gCD function

Generalized Cook's Distance

Compute generalize Cook's distances (gCD's) for exploratory and confirmatory FA. Can return DFBETA matrix if requested. If mirt is used, then the values will be associated with the unique response patterns instead.

gCD(data, model, vcov_drop = FALSE, progress = TRUE, ...)

## S3 method for class 'gCD'
print(x, ncases = 10, DFBETAS = FALSE, ...)

## S3 method for class 'gCD'
plot(
  x,
  y = NULL,
  main = "Generalized Cook Distance",
  type = c("p", "h"),
  ylab = "gCD",
  ...
)

Arguments

• data: matrix or data.frame
• model: if a single numeric number declares number of factors to extract in exploratory factor analysis (requires complete dataset, i.e., no missing). If class(model) is a sem (semmod), or lavaan (character), then a confirmatory approach is performed instead
• vcov_drop: logical; should the variance-covariance matrix of the parameter estimates be based on the unique data[-i, ] models (Pek and MacCallum, 2011) or original data?
• progress: logical; display the progress of the computations in the console?
• ...: additional parameters to be passed
• x: an object of class gCD
• ncases: number of extreme cases to display
• DFBETAS: logical; return DFBETA matrix in addition to gCD? If TRUE, a list is returned
• y: a NULL value ignored by the plotting function
• main: the main title of the plot
• type: type of plot to use, default displays points and lines
• ylab: the y label of the plot

Details

Note that gCD is not limited to confirmatory factor analysis and can apply to nearly any model being studied where detection of influential observations is important.

Examples

## Not run:

#run all gCD functions using multiple cores
setCluster()

#Exploratory
nfact <- 3
(gCDresult <- gCD(holzinger, nfact))
(gCDresult.outlier <- gCD(holzinger.outlier, nfact))
plot(gCDresult)
plot(gCDresult.outlier)

#-------------------------------------------------------------------
#Confirmatory with sem
model <- sem::specifyModel()
   F1 -> Remndrs,    lam11
          F1 -> SntComp,    lam21
          F1 -> WrdMean,    lam31
          F2 -> MissNum,    lam41
          F2 -> MxdArit,    lam52
          F2 -> OddWrds,    lam62
          F3 -> Boots,      lam73
  F3 -> Gloves,     lam83
          F3 -> Hatchts,    lam93
          F1 <-> F1,   NA,     1
          F2 <-> F2,   NA,     1
          F3 <-> F3,   NA,     1

(gCDresult2 <- gCD(holzinger, model))
(gCDresult2.outlier <- gCD(holzinger.outlier, model))
plot(gCDresult2)
plot(gCDresult2.outlier)

#-------------------------------------------------------------------
#Confirmatory with lavaan
model <- 'F1 =~  Remndrs + SntComp + WrdMean
F2 =~ MissNum + MxdArit + OddWrds
F3 =~ Boots + Gloves + Hatchts'

(gCDresult2 <- gCD(holzinger, model, orthogonal=TRUE))
(gCDresult2.outlier <- gCD(holzinger.outlier, model, orthogonal=TRUE))
plot(gCDresult2)
plot(gCDresult2.outlier)

# categorical data with mirt
library(mirt)
data(LSAT7)
dat <- expand.table(LSAT7)
model <- mirt.model('F = 1-5')
result <- gCD(dat, model)
plot(result)

mod <- mirt(dat, model)
res <- mirt::residuals(mod, type = 'exp')
cbind(res, gCD=round(result$gCD, 3))
## End(Not run)

References

Chalmers, R. P. & Flora, D. B. (2015). faoutlier: An R Package for Detecting Influential Cases in Exploratory and Confirmatory Factor Analysis. Applied Psychological Measurement, 39, 573-574. tools:::Rd_expr_doi("10.1177/0146621615597894")

Flora, D. B., LaBrish, C. & Chalmers, R. P. (2012). Old and new ideas for data screening and assumption testing for exploratory and confirmatory factor analysis. Frontiers in Psychology, 3, 1-21. tools:::Rd_expr_doi("10.3389/fpsyg.2012.00055")

Pek, J. & MacCallum, R. C. (2011). Sensitivity Analysis in Structural Equation Models: Cases and Their Influence. Multivariate Behavioral Research, 46(2), 202-228.

See Also

LD, obs.resid, robustMD, setCluster

Author(s)

Phil Chalmers rphilip.chalmers@gmail.com