influence.SEM (version 2.3)

genCookDist: Generalized Cook Distance.

Description

Case influence on a vector of parameters may be quantified by generalized Cook's Distance (\(gCD\); Cook 1977, 1986):

$$gCD_i=(\hat{\mathbf{\theta}}-\hat{\mathbf{\theta}}_{(i)})' _a\hat{\mathbf{\Sigma}}(\hat{\mathbf{\theta}}_{(i)})^{-1} (\hat{\mathbf{\theta}}-\hat{\mathbf{\theta}}_{(i)})$$

where \(\hat{\mathbf{\theta}}\) and \(\hat{\mathbf{\theta}}_{(i)}\) are \(l \times 1\) vectors of parameter estimates obained from the original and delete \(i\) samples, and \(_a\hat{\mathbf{\Sigma}}(\hat{\mathbf{\theta}}_{(i)})\) is the estimated asymptotic covariance matrix of the parameter estimates obtained from reduced sample.

Usage

genCookDist(model, data, ...)

Arguments

model

A description of the user-specified model using the lavaan model syntax. See lavaan for more information.

data

A data frame containing the observed variables used in the model. If any variables are declared as ordered factors, this function will treat them as ordinal variables.

…

Additional parameters for sem function.

Value

Returns a vector of \(gCD_i\).

References

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

Cook, R.D. (1986). Assessment of local influence. Journal of the Royal Statistical Society B, 48, 133-169.

Pek, J., MacCallum, R.C. (2011). Sensitivity Analysis in Structural Equation Models: Cases and Their Influence. Multivariate Behavioral Research, 46, 202-228.

Examples

# NOT RUN {
## not run: this example take several minutes
data("PDII")
model <- "
  F1 =~ y1+y2+y3+y4
"
# fit0 <- sem(model, data=PDII)
# gCD <- genCookDist(model,data=PDII)
# plot(gCD,pch=19,xlab="observations",ylab="Cook distance")

## not run: this example take several minutes
## an example in which the deletion of a case produces solution 
## with negative estimated variances
model <- "
  F1 =~ x1+x2+x3
  F2 =~ y1+y2+y3+y4
  F3 =~ y5+y6+y7+y8
"

# fit0 <- sem(model, data=PDII)
# gCD <- genCookDist(model,data=PDII)
# plot(gCD,pch=19,xlab="observations",ylab="Cook distance")
# }