CaseDeletion {HeckmanEM}

Case deletion analysis for Heckman selection model

Description

This function performs case deletion analysis based on a HeckmanEM object (not available for the contaminated normal model).

Usage

CaseDeletion(object)

Arguments

object

A HeckmanEM object.

Details

This function uses the case deletion approach to study the impact of deleting one or more observations from the dataset on the parameters estimates, using the ideas of Cook (1977) and Zhu et.al. (2001). The GD vector contains the generalized Cook distances

\textrm{GD}^1_i = \dot{Q}_{[i]}(\widehat{\boldsymbol{\theta}} \mid \widehat{\boldsymbol{\theta}})^{\top} \left\{-\ddot{Q}(\widehat{\boldsymbol{\theta}} \mid \widehat{\boldsymbol{\theta}})\right\}^{-1}\dot{Q}_{[i]}(\widehat{\boldsymbol{\theta}} \mid \widehat{\boldsymbol{\theta}}),

where \dot{Q}_{[i]}(\widehat{\boldsymbol{\theta}}\mid \widehat{\boldsymbol{\theta}}) is the gradient vector after dropping the ith observation, and \ddot{Q}(\widehat{\boldsymbol{\theta}} \mid \widehat{\boldsymbol{\theta}}) is the Hessian matrix. The benchmark was adapted using the suggestion of Barros et al. (2010). We use (2 \times \textrm{npar})/n as the benchmark for the \textrm{GD}_i, with \textrm{npar} representing the number of estimated model parameters.

Value

A list of class HeckmanEM.deletion with a vector GD of dimension n (see details), and a benchmark value.

References

M. Barros, M. Galea, M. González, V. Leiva, Influence diagnostics in the Tobit censored response model, Statistical Methods & Applications 19 (2010) 379–397.

R. D. Cook, Detection of influential observation in linear regression, Technometrics 19 (1977) 15–18.

H. Zhu, S. Lee, B. Wei, J. Zhou, Case-deletion measures for models with incomplete data, Biometrika 88 (2001) 727–737.

Examples

n    <- 100
nu   <- 3
cens <- 0.25

set.seed(13)
w <- cbind(1, runif(n, -1, 1), rnorm(n))
x <- cbind(w[,1:2])
c <- qt(cens, df = nu)

sigma2   <- 1
beta     <- c(1, 0.5)
gamma    <- c(1, 0.3, -.5)
gamma[1] <- -c * sqrt(sigma2)

datas <- rHeckman(x, w, beta, gamma, sigma2, rho = 0.6, nu, family = "T")
y     <- datas$y
cc    <- datas$cc

heckmodel <- HeckmanEM(y, x, w, cc, family = "Normal", iter.max = 50)

global <- CaseDeletion(heckmodel)
plot(global)