CRE_SS: A Sample Selection Model with Correlated Random Effects

Description

Estimate a sample selection model in panel counting data, in which the selection equation is a Probit model with random effects on individuals, and the outcome equation is a Poisson Lognormal model with random effects on the same individuals. The random effects on the same individual and the error terms on the same <individual, time> dyad are both correlated across two equations.

Usage

CRE_SS(sel_form, out_form, id, data = NULL, par = NULL, killed_par = NULL,
  par_files = NULL, delta = 1, sigma = 1, gamma = 1, max_delta = 3,
  max_sigma = 3, max_gamma = 5, rho = 0, tau = 0, lower = c(rho = -1,
  tau = -1), upper = c(rho = 1, tau = 1), method = "L-BFGS-B", H = c(10,
  10), psnH = 20, prbH = 20, plnreH = 20, accu = 10000,
  reltol = sqrt(.Machine$double.eps), verbose = 0, tol_gtHg = Inf)

Value

A list containing the results of the estimated model

Arguments

sel_form: Formula for selection equation, a probit model with random effects
out_form: Formula for outcome equation, a Poisson model with random effects
id: A vector that represents the identity of individuals, numeric or character
data: Input data, a data frame
par: Starting values for estimates
killed_par: correlation parameters to swtich off
par_files: Loading initial values from saved ProbitRE and PoissonRE estimates
delta: Variance of random effects on the individual level for ProbitRE
sigma: Variance of random effects on the individual level for PLN_RE
gamma: Variance of random effects on the <individual, time> level for PLN_RE
max_delta: Largest allowed initial delta
max_sigma: Largest allowed initial sigma
max_gamma: Largest allowed initial gamma
rho: Correlation between random effects on the individual level
tau: Correlation between error terms on the <individual, time> level
lower: Lower bound for estiamtes
upper: Upper bound for estimates
method: Searching algorithm, don't change default unless you know what you are doing
H: A vector of length 2, specifying the number of points for inner and outer Quadratures
psnH: Number of Quadrature points for Poisson RE model
prbH: Number of Quddrature points for Probit RE model
plnreH: Number of Quddrature points for PLN_RE model
accu: L-BFGS-B only, 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See optim
reltol: Relative convergence tolerance. default typically 1e-8
verbose: Level of output during estimation. Lowest is 0.
tol_gtHg: tolerance on gtHg, not informative for L-BFGS-B

References

1. Jing Peng and Christophe Van den Bulte. Participation vs. Effectiveness of Paid Endorsers in Social Advertising Campaigns: A Field Experiment. Working Paper.

2. Jing Peng and Christophe Van den Bulte. How to Better Target and Incent Paid Endorsers in Social Advertising Campaigns: A Field Experiment. In Proceedings of the 2015 International Conference on Information Systems.

Examples

Run this code

# \donttest{
data(rt)
# Note: estimation may take up 10~15 minutes
est = CRE_SS(isRetweet~fans+tweets+as.factor(tweet.id),
                       num.words~fans+tweets+as.factor(tweet.id),
                       id=rt$user.id, data=rt)
# }