# Goodness of Fit Distance Compute Goodness of Fit distances between models when removing the $i_{th}$ case. If mirt is used, then the values will be associated with the unique response patterns instead. ```r GOF(data, model, M2 = TRUE, progress = TRUE, ...) ## S3 method for class 'GOF' print(x, ncases = 10, digits = 5, ...) ## S3 method for class 'GOF' plot( x, y = NULL, main = "Goodness of Fit Distance", type = c("p", "h"), ylab = "GOF", absolute = FALSE, ... ) ``` ## 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. Finally, if the model is defined with `mirt::mirt.model()` then distances will be computed for categorical data with the mirt package - `M2`: logical; use the M2 statistic for when using mirt objects instead of G2? - `progress`: logical; display the progress of the computations in the console? - `...`: additional parameters to be passed - `x`: an object of class `GOF` - `ncases`: number of extreme cases to display - `digits`: number of digits to round in the printed result - `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 - `absolute`: logical; use absolute values instead of deviations? ## Details Note that `GOF` is not limited to confirmatory factor analysis and can apply to nearly any model being studied where detection of influential observations is important. ## Examples ```r ## Not run: #run all GOF functions using multiple cores setCluster() #Exploratory nfact <- 3 (GOFresult <- GOF(holzinger, nfact)) (GOFresult.outlier <- GOF(holzinger.outlier, nfact)) plot(GOFresult) plot(GOFresult.outlier) ## include a progress bar GOFresult <- GOF(holzinger, nfact, progress = TRUE) #------------------------------------------------------------------- #Confirmatory with sem model <- sem::specifyModel() F1 -> Remndrs, lam11 F1 -> SntComp, lam21 F1 -> WrdMean, lam31 F2 -> MissNum, lam42 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 (GOFresult <- GOF(holzinger, model)) (GOFresult.outlier <- GOF(holzinger.outlier, model)) plot(GOFresult) plot(GOFresult.outlier) #------------------------------------------------------------------- #Confirmatory with lavaan model <- 'F1 =~ Remndrs + SntComp + WrdMean F2 =~ MissNum + MxdArit + OddWrds F3 =~ Boots + Gloves + Hatchts' (GOFresult <- GOF(holzinger, model, orthogonal=TRUE)) (GOFresult.outlier <- GOF(holzinger.outlier, model, orthogonal=TRUE)) plot(GOFresult) plot(GOFresult.outlier) # categorical data with mirt library(mirt) data(LSAT7) dat <- expand.table(LSAT7) model <- mirt.model('F = 1-5') result <- GOF(dat, model) plot(result) ## 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") ## See Also `gCD`, `LD`, `obs.resid`, `robustMD`, `setCluster` ## Author(s) Phil Chalmers rphilip.chalmers@gmail.com