbinom(sum(nvec[z]*(nvec[z] - 1)), 1, 0.3), nvec[z])
  diag(Gz) <- 0
  Gz
}) 
tau  <- seq(0, 1, 0.25)
X    <- cbind(rnorm(n), rpois(n, 2))
l    <- c(0.2, 0.1, 0.05, 0.1, 0.2)
b    <- c(2, -0.5, 1)
y    <- qpeer.sim(formula = ~X, Glist = G, tau = tau, lambda = l, beta = b)$y
Inst <- qpeer.instruments(formula = ~ X, Glist = G, tau = tau, max.distance = 2)$instruments
summary(Inst)

Simulating Linear Models with Quantile Peer Effects

Description

qpeer.sim simulates the quantile peer effect models developed by Houndetoungan (2025).

Usage

qpeer.sim(
  formula,
  Glist,
  tau,
  parms,
  lambda,
  beta,
  epsilon,
  structural = FALSE,
  init,
  type = 7,
  tol = 1e-10,
  maxit = 500,
  details = TRUE,
  data
)

Arguments

Value

A list containing:

References

Houndetoungan, A. (2025). Quantile peer effect models. arXiv preprint arXiv:2405.17290, doi:10.48550/arXiv.2506.12920.

Hyndman, R. J., & Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361-365, doi:10.1080/00031305.1996.10473566.

See Also

qpeer, qpeer.instruments

Examples

set.seed(123)
ngr  <- 50
nvec <- rep(30, ngr)
n    <- sum(nvec)
G    <- lapply(1:ngr, function(z){
  Gz <- matrix(rbinom(nvec[z]^2, 1, 0.3), nvec[z])
  diag(Gz) <- 0
  Gz
}) 
tau  <- seq(0, 1, 0.25)
X    <- cbind(rnorm(n), rpois(n, 2))
l    <- c(0.2, 0.1, 0.05, 0.1, 0.2)
b    <- c(2, -0.5, 1)

out  <- qpeer.sim(formula = ~ X, Glist = G, tau = tau, lambda = l, beta = b)
summary(out$y)
out$iteration

Specification Tests for Peer Effects Models

Description

qpeer.test performs specification tests on peer effects models. These include monotonicity tests on quantile peer effects, as well as tests for instrument validity when an alternative set of instruments is available.

Usage

qpeer.test(
  model1,
  model2 = NULL,
  which,
  full = FALSE,
  boot = 10000,
  maxit = 1e+06,
  eps_f = 1e-09,
  eps_g = 1e-09
)

Arguments

Details

The monotonicity tests evaluate whether the quantile peer effects \lambda_{\tau} are constant, increasing, or decreasing. In this case, model1 must be an object of class qpeer, and the which argument specifies the null hypothesis: "uniform", "increasing", or "decreasing". For the "uniform" test, a standard Wald test is performed. For the "increasing" and "decreasing" tests, the procedure follows Kodde and Palm (1986).

The instrument validity tests assess whether a second set of instruments Z_2 is valid, assuming that a baseline set Z_1 is valid. In this case, both model1 and model2 must be objects of class qpeer, linpeer, or genpeer. The test compares the estimates obtained using each instrument set. If Z_2 nests Z_1, it is recommended to compare the overidentification statistics from both estimations (see Hayashi, 2000, Proposition 3.7). If Z_2 does not nest Z_1, the estimates themselves are compared. To compare the overidentification statistics, set the which argument to "sargan". To compare the estimates directly, set the which argument to "wald".

Given two competing models, it is possible to test whether one is significantly worse using an encompassing test by setting which to "encompassing". The null hypothesis is that model1 is not worse.

Value

A list containing:

References

Hayashi, F. (2000). Econometrics. Princeton University Press.

Kodde, D. A., & Palm, F. C. (1986). Wald criteria for jointly testing equality and inequality restrictions. Econometrica, 54(5), 1243–1248.

Examples

set.seed(123)
ngr  <- 50  # Number of subnets
nvec <- rep(30, ngr)  # Size of subnets
n    <- sum(nvec)

### Simulating Data
## Network matrix
G <- lapply(1:ngr, function(z) {
  Gz <- matrix(rbinom(nvec[z]^2, 1, 0.3), nvec[z], nvec[z])
  diag(Gz) <- 0
  # Adding isolated nodes (important for the structural model)
  niso <- sample(0:nvec[z], 1, prob = (nvec[z] + 1):1 / sum((nvec[z] + 1):1))
  if (niso > 0) {
    Gz[sample(1:nvec[z], niso), ] <- 0
  }
  Gz
})

tau <- seq(0, 1, 1/3)
X   <- cbind(rnorm(n), rpois(n, 2))
l   <- c(0.2, 0.15, 0.1, 0.2)
b   <- c(2, -0.5, 1)
eps <- rnorm(n, 0, 0.4)

## Generating `y`
y <- qpeer.sim(formula = ~ X, Glist = G, tau = tau, lambda = l, 
               beta = b, epsilon = eps)$y

### Estimation
## Computing instruments
Z1 <- qpeer.inst(formula = ~ X, Glist = G, tau = seq(0, 1, 0.1), 
                 max.distance = 2, checkrank = TRUE)$instruments
Z2 <- qpeer.inst(formula = y ~ X, Glist = G, tau = seq(0, 1, 0.1), 
                 max.distance = 2, checkrank = TRUE)$instruments

## Reduced-form model 
rest1 <- qpeer(formula = y ~ X, excluded.instruments = ~ Z1, Glist = G, tau = tau)
summary(rest1, diagnostic = TRUE)  
rest2 <- qpeer(formula = y ~ X, excluded.instruments = ~ Z1 + Z2, Glist = G, tau = tau)
summary(rest2, diagnostic = TRUE)  

qpeer.test(model1 = rest1, which = "increasing")
qpeer.test(model1 = rest1, which = "decreasing")
qpeer.test(model1 = rest1, model2 = rest2, which = "sargan")

#' A model with a mispecified tau
rest3 <- qpeer(formula = y ~ X, excluded.instruments = ~ Z1 + Z2, Glist = G, tau = c(0, 1))
summary(rest3)
#' Test is rest3 is worse than rest1
qpeer.test(model1 = rest3, model2 = rest1, which = "encompassing")

Summary for the Estimation of CES-based Peer Effects Models

Description

Summary and print methods for the class cespeer.

Usage

## S3 method for class 'cespeer'
summary(object, fullparameters = TRUE, ...)

## S3 method for class 'summary.cespeer'
print(x, ...)

## S3 method for class 'cespeer'
print(x, ...)

Arguments

Value

A list containing:

Summary for the Estimation of Quantile Peer Effects Models

Description

Summary and print methods for the class qpeer.

Usage

## S3 method for class 'genpeer'
summary(
  object,
  fullparameters = TRUE,
  diagnostic = FALSE,
  diagnostics = FALSE,
  ...
)

## S3 method for class 'summary.genpeer'
print(x, ...)

## S3 method for class 'genpeer'
print(x, ...)

## S3 method for class 'linpeer'
summary(
  object,
  fullparameters = TRUE,
  diagnostic = FALSE,
  diagnostics = FALSE,
  ...
)

## S3 method for class 'summary.linpeer'
print(x, ...)

## S3 method for class 'linpeer'
print(x, ...)

## S3 method for class 'qpeer'
summary(
  object,
  fullparameters = TRUE,
  diagnostic = FALSE,
  diagnostics = FALSE,
  ...
)

## S3 method for class 'summary.qpeer'
print(x, ...)

## S3 method for class 'qpeer'
print(x, ...)

Arguments

Value

A list containing: