biprobit_latent {endogeneity}R Documentation

Recursive Bivariate Probit Model with Latent First Stage

Description

Estimate two probit models with bivariate normally distributed error terms, in which the dependent variable of the first stage model is unobserved. The identification of this model is weak if the first-stage does not include regressors that are good predictors of the first-stage dependent variable.

Usage

biprobit_latent(
  form1,
  form2,
  data = NULL,
  EM = FALSE,
  par = NULL,
  method = "BFGS",
  verbose = 0,
  accu = 10000,
  maxIter = 500,
  tol = 1e-05,
  tol_LL = 1e-06
)

Arguments

form1

Formula for the first probit model, in which the dependent variable is unobserved. Use a formula like ~x to avoid specifying the dependent variable.

form2

Formula for the second probit model, the latent dependent variable of the first stage is automatically added as a regressor in this model

data

Input data, a data frame

EM

Whether to maximize likelihood use the Expectation-Maximization (EM) algorithm.

par

Starting values for estimates

method

Optimization algorithm. Default is BFGS

verbose

Level of output during estimation. Lowest is 0.

accu

1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See optim

maxIter

max iterations for EM algorithm

tol

tolerance for convergence of EM algorithm

tol_LL

tolerance for convergence of likelihood

Value

A list containing the results of the estimated model

References

Peng, Jing. (2022) Identification of Causal Mechanisms from Randomized Experiments: A Framework for Endogenous Mediation Analysis. Information Systems Research (Forthcoming), Available at SSRN: https://ssrn.com/abstract=3494856

See Also

Other endogeneity: bilinear(), biprobit_partial(), biprobit(), pln_linear(), pln_probit(), probit_linear_latent(), probit_linear_partial(), probit_linear()

Examples


library(MASS)
N = 2000
rho = -0.5
set.seed(1)

x = rbinom(N, 1, 0.5)
z = rnorm(N)

e = mvrnorm(N, mu=c(0,0), Sigma=matrix(c(1,rho,rho,1), nrow=2))
e1 = e[,1]
e2 = e[,2]

y1 = as.numeric(1 + x + z + e1 > 0)
y2 = as.numeric(1 + x + z + y1 + e2 > 0)

est = biprobit(y1~x+z, y2~x+z+y1)
est$estimates

est_latent = biprobit_latent(~x+z, y2~x+z)
est_latent$estimates


[Package endogeneity version 2.0.1 Index]