influence.SEM (version 2.3)

Deltachi: Chi-square difference.

Description

Quantifies case influence on overall model fit by change in the test statistic

$$\Delta_{\chi^2_i}=\chi^2-\chi^2_{(i)}$$

where \(\chi^2\) and \(\chi^2_{(i)}\) are the test statistics obtained from original and deleted \(i\) samples.

Usage

Deltachi(model, data, ..., scaled = FALSE)

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.

scaled

Logical, if TRUE the function uses the scaled \(\chi^2\) (Rosseel, 2013).

Value

Returns a vector of \(\Delta_{\chi^2_i}\).

References

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

Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48, 1-36.

Rosseel, Y. (2022). The lavaan tutorial. URL: https://lavaan.ugent.be/tutorial/.

Examples

# NOT RUN {
## not run: this example take several minutes
data("PDII")
model <- "
  F1 =~ y1+y2+y3+y4
"

# fit0 <- sem(model, data=PDII)
# Dchi <- Deltachi(model,data=PDII)
# plot(Dchi,pch=19,xlab="observations",ylab="Delta chisquare")

## 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)
# Dchi <- Deltachi(model,data=PDII)
# plot(Dchi,pch=19,xlab="observations",ylab="Delta chisquare",main="Deltachi function")

## the case that produces negative estimated variances
# sem(model,data=PDII[-which(is.na(Dchi)),])

## same results 
# Dchi <- fitinfluence("chisq",model,data=PDII)$Dind$chisq
# plot(Dchi,pch=19,xlab="observations",ylab="Delta chisquare",main="fitinfluence function")

# }