Package {LRErdd}

Expectation step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for binary outcomes

Description

E.step.bin() implements the Expectation step of the EM algorithm to calculate the MLE of CACE for binary outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

E.step.bin(theta, dat)

Arguments

Value

A vector with the expected compliance status for each unit in the data set

Expectation step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for binary outcomes

Description

E.step.bin2() implements the Expectation step of the EM algorithm to calculate the MLE of CACE for binary outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

E.step.bin2(theta, dat)

Arguments

Value

A vector with the expected compliance status for each unit in the data set

Expectation step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

E.step.gauss() implements the Expectation step of the EM algorithm to calculate the MLE of CACE for continuous normally distributed outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

E.step.gauss(theta, dat)

Arguments

Value

A vector with the expected compliance status for each unit in the data set

Expectation step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

E.step.gauss2() implements the Expectation step of the EM algorithm to calculate the MLE of CACE for continuous normally distributed outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

E.step.gauss2(theta, dat)

Arguments

Value

A vector with the expected compliance status for each unit in the data set

Maximum Likelihood Estimate (MLE) of the Complier Average Causal Effect (CACE) for binary outcomes

Description

EM.bin() uses the Expectation-Maximization (EM) algorithm to calculate the MLEs of CACE for binary outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

EM.bin(dat, tol = 1e-04, maxit = 1000)

Arguments

Value

The value of the MLE of CACE for binary outcomes (at either convergence or the last iteration if the maximum number of iterations has been reached before convergence)

Maximum Likelihood Estimate (MLE) of the Complier Average Causal Effect (CACE) for binary outcomes

Description

EM.bin2() uses the Expectation-Maximization (EM) algorithm to calculate the MLEs of CACE for binary outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

EM.bin2(dat, tol = 1e-04, maxit = 1000)

Arguments

Value

The value of the MLE of CACE for binary outcomes (at either convergence or the last iteration if the maximum number of iterations has been reached before convergence)

Maximum Likelihood Estimate (MLE) of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

EM.gauss() uses the Expectation-Maximization (EM) algorithm to calculate the MLEs of CACE for continuous normally distributed outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

EM.gauss(dat, tol = 1e-04, maxit = 1000)

Arguments

Value

The value of the MLE of CACE for continuous outcomes (at either convergence or the last iteration if the maximum number of iterations has been reached before convergence)

Maximum Likelihood Estimate (MLE) of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

EM.gauss2() uses the Expectation-Maximization (EM) algorithm to calculate the MLEs of CACE for continuous normally distributed outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

EM.gauss2(dat, tol = 1e-04, maxit = 1000)

Arguments

Value

The value of the MLE of CACE for continuous outcomes (at either convergence or the last iteration if the maximum number of iterations has been reached before convergence)

Maximization step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for binary outcomes

Description

M.step.bin() implements the Maximization step of the EM algorithm to calculate the MLE of CACE for binary outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

M.step.bin(G, dat)

Arguments

Value

A list with the values of the parameters: pi.c = proportion of compliers; py.c0, py.c1 = probabilities that the outcome takes on value 1 for compliers under control and under treatment; py.nt = probability that the outcome takes on value 1 for never-takers

Maximization step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for binary outcomes

Description

M.step.bin2() implements the Maximization step of the EM algorithm to calculate the MLE of CACE for binary outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

M.step.bin2(G, dat)

Arguments

Value

A list with the values of the parameters: pi.c = proportion of compliers; py.c0, py.c1 = probabilities that the outcome takes on value 1 for compliers under control and under treatment; py.nt = probability that the outcome takes on value 1 for never-takers; py.at = probability that the outcome takes on value 1 for always-takers

Maximization step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

M.step.gauss() implements the Maximization step of the EM algorithm to calculate the MLE of CACE for continuous normally distributed outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

M.step.gauss(G, dat)

Arguments

Value

A list with the values of the parameters: pi.c = proportion of compliers; mu.c0, sigma2.c0, mu.c1, sigma2.c1 = means and variances of the Normal distributions of the outcome for compliers under control and under treatment; mu.nt, sigma2.nt = mean and variance of the Normal distribution of the outcome for never-takers

Maximization step of the Expectation-Maximization (EM) algorithm to calculate the MLE of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

M.step.gauss2() implements the Maximization step of the EM algorithm to calculate the MLE of CACE for continuous normally distributed outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

M.step.gauss2(G, dat)

Arguments

Value

A list with the values of the parameters: pi.c = proportion of compliers; mu.c0, sigma2.c0, mu.c1, sigma2.c1 = means and variances of the Normal distributions of the outcome for compliers under control and under treatment; mu.nt, sigma2.nt = mean and variance of the Normal distribution of the outcome for never-takers; mu.at, sigma2.at = mean and variance of the Normal distribution of the outcome for always-takers

Class providing object with RegressionDiscontinuityClass

Description

Class providing object with RegressionDiscontinuityClass

Class providing object with RegressionDiscontinuityClass

Format

R6::R6Class

Value

Object of R6::R6Class with methods for Regression discontinuity analysis

Methods

new(RegressionDiscontinuityClass)

This method is used to create object of this class with the next variables.

initialize(data, forcing, threshold, Z1S1, covariates)

This method initialize the object with the corresponding information.

full_print()

This method print a summary of the object.

summary_statistics_mean()

This method a summary of the variables based on the mean.

bandwidth_selection(typerange = "percentage", range_value = 50, num_it = 50, plot = TRUE)

This methods defines the type of bandwidth that will be considered for the analysis.

distribution_plot(typerange = "percentage", range_value = 25, num_it = 50, covariate, typecov)

This method plots the selected variables and the bandwidths.

summary_bandwidth(buffers = c(100, 500, 1000), num_it = 50)

This method create a table with the summary of the selected variables.

causal_effect(method = 'Sharp FEP', buffers = c(100, 500, 1000), num_it = 50, outcome = "dropout", typeoutcome, sided = "onesided", cin = 0.05, treatm_cov = self$W, num_it_fuzzy = 5, plot = TRUE)

This method is the main function of the package, implementing the four modes of inference on causal effects.

Public fields

Methods

Public methods

• RegressionDiscontinuityClass$new()

• RegressionDiscontinuityClass$full_print()

• RegressionDiscontinuityClass$summary_statistics_mean()

• RegressionDiscontinuityClass$bandwidth_selection()

• RegressionDiscontinuityClass$distribution_plot()

• RegressionDiscontinuityClass$summary_bandwidth()

• RegressionDiscontinuityClass$causal_effect()

• RegressionDiscontinuityClass$clone()

Method new()

Usage

RegressionDiscontinuityClass$new(data, forcing, threshold, Z1S1, covariates)

Method full_print()

Usage

RegressionDiscontinuityClass$full_print()

Method summary_statistics_mean()

Usage

RegressionDiscontinuityClass$summary_statistics_mean()

Method bandwidth_selection()

Usage

RegressionDiscontinuityClass$bandwidth_selection(
  typerange = "percentage",
  range_value = 50,
  num_it = 50,
  plot = TRUE
)

Method distribution_plot()

Usage

RegressionDiscontinuityClass$distribution_plot(
  typerange = "percentage",
  range_value = 25,
  num_it = 50,
  covariate,
  typecov
)

Method summary_bandwidth()

Usage

RegressionDiscontinuityClass$summary_bandwidth(
  buffers = c(100, 500, 1000),
  num_it = 50
)

Method causal_effect()

Usage

RegressionDiscontinuityClass$causal_effect(
  method = "Sharp FEP",
  buffers = c(100, 500, 1000),
  num_it = 50,
  outcome = "dropout",
  typeoutcome,
  sided = "onesided",
  cin = 0.05,
  treatm_cov = self$W,
  num_it_fuzzy = 5,
  plot = TRUE
)

Method clone()

The objects of this class are cloneable with this method.

Usage

RegressionDiscontinuityClass$clone(deep = FALSE)

Arguments

Examples

library (LRErdd)
library (R6)
library(ggplot2)

data(grants)

# Selection of the covariates of interest
cov <- c("HSTech", "hsgrade","Y2005")
# Create a RegressionDiscontinuityClass with the required information
rdo <- RegressionDiscontinuityClass$new( data = grants , forcing = "S",
                                         threshold = 15000 , Z1S1 = "lower",
                                         covariates = cov)

# New object structure
rdo
# Summary of the class
rdo$full_print()
# Summary of statistics
rdo$summary_statistics_mean()


rdo$bandwidth_selection(typerange="percentage",range_value=25,
                        num_it=50,plot=TRUE)

#Distributionpreandpostmatching
rdo$distribution_plot(typerange="percentage",range_value=25,
                      num_it=50,covariate="sex",typecov="binary")

# Summary of bandwidths
rdo$summary_bandwidth(buffers=c(100,500,1000),num_it=1000)


# Causal effect with the four methods :
# sharp FEP , sharp Neyman , Fuzzy Neyman and Fuzzy FEP
rdo$causal_effect(method='Sharp FEP',buffers=c(100,500,1000),
                  num_it=50,outcome="dropout",typeoutcome="binary",plot=TRUE)

rdo$causal_effect(method='Sharp Neyman',buffers=c(100,500,1000),
                  num_it=50,outcome="dropout",typeoutcome="binary",
                  sided="onesided",cin=0.05,plot=TRUE)

rdo$causal_effect(method='Fuzzy Neyman',buffers=c(100,500,1000),
                  num_it=50,outcome="dropout",typeoutcome="binary",
                  treatm_cov="W",plot=TRUE)

rdo$causal_effect(method='Fuzzy FEP',buffers=c(100,500,1000),
                  num_it=50,outcome="dropout",typeoutcome="binary",
                  sided="twosided",treatm_cov="W",num_it_fuzzy=5,
                  plot=TRUE)

Absolute difference in means between treatment groups

Description

Internal helper that computes the absolute value of the difference in means of a variable between the two assignment groups. It is used as test statistic in the randomization-based balance tests.

Usage

Tave(x, z)

Arguments

Value

A numeric value: the absolute difference in means between the two groups.

From binomial to numerical

Description

all_binom2num() analizes a data frame, detects the binomial columns and convert them to numeric format.

Usage

all_binom2num(data)

Arguments

Details

In the shiny application we need to verify some conditions and this function helps us to check it.

Value

A new dataset. Convert every binomial column in the dataset as numerical to avoid errors

Examples

 

df <- data.frame(
gp = factor(rep(letters[1:3], each = 10)),
y = rnorm(30),
a = sample(c('0','1'), 30, replace = TRUE))

all_binom2num(df)

Selection of the cutting range

Description

cutting_range() defines the values of the forcing values taking into account the threshold, the type of selection and the range value.

Usage

cutting_range(forcingvalues, threshold, typerange, range_value)

Arguments

Value

a list with two values that define the lower and upper values to create the selection of the data

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for binary outcomes

Description

da.bin() implements the Data Augmentation (DA) method to impute the compliance status of each unit for binary outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

da.bin(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for a binary outcome under the sharp null hypothesis of no effect

Description

da.bin.h0() implements the Data Augmentation (DA) method to impute the compliance status of each unit for binary outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers and under the sharp null hypothesis of no effect

Usage

da.bin.h0(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set under the sharp null hypothesis of no effect

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for a binary outcome under the sharp null hypothesis of no effect

Description

da.bin.h02() implements the Data Augmentation (DA) method to impute the compliance status of each unit for binary outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers and under the sharp null hypothesis of no effect

Usage

da.bin.h02(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set under the sharp null hypothesis of no effect

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for binary outcomes

Description

da.bin2() implements the Data Augmentation (DA) method to impute the compliance status of each unit for binary outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

da.bin2(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

da.gauss() implements the Data Augmentation (DA) method to impute the compliance status of each unit for normally distributed outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

da.gauss(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for a Gaussian outcome under the sharp null hypothesis of no effect

Description

da.gauss.h0() implements the Data Augmentation (DA) method to impute the compliance status of each unit for a continuous normally distributed outcome in the presence of one-sided noncompliance under exclusion restriction for never-takers and under the sharp null hypothesis of no effect

Usage

da.gauss.h0(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set under the sharp null hypothesis of no effect

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for a Gaussian outcome under the sharp null hypothesis of no effect

Description

da.gauss.h02() implements the Data Augmentation (DA) method to impute the compliance status of each unit for a continuous normally distributed outcome in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers and under the sharp null hypothesis of no effect

Usage

da.gauss.h02(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set under the sharp null hypothesis of no effect

Data Augmentation (DA) step of Markov Chain Monte Carlo (MCMC) algorithm to derive the posterior median of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

da.gauss2() implements the Data Augmentation (DA) method to impute the compliance status of each unit for normally distributed outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

da.gauss2(theta, dat)

Arguments

Value

A vector with the imputed compliance status for each unit in the data set

Fuzzy - FEP approach for binary one sided

Description

Fuzzy - FEP approach for binary one sided

Usage

fuzzy_fep1sided(dataset, Y, W, Z, Y_name, M2 = 10)

Arguments

Details

This is for the cases where the noncompliance is one sided and binary

Value

A list with values of pppv, Tsim, Tobs

Fuzzy - FEP binary two sided

Description

Fuzzy - FEP binary two sided

Usage

fuzzy_fep2sided(dataset, Y, W, Z, Y_name, M2 = 10)

Arguments

Details

This is for the cases where the noncompliance is two sided and binary

Value

A list with values of pppv, Tsim, Tobs

Bandwidth selection for Fuzzy - FEP bandwidth

Description

fuzzy_fep() was defined to calculate just for one dataset. For the cases where the user wants to test several bandwidths this functions is applied.

Usage

fuzzy_fep_bw(
  dataset,
  forcing_var_name = "S",
  Y_name = "dropout",
  niter = 1000,
  W_name = "W",
  bandwidth = c(500, 1000, 1500),
  cut_value = 15000,
  M2 = 5,
  whichunder = 1,
  typemod = "binary",
  typesided = "onesided"
)

Arguments

Value

data frame with variable and value and bandwidth

Fuzzy - FEP 1 sided numerical

Description

Fuzzy - FEP 1 sided numerical

Usage

fuzzy_fep_numeric1sided(dataset, Y, W, Z, Y_name, M2 = 10)

Arguments

Details

This is for the cases where the noncompliance is two sided and numerical

Value

A list with values of pppv, Tsim, Tobs

Fuzzy - FEP 2 sided numerical

Description

Fuzzy - FEP 2 sided numerical

Usage

fuzzy_fep_numeric2sided(dataset, Y, W, Z, Y_name, M2 = 10)

Arguments

Details

This is for the cases where the noncompliance is one sided and numerical

Value

A list with values of pppv, Tsim, Tobs

Fuzzy - neyman approach

Description

fuzzy_neyman() calculates the causal effect with the fuzzy neyman approach

Usage

fuzzy_neyman(Y, Wh, Z, cin = 0.05)

Arguments

Details

The focus will be on the sharp nullhypothesis that disallows any effect of assignment to treatment versus control for compliersbelonging toUs0:H0:Yi(0) =Yi(1)for alli?\210\210 Us0withGi=c, which can be interpreted asthe null hypothesis of no effect of ?\200?receipt?\200\235 of treatment on outcome for the subpopulationof compliers belonging toUs.

Value

A vector with information about the effects and confidence intervals.

Bandwidth selection for Fuzzy - neyman bandwidth

Description

fuzzy_neyman() was defined to calculate just for one dataset. For the cases where the user wants to test several bandwidths this functions is applied.

Usage

fuzzy_neyman_bw(
  dataset,
  forcing_var_name = "S",
  Y_name = "dropout",
  niter = 1000,
  W = "W",
  bandwidth = c(500, 1000, 1500),
  cut_value = 15000,
  whichunder = 1,
  cin = 0.05
)

Arguments

Value

A data frame with effect and bandwidths

Italian university grants and student dropout

Description

Data from an Italian study concerning the effects of university grants on student dropout (Li, Mattei and Mealli, 2015). Eligibility for the grant is determined by a measure of the economic situation of the student's family falling below a threshold of 15,000 euros, which makes it a natural regression discontinuity design.

Usage

data(grants)

Format

A data frame with 15984 rows (students) and 21 columns:

S

Forcing variable: measure of the family's economic situation (in euros); students with S below 15,000 are eligible for the grant

Z

Eligibility indicator (1 = eligible, i.e. S below the threshold; 0 = not eligible)

A

Grant application indicator (1 = applied)

W

Treatment received: grant receipt indicator (1 = received the grant)

dropout

Outcome: 1 if the student dropped out, 0 otherwise

sex

Student's sex (binary indicator)

HSHumanity

High school type: humanities (binary indicator)

HSScience

High school type: science (binary indicator)

HSTech

High school type: technical (binary indicator)

HSOther

High school type: other (binary indicator)

hsgrade

High school grade

Y2004

Cohort indicator: year 2004

Y2005

Cohort indicator: year 2005

Y2006

Cohort indicator: year 2006

University

University indicator

Humanity

Field of study: humanities (binary indicator)

Science

Field of study: science (binary indicator)

Social.Science

Field of study: social science (binary indicator)

BioMed

Field of study: biology and medicine (binary indicator)

Tech

Field of study: technical (binary indicator)

Other

Field of study: other (binary indicator)

References

Li, F., Mattei, A. and Mealli, F. (2015). Bayesian inference for regression discontinuity designs with application to the evaluation of Italian university grants. The Annals of Applied Statistics, 9(4), 1906-1931. doi:10.1214/15-AOAS809

Posterior median of the Complier Average Causal Effect (CACE) for binary outcomes

Description

mcmc.bin() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for binary outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

mcmc.bin(n.iter, n.burn, dat)

Arguments

Value

The value of the posterior median of CACE for binary outcomes

Posterior distributions of the parameter vector and the compliance status of each unit for a binary outcome under the sharp null hypothesis of no effect

Description

mcmc.bin.h0() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for a binary outcome in the presence of one-sided noncompliance under exclusion restriction for never-takers and under the sharp null hypothesis of no effect

Usage

mcmc.bin.h0(n.iter, n.burn, dat)

Arguments

Value

A list of two elements: THETA = a matrix with the simulated posterior distribution of the parameter vector for a binary outcome under the sharp null hypothesis of no effect Gstatus = a matrix with simulated posterior distribution of the compliance status of each unit under the sharp null hypothesis of no effect

Posterior distributions of the parameter vector and the compliance status of each unit for a binary outcome under the sharp null hypothesis of no effect

Description

mcmc.bin.h02() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for a binary outcome in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers and under the sharp null hypothesis of no effect

Usage

mcmc.bin.h02(n.iter, n.burn, dat)

Arguments

Value

A list of two elements: THETA = a matrix with the simulated posterior distribution of the parameter vector for a binary outcome under the sharp null hypothesis of no effect Gstatus = a matrix with simulated posterior distribution of the compliance status of each unit under the sharp null hypothesis of no effect

Posterior median of the Complier Average Causal Effect (CACE) for binary outcomes

Description

mcmc.bin2() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for binary outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

mcmc.bin2(n.iter, n.burn, dat)

Arguments

Value

The value of the posterior median of CACE for binary outcomes

Posterior median of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

mcmc.gauss() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for normally distributed outcomes in the presence of one-sided noncompliance under exclusion restriction for never-takers

Usage

mcmc.gauss(n.iter, n.burn, dat)

Arguments

Value

The value of the posterior median of CACE for Gaussian outcomes

Posterior distributions of the parameter vector and the compliance status of each unit for a Gaussian outcome under the sharp null hypothesis of no effect

Description

mcmc.gauss.h0() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for a normally distributed outcome in the presence of one-sided noncompliance under exclusion restriction for never-takers and under the sharp null hypothesis of no effect

Usage

mcmc.gauss.h0(n.iter, n.burn, dat)

Arguments

Value

A list of two elements: THETA = a matrix with the simulated posterior distribution of the parameter vector for a Gaussian outcome under the sharp null hypothesis of no effect Gstatus = a matrix with simulated posterior distribution of the compliance status of each unit under the sharp null hypothesis of no effect

Posterior distributions of the parameter vector and the compliance status of each unit for a Gaussian outcome under the sharp null hypothesis of no effect

Description

mcmc.gauss.h02() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for a normally distributed outcome in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers and under the sharp null hypothesis of no effect

Usage

mcmc.gauss.h02(n.iter, n.burn, dat)

Arguments

Value

A list of two elements: THETA = a matrix with the simulated posterior distribution of the parameter vector for a Gaussian outcome under the sharp null hypothesis of no effect Gstatus = a matrix with simulated posterior distribution of the compliance status of each unit under the sharp null hypothesis of no effect

Posterior median of the Complier Average Causal Effect (CACE) for Gaussian outcomes

Description

mcmc.gauss2() uses the Markov Chain Monte Carlo (MCMC) algorithm with the Data Augmentation (DA) method to derive the posterior median of CACE for normally distributed outcomes in the presence of two-sided noncompliance under monotonicity (no defiers) and exclusion restrictions for both never-takers and always-takers

Usage

mcmc.gauss2(n.iter, n.burn, dat)

Arguments

Value

The value of the posterior median of CACE for Gaussian outcomes

Example of 'LRErdd' in shiny version

Description

With this function a shiny app will be opened with all the functionalities of 'LRErdd'

Usage

open_LRErdd_framework()

Value

A shiny app will be opened

Examples

if (interactive()) {
  open_LRErdd_framework()
}

Shift probabilities away from the boundaries of the unit interval

Description

Internal helper that adds (or subtracts) 0.01 to probabilities equal or close to 0 (or 1) to avoid numerical problems in likelihood evaluations.

Usage

plus(x)

Arguments

Value

A numeric vector of the same length as x with values moved slightly away from 0 and 1.

Randomization-based tests adjusted for multiple testing

Description

rand_pajd() calculates, for each of the selected variables and in the selected subpopulation the meand difference and adjusted p-value.

Usage

rand_pajd(
  dataset,
  forcing_var_name = "S",
  covariates = c("sex", "HSHumanity", "HSTech", "HSOther", "hsgrade", "Y2004"),
  niter = 1000,
  bandwidth = 1000,
  cut_value = 15000,
  whichunder = 1
)

Arguments

Details

The table shows the mean difference of each variable between treatment groups, and the corresponding p-value derived using randomization-based tests adjusted for multiple testing.

Value

A data frame with the selected variables and the correponding mean difference with adjusted p-value.

Examples

 

data(grants)
rand_pajd(dataset = grants, forcing_var_name = 'S', 
covariates = c('sex', 'HSHumanity', 'HSTech', 'HSOther', 
'hsgrade', 'Y2004'), niter = 1000, bandwidth = 1000, 
cut_value = 15000, whichunder = 1)

Bandwidth selection for Randomization-based tests adjusted for multiple testing

Description

Randomization-based tests adjusted for multiple testing (rand_pajd function) was defined to calculate just for one bandwidth. For the cases where the user wants to test several bandwidths this functions is applied.

Usage

rand_pajd_bw(
  dataset,
  forcing_var_name = "S",
  covariates = c("sex", "HSHumanity", "HSTech", "HSOther", "hsgrade", "Y2004"),
  niter = 1000,
  bandwidth = c(500, 1000, 5000),
  cut_value = 15000,
  whichunder = 1
)

Arguments

Value

A data frame with the selected variables and bandwidths, and the correponding mean difference with adjusted p-value.

Examples

 

data(grants)
rand_pajd_bw(dataset = grants, forcing_var_name = 'S', 
covariates = c('sex', 'HSHumanity', 'HSTech', 'HSOther', 
'hsgrade', 'Y2004'), niter = 1000, 
bandwidth = c(500, 1000, 5000), cut_value = 15000, 
whichunder = 1)

Calculate Fisher Exact p-value

Description

sharp_fep implements the Fisher exact p?\210?value approach (Fisher 1925) for drawing inference on causal effects in the dataset

Usage

sharp_fep(dataset, forcing_bin_var_name = "Z", Y_name = "dropout", niter = 100)

Arguments

Details

This approach is randomization-based mode of inference because it assumes randomized experiments: it treats the potential outcome as fixed unknown quantities, viewing the assignment variable, Si, and thus, treatment assignment, Zi, as the only source of randomness. Randomization-based modes of inference, not relying on asymptotic approximations, are particularly attractive in RD settings where the analysis may depend on small samplesize. We implement the Fisher exactp?\210?value approach focusing on assessing the sharp (exact) null hypothesis of no effect of the treatment whatsoever, that is, the null hypothesis under which,for each unit in theUs0, both values of the potential outcomes are identical.

Value

A data frame the correponding effect of the selection.

Examples

 

data(grants)
sharp_fep(dataset = grants, forcing_bin_var_name = 'Z', 
Y_name = 'dropout', niter = 100)

Bandwidth selection for Fisher Exact p-value

Description

shar_fep() was defined to calculate just for one dataset. For the cases where the user wants to test several bandwidths this functions is applied.

Usage

sharp_fep_bw(
  dataset,
  forcing_var_name = "S",
  Y_name = "dropout",
  niter = 1000,
  bandwidth = c(500, 1000, 1500),
  cut_value = 15000,
  whichunder = 1
)

Arguments

Value

A data frame with the selected bandwidths and the correponding effect.

SHARP RDD: RANDOMIZATION-BASED INFERENCE - NEYMAN APPROACH

Description

sharp_neyman() implements the Neyman approach (Neyman 1923, 1990) for drawing inference on causal effects in the dataset

Usage

sharp_neyman(Y, Z, cin)

Arguments

Details

When the Neyman approach is used for inference, the function calculate the estimate of the average causal effect in this Equation (1) derived using the estimator proposed by Neyman,that is, the difference between the observed averages for units exposed to treatment and units exposed to control.

Value

A vector with values for the effect and the confidence intervals.

Bandwidth selection for Sharp - neyman approach

Description

sharp_neyman() was defined to calculate just for one dataset. For the cases where the user wants to test several bandwidths this functions is applied.

Usage

sharp_neyman_bw(
  dataset,
  forcing_var_name = "S",
  Y_name = "dropout",
  niter = 1000,
  bandwidth = c(500, 1000, 1500),
  cut_value = 15000,
  whichunder = 1,
  cin = 0.05
)

Arguments

Details

We focus on the sharp null hypothesis of no effect of assignment of treatment on outcome: H0:Yi(0) =Yi(1)for alli ?\210\210 Us0

Value

data frame with variable and value and bandwidth