Type: Package
Title: Strategic Selection Estimator
Version: 1.4
Description: Provides functions to estimate a strategic selection estimator. A strategic selection estimator is an agent error model in which the two random components are not assumed to be orthogonal. In addition this package provides generic functions to print and plot objects of its class as well as the necessary functions to create tables for LaTeX. There is also a function to create dyadic data sets.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends: R (≥ 3.5.0), MASS, memisc, Formula, mnormt, pbivnorm
LazyData: TRUE
NeedsCompilation: no
Packaged: 2025-03-24 20:14:41 UTC; lleemann
Author: Lucas Leemann [aut, cre]
Maintainer: Lucas Leemann <lleemann@gmail.com>
Repository: CRAN
Date/Publication: 2025-03-24 20:40:02 UTC

This package allows to estimate strategic selection models.

Description

This package provides functionality to estimate, summarize, plot, predict, and export strategic selection estimates. It allows researchers to incorporate the strategic nature of the DGP while not constraining the errors to be orthogonal. By relaxing the assumptions, this estimator becomes a blend of an agent error model and a Heckman selection model.

Details

Package: StratSel
Type: Package
Version: 1.4
Date: 2025-03-24
License: GPL (>= 2)

Author(s)

Lucas Leemann lleemann@gmail.com

References

Lucas Leemann. 2014. "Strategy and Sample Selection - A Strategic Selection Estimator", Political Analysis 22: 374-397.

See Also

games

Examples

# replicate the example from Leemann (2014):
library(memisc)
data(war1800)
## Not run: out1 <- StratSel(Y ~ s_wt_re1 + revis1 | dem1 + mixed1 | balanc +
 dem2 + mixed2, data=war1800, corr=TRUE)
## End(Not run)
out2 <- StratSel(Y ~ s_wt_re1 + revis1 | dem1 + mixed1 | balanc +
 dem2 + mixed2, data=war1800, corr=FALSE)
setStratSelDefault()
## Not run: z <- mtable(out1,out2)
# toLatex(z) for a LaTeX output or just regular table:

Fitting Strategic Selection Models

Description

This function estimates a strategic selection estimator. This function fits a strategic selection estimator which is based on an agent error model (belongs to the general class of quantal response models). The underlying formal structure is 

       1 
      /\  
     /  \  
    /    \ 2  
   u11   /\  
        /  \  
       /    \  
      0     u14  
      0     u24

and shows a game where there are two players which move sequentially. Player 1 decides to move left or right and if she does move right player 2 gets to move. The final outcome in this case depends on the move of player 2.

Usage

StratSel(formula, corr = TRUE, Startval, optim.method = "BFGS", data, ...)

Arguments

formula

The formula has the following form Y ~ X11 | X14 | X24 whereas Y is the outcome variable taking values 1, 3, or 4 depending on which outcome resulted. The explanatory variables are supplied via X11, X14, and X24 depending on which part of the utility function they should explain.

corr

Logical. If corr=TRUE a strategic selection estimator is estimated. If corr=FALSE an ordinary agent error model is estimated as the command egame12 in the games package does. Note, that the variance of the error terms is fixed differently and hence the coefficients will be different, but all resulting statistics (z-values, predicted probabilities, ...) are identical as the fixed variances are identifying assumptions. See logLikStratSel for details.

Startval

Vector. Allows the user to specify starting values. If there is no user-supplied vector the function will generate starting values itself. It is strongly recommended to to let the function determine the optimal starting values.

optim.method

Optimization method to be used by optim; can be: "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", or "Brent". See optim for details. The default is "BFGS".

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which StratSel is called.

...

additional arguments.

Value

StratSel returns an object of class StratSel for which appropriate plot, print, summary, and predict functions exist.

Author(s)

Lucas Leemann lleemann@gmail.com

References

Lucas Leemann. 2014. "Strategy and Sample Selection - A Strategic Selection Estimator", Political Analysis 22: 374-397.

Curtis S. Signorino. 2003. "Structure and Uncertainty in Discrete Choice Models." Political Analysis 11:316–344.

Examples

# replicate the example from Leemann (2014):
data(war1800)
## Not run: out1 <- StratSel(Y ~ s_wt_re1 + revis1 | dem1 + mixed1 | balanc
 + dem2 + mixed2, data=war1800, corr=TRUE)
## End(Not run)
out2 <- StratSel(Y ~ s_wt_re1 + revis1 | dem1 + mixed1 | balanc
 + dem2 + mixed2, data=war1800, corr=FALSE)

Fake Data for Illustration

Description

This data is just for illustration. The code to generate it is:

set.seed(124)
n <- 1000
x24 <- cbind(rnorm(n), rnorm(n))
error <- rmnorm(n,c(0,0),matrix(c(1,0.6,0.6,1),2,2))
e24 <- error[,2]
y24.latent <- x24%*%c(1,1) + e24
y2 <- rep(NA,n)
y2[y24.latent>0] <- 1
y2[y24.latent<0] <- 0
mod2 <- glm(y2 ~ x24, family=binomial(link=probit))
p24 <- pnorm(predict(mod2))
x11 <- cbind(rnorm(n, sd=0.2), rnorm(n, sd=0.2))
x14 <- cbind(x24[,2],rnorm(n))
e14 <- error[,1]
y14.latent <- x14%*%c(2,1) * p24 - x11%*%c(1,1) + e14
y1 <- rep(NA,n)
y1[y14.latent>0] <- 1
y1[y14.latent<0] <- 0
Y <- rep(NA,n)
Y[y1==0] <- 1
Y[y1==1&y2==0] <- 3
Y[y1==1&y2==1] <- 4
colnames(x11) <- c("var A", "var B")
colnames(x14) <- c("var C", "var D")
colnames(x24) <- c("var E", "var C")
data.fake <- data.frame(Y,x11,x14,x24)

Usage

data(data.fake)

Format

A data frame with 1000 observations on the following 7 variables.

Y

A numeric vector with values 1,3, and 4 depending on which outcome occurred.

var.A

A numeric vector mimicking an explanatory variable as part of X11.

var.B

A numeric vector mimicking an explanatory variable as part of X11.

var.C

A numeric vector mimicking an explanatory variable as part of X14 and of X24.

var.D

A numeric vector mimicking an explanatory variable as part of X14.

var.E

A numeric vector mimicking an explanatory variable as part of X24.

var.C.1

A numeric vector mimicking an explanatory variable as part of X14 and of X24. Identical to var.C.

Source

Can be independently re-created by anybody.

Examples

data(data.fake)
summary(data.fake)
## Not run: out1 <- StratSel(Y ~ var.A + var.B | var.C + var.D | 
	var.E + var.C, data=data.fake, corr=TRUE)
## End(Not run)
## Not run: summary(out1)
# True parameters are 1 or 2 except the three constant terms (which are 0). 
# The correlation parameter was set to +0.6.

Function to transform f(\rho) back to \rho

Description

The model has a correlation parameter which is estimated and theoretically bound between -1 and +1. To ensure that the estimated parameters are within the theoretical bounds a transformation is necessary. The chosen transformation is:

f(\rho): \rho = \frac{2}{(1-exp(-\theta))}- 1

Whereas \rho is the actual correlation coefficient and \theta is the parameter we estimate in the model. This parametrization has been worked into the likelihood function and ensures that \rho will be between -1 and +1.

Usage

fetch.rho.b(b)

Arguments

b

The vector of estimated coefficients (\beta) whereas the last element is the transformed correlation coefficient (here: \theta).

Details

This function is for internal use but documented as a regular function to enable any user to assess the estimator and its functionality.

Value

The function returns the correct estimate for \rho.

Note

We want to estimate \rho but because it is theoretically bound, we estimate \theta which is not bound can range from -\infty to +\infty.

Author(s)

Lucas Leemann lleemann@gmail.com

See Also

StratSel

Examples

test <- c(1,1,-2.35)
fetch.rho.b(test)

Function to transform var(\theta) back to var(\rho)

Description

The model has a correlation parameter which is estimated and theoretically bound between -1 and +1. To ensure that the estimated parameters are within the theoretical bounds a transformation is necessary. The chosen transformation is:

f(\rho): \rho = \frac{2}{(1-exp(-\theta))}- 1

Whereas \rho is the actual correlation coefficient and \theta is the parameter we estimate in the model. This parametrization has been worked into the likelihood function and ensures that \rho will be between -1 and +1.

The variance covariance matrix thus contains entries based on \theta but not \rho. Hence, this function takes the variance of the transformed correlation parameter (\theta) and produces the value correct for \rho.

To create the correct measure of var(\rho) this function simulates 1,000 \theta's and then transforms them to \rho's. The variance of these \rho's is then reported. Note, this means that the variance-covariance returned by StratSel is only correct for all diagonals and off-diagonals for the parameters (\beta) but for the correlation coefficient only the variance is correct. Given that there is no reason to use the full variance-covariance for post-estimation commands this is not a problem.

Usage

fetch.rho.v(v, b)

Arguments

v

Variance-covariance matrix based on the regular parameters (\beta) and \theta.

b

Coefficient vector, first n elements are for the regular parameter estimates and the last element is \theta.

Details

This function is for internal use but documented as a regular function to enable any user to assess the estimator and its functionality.

Value

Returns the correct variance estimate for the estimate of the correlation coefficient \rho.

Author(s)

Lucas Leemann lleemann@gmail.com

See Also

StratSel

Examples

fetch.rho.v(matrix(c(1,0,0,1),2,2),c(0,0))
fetch.rho.v(matrix(c(1,0,0,2),2,2),c(0,0))

Generates good starting values for a strategic selection model

Description

The function creates good starting values based on the supplied data and model which are to be estimated. To do so, the function runs two probit models, whereas the first one is just on the lower node of the game tree (see StratSel). It then creates predicted probabilities (p24) to estimate a second probit at the first node whereas the variables which are part of X14 are weighted by p24.

Usage

gen.Startval(Startval, user.supplied.startval, corr, ys, xs11, xs14, xs24,
		dim.x11, dim.x14, dim.x24)

Arguments

Startval

Optional. A vector of user supplied starting values.

user.supplied.startval

Logical. If TRUE this function just returns the vector Startval. If the estimated model does not restrict the correlation (so corr=TRUE) then a 0 is attached to the vector Startval.

corr

Logical. Indicates whether the estimated agent error model assumes orthogonal errors (=FALSE) or whether the correlation is estimated (=TRUE).

ys

Vector. The outcome variable which is supplied by the user to StratSel.

xs11

Matrix. Explanatory variables for player 1 and measuring utility from outcome 1.

xs14

Matrix. Explanatory variables for player 1 and measuring utility from outcome 4.

xs24

Matrix. Explanatory variables for player 2 and measuring utility from outcome 4.

dim.x11

Vector. Has two elements for the dimension of X11.

dim.x14

Vector. Has two elements for the dimension of X14.

dim.x24

Vector. Has two elements for the dimension of X24.

Details

This function is for internal use but documented as a regular function to enable any user to assess the estimator and its functionality.

Value

Vector. Has length of the number of parameters to be estimated.

Author(s)

Lucas Leemann lleemann@gmail.com

See Also

StratSel

getSummary Method for extending mtable()

Description

This function extends the mtable() to report strategic selection models (StratSel). Together with setStratSelDefault and the mtable command from the memisc package users can create multi-model tables and export them to LaTeX.

Usage

## S3 method for class 'StratSel'
getSummary(obj, alpha = 0.05, ...)

Arguments

obj

An object of class StratSel.

alpha

Significance level.

...

additional arguments

Value

Returns a list of objects to be fed to mtable. Do not use this command directly. The command mtable will automatically call this function for an object of the StratSel class.

Author(s)

Lucas Leemann lleemann@gmail.com

References

Elff, Martin. (2013). memisc: Tools for Management of Survey Data, Graphics, Programming, Statistics, and Simulation R package version 0.96-7.

See Also

toLatex, mtable

Examples

data(data.fake)
out1 <- StratSel(Y ~ var.A | var.D | var.E , data=data.fake, corr=FALSE)
out2 <- StratSel(Y ~ var.A | var.C | var.E, data=data.fake, corr=FALSE)
mtable(out1,out2)

Function to Extract Log-Likelihood from Objects of Class StratSel

Description

Generic logLik function for objects of class StratSel.

Usage

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

Arguments

object

An object of class StratSel

...

additional arguments.

Author(s)

Lucas Leemann lleemann@gmail.com

Log-Likelihood Function of an Agent Error Model

Description

This function calculates the log-likelihood value for an agent error model (belongs to the general class of quantal response models). The underlying formal structure is 

       1 
      /\  
     /  \  
    /    \ 2  
   u11   /\  
        /  \  
       /    \  
      0     u14  
      0     u24

and shows a game where there are two players which move sequentially. Player 1 decides to move left or right and if she does move right player 2 gets to move. The final outcome in this case depends on the move of player 2.

Usage

logLikStrat(x11, x14, x24, y, beta)

Arguments

x11

A vector or a matrix containing the explanatory variables used to parametrize u11.

x14

A vector or a matrix containing the explanatory variables used to parametrize u14.

x24

A vector or a matrix containing the explanatory variables used to parametrize u24.

y

Vector. Outcome variable which can take values 1, 3, and 4 depending on which outcome occurred.

beta

Vector. Coefficients of the model.

Details

This function provides the likelihood of an agent error model (Signorino, 2003). Note, that to derive it one assumes that the two errors are independent. Further, as with probit and logit models, one needs to assume an error variance to achieve identification. Signorino uses \sqrt 2 while logLikStrat uses 1. Hence, the numeric results will differ, but all relevant statistics (predicted probabilities, z-values, ...) will be identical. Finally, u13 and u23 are set to 0 to achieve identification.

Value

Returns a numeric value for the log-likelihood function evaluated for \beta.

Note

The log-likelihood function:

\ell\ell = \sum_{i=1}^n \left(\log(p_{i1})\cdot I(Y_{i}=1) + \log((1-p_{i1})(1-p_{i4}))\cdot I(Y_{i}=3) + \log((1-p_{i1})(p_{i4}))\cdot I(Y_{i}=4) \right)

whereas

p_{i24} = \Phi(x_{24}\cdot\beta_{24})

and

p_{i1} = \Phi(x_{11}\cdot\beta_{11}-p_{24}(x_{14}\cdot\beta_{14}))

Author(s)

Lucas Leemann lleemann@gmail.com

References

Curtis S. Signorino. 2003. "Structure and Uncertainty in Discrete Choice Models." Political Analysis 11:316–344.

See Also

StratSel

Log-Likelihood Function of an Agent Error Model with Correlated Errors (strategic selection model)

Description

This function calculates the log-likelihood value for an agent error model (belongs to the general class of quantal response models) with correlated errors. The underlying formal structure is 

       1 
      /\  
     /  \  
    /    \ 2  
   u11   /\  
        /  \  
       /    \  
      0     u14  
      0     u24

and shows a game where there are two players which move sequentially. Player 1 decides to move left or right and if she does move right player 2 gets to move. The final outcome in this case depends on the move of player 2.

Usage

logLikStratSel(x11, x14, x24, y, beta)

Arguments

x11

A vector or a matrix containing the explanatory variables used to parametrize u11.

x14

A vector or a matrix containing the explanatory variables used to parametrize u14.

x24

A vector or a matrix containing the explanatory variables used to parametrize u24.

y

Vector. Outcome variable which can take values 1, 3, and 4 depending on which outcome occurred.

beta

Vector. Coefficients of the model whereas the last element is the correlation coefficient \rho. Note, that this parameter has been re-paramterized (see details).

Details

This function provides the likelihood of an agent error model (Signorino, 2003) but in addition allows the random components to be correlated and hence can take selection into account. The correlation parameter is re-paramaterized (see Note). Further, as with probit and logit models, one needs to assume an error variance to achieve identification, here 1 is chosen as with a regular probit model. Finally, u13 and u23 are set to 0 to achieve identification.

Value

Returns a numeric value for the log-likelihood function evaluated for \beta.

Note

The notation \boldsymbol{\Phi_2}(a;b;c) indicates a bivariate standard normal cumulative distribution evaluated at the values a,b whereas the two random variables have a correlation of c.

\ell\ell = \sum_{i=1}^n \log\left(\boldsymbol{\Phi_2}(p_{i4}(\mathbf{x}_{i14} \boldsymbol{\beta}_{14})-\mathbf{x}_{i11}\boldsymbol{\beta}_{11}; \mathbf{x}_{i24} \boldsymbol{\beta}_{24}; -\rho)^{(1-I(y_{i}=1))(1-I(y_{i}=4))} \right)

+ \sum_{i=1}^n \log\left(\boldsymbol{\Phi_2}(p_{i4}(\mathbf{x}_{i14} \boldsymbol{\beta}_{14})-\mathbf{x}_{i11}\boldsymbol{\beta}_{11}; \mathbf{x}_{i24} \boldsymbol{\beta}_{24}; \rho)^{(1-I(y_{i}=1))I(y_{i}=4)} \right)

+ \sum_{i=1}^n \log\left(1-\Phi(p_{i4} \mathbf{x}_{i14} \boldsymbol{\beta}_{14} -\mathbf{x}_{i1} \boldsymbol{\beta}_{11})\right)

whereas

p_{i24} = \Phi(x_{24}\cdot\beta_{24})

and

p_{i1} = \Phi(x_{11}\cdot\beta_{11}-p_{24}(x_{14}\cdot\beta_{14}))

The re-parametrization is as follows:

\rho = \frac{2}{1-exp(-\theta)}- 1

Author(s)

Lucas Leemann lleemann@gmail.com

References

Lucas Leemann. 2014. "Strategy and Sample Selection - A Strategic Selection Estimator", Political Analysis 22: 374-397.

See Also

StratSel

A Function To Create Dyadic Data Sets

Description

This function allows the user to create dyadic data sets which can be directed or undirected.

Usage

makeDyadic(x, directed = FALSE, show.progress = 5)

Arguments

x

The data matrix whereas the first variable is the country code and the second column has to be the time variable.

directed

Logical. If directed=TRUE the dyadic data set will be directed and have variables with amended names (creating sen_varname for sender and rec_varname for receiver).

show.progress

Logical. The process may take some time depending on the size of the supplied data matrix. This option allows users to receive feedback of how far along the process is at periodical steps. Default is set to 5.

Details

This function was first written for Simon Collrad-Wexler and then later amended for Fabio Wasserfallen.

Value

Returns a data frame with the dyadic data set.

Author(s)

Lucas Leemann lleemann@gmail.com

Examples

dataOrig <- matrix(c( rep(c(1:4),3), rep(1,4), rep(2,4), rep(3,4),
 rnorm(4,1.5,0.1), rnorm(4,2.5,0.1), rnorm(4,3.5,0.1), rnorm(4,4.5,0.1),
 rnorm(4,5.5,0.1), rnorm(4,6.5,0.1)),12,4)
colnames(dataOrig) <- c("countryCODE", "Year", "Variable 1", "Variable 2")
dataNew <- makeDyadic(dataOrig, directed=TRUE)

Plots a StratSel Object

Description

Plots predicted probabilities for all three possible outcomes based on an object of class StratSel.

Usage

	## S3 method for class 'StratSel'
plot(x, profile, x.move, x.range, uncertainty = FALSE, 
 n.sim = 100, ci = 0.95, ylim, xlab, ylab1, ylab2, ylab3, plot.nr, ...)

Arguments

x

An object of class StratSel

profile

Vector. The values of all independent variables including the three constants.

x.move

Scalar. Indicates which variable is changing (and displayed on the x-axis).

x.range

Vector. A vector with two elements. The x which is moving will start at x.range[1] and end at x.range[2].

uncertainty

Logical. Indicates whether confidence bands should be displayed or not.

n.sim

Scalar. If uncertainty=TRUE the prediction uncertainty is generated with a simulation based on n.sim simulations. Default is 100. It is recommended to use 1000 simulations.

ci

Scalar. Indicates which confidence interval should be plotted, the default is 0.95.

ylim

Vector. A vector with two elements defining the range of the plotted y (predicted probability).

xlab

String. A label to be used for the x-axis. Will be recycled in all three plots.

ylab1

String. Label for the y-axis of the first plot (predicted probability of outcome 1).

ylab2

String. Label for the y-axis of the second plot (predicted probability of not outcome 1).

ylab3

String. Label for the y-axis of the third plot (predicted probability of outcome 4).

plot.nr

Vector. If one does not want to plot all three outcomes, one can use this vector to indicate which plot(s) should be shown.

...

Further arguments to be supplied to plot.

Author(s)

Lucas Leemann lleemann@gmail.com

Examples

data(data.fake)
# Running just an agent error model (note: corr=FALSE) with \code{var.C} being 
#part of both actors' utilities
out1 <- StratSel(Y ~ var.A + var.B | var.C + var.D | var.E + var.C, data=data.fake, corr=FALSE)
par(mfrow=c(3,1))
plot(out1, profile=c(1,0.2,-0.2,1,0.2,-0.2,1,0.1,-0.3), 
 x.move=c(5,9),x.range=c(-15,15), ci=0.7, uncertainty=TRUE)

Prediction Function for Objects of the StratSel Class

Description

Prediction function for objects of the StratSel class. Provides either predictions for all observations in a model or for a specified profile. In addition, the function will either predict an outcome or three probabilities (indicating the probability for each outcome).

Usage

	## S3 method for class 'StratSel'
predict(object, prob = FALSE, profile, ...)

Arguments

object

An object of class StratSel.

prob

Logical. If prob=TRUE the function will compute the predicted probabilities for each of the three possible outcomes. Default is prob=FALSE.

profile

Vector. A vector defining a specific profile for which the prediction is made.

...

...

Value

Either a matrix with dimension n * m, where there are n observations in the original model and m is three (for the three possible outcomes) or it will be a vector with n elements indicating for each observation which the most likely outcome would be.

Author(s)

Lucas Leemann lleemann@gmail.com

Examples

data(data.fake)
out1 <- StratSel(Y ~ var.A + var.B | var.C + var.D | var.E + var.C, data=data.fake, corr=FALSE)
predict(out1)
predict(out1, prob=TRUE)
predict(out1, profile=c(1,0.2,0.2,1,0.2,0.2,1,0.2,0.2))

Print Function for Objects of Class StratSel

Description

Generic print function for objects of class StratSel.

Usage

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

Arguments

x

An object of class StratSel

...

additional arguments.

Author(s)

Lucas Leemann lleemann@gmail.com

Function to Print the Summary Output of an Object of Class StratSel

Description

Function to print the summary output of an object of class StratSel

Usage

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

Arguments

x

An object of class StratSel

...

additional arguments.

Author(s)

Lucas Leemann lleemann@gmail.com

Function Changes Default Settings to Use mtable Command

Description

Function changes default settings to use mtable command.

Usage

setStratSelDefault()

Author(s)

Lucas Leemann lleemann@gmail.com

References

Elff, Martin. (2013). memisc: Tools for Management of Survey Data, Graphics, Programming, Statistics, and Simulation R package version 0.96-7.

See Also

See link[memisc]{mtable} table command in the memisc package.

Summary Function for StratSel Objects

Description

Summary function for StratSel objects which displays a table of estimated coefficients and their standard errors.

Usage

	## S3 method for class 'StratSel'
summary(object, ...)

Arguments

object

An object of class StratSel

...

...

Note

See StratSel help-file for an example.

Author(s)

Lucas Leemann lleemann@gmail.com

Functionto Extract Variance-Covariance from Objects of Class StratSel

Description

Generic vcov function for objects of class StratSel.

Usage

## S3 method for class 'StratSel'
vcov(object,...)

Arguments

object

An object of class StratSel

...

additional arguments.

Author(s)

Lucas Leemann lleemann@gmail.com

A Data Set for Illustrative Purposes

Description

This is a subset (only some variables included) of the data set which is also included in the package games. The data set can also be used to replicate the example that is provided in Leemann (2014) illustrating the strategic selection estimator. It is a data set of militarized international disputes between 1816 and 1899.

Usage

data(war1800)

Format

A data frame with 313 observations on the following 10 variables.

esc

a numeric vector

war

a numeric vector

dem1

a numeric vector

mixed1

a numeric vector

dem2

a numeric vector

mixed2

a numeric vector

s_wt_re1

a numeric vector

revis1

a numeric vector

balanc

a numeric vector

Y

a numeric vector

Source

This data set is taken from the package games.

References

Daniel M. Jones, Stuart A. Bremer and J. David Singer. 1996. "Militarized Interstate Disputes, 1816-1992: Rationale, Coding Rules, and Empirical Patterns." Conflict Management and Peace Science 15(2): 163–213.

Lucas Leemann. 2014. "Strategy and Sample Selection - A Strategic Selection Estimator", Political Analysis 22: 374-397.

Examples

data(war1800)
summary(war1800)