Likelihood Distance.

Description

A general model-based measure of case influence on model fit is likelihood distance (Cook, 1977, 1986; Cook & Weisberg, 1982) defined as

LD_i=2[L(hat{mathbf{θ}})-L(hat{mathbf{θ}}_{(i)})]

where hat{mathbf{θ}} and hat{mathbf{θ}}_{(i)} are the k \times 1 vectors of estimated model parameters on the original and deleted i samples, respectively, where i = 1, …, N. The subscript (i) indicates that the estimate was computed on the sample excluding case i. L(hat{mathbf{θ}}) and L(hat{mathbf{θ}}_{(i)}) are the log-likelihoods based on the original and the deleted i samples, respectively.

Usage

Likedist(model, data, ...)

Arguments

Value

Returns a vector of LD_i.

Note

If for observation i model does not converge or yelds a solution with negative estimated variances, the associated value of LD_i is set to NA.

Author(s)

Massimiliano Pastore, Gianmarco Altoe'

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.

Cook, R.D., Weisberg, S. (1986). Residuals and influence in regressions. New York, NY: Chapman & Hall.

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: this example take several minutes
data("PDII")
model <- "
  F1 =~ y1+y2+y3+y4
"
# fit0 <- sem(model, data=PDII)
# LD <-Likedist(model,data=PDII)
# plot(LD,pch=19,xlab="observations",ylab="Likelihood distances")

## not run: this example take several minutes
## an example in which the deletion of a case yelds a 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)
# LD <-Likedist(model,data=PDII)
# plot(LD,pch=19,xlab="observations",ylab="Likelihood distances")

Results