Goldberg (2006) described a hierarchical factor structure organization from the ``top down". The original idea was to do successive factor analyses from 1 to nf factors organized by factor score correlations from one level to the next. Waller (2007) discussed a simple way of doing this for components without finding the scores. Using the factor correlations (from Gorsuch) to organize factors hierarchically results may be organized at many different levels. The algorithm may be applied to principal components (pca) or to true factor analysis.
bassAckward(r, nfactors = 1, fm = "minres", rotate = "oblimin", scores = "tenBerge",
adjust=TRUE, plot=TRUE,cut=.3, use = "pairwise", cor = "cor", weight = NULL,
correct = 0.5,...)
bassAckward.diagram(x,digits=2,cut = .3,labels=NULL,marg=c(1.5,.5,1.0,.5),
main="BassAckward",items=TRUE,sort=TRUE,lr=TRUE,curves=FALSE,organize=TRUE,...)A correlation matrix or a data matrix suitable for factoring
Factors from 1 to nfactors will be extracted. If nfactors is a a vector, then just the number of factors specified in the vector will be extracted. (See examples).
Factor method. The default is 'minres' factoring. Although to be consistent with the original Goldberg article, we can also do principal components (fm ="pca").
What type of rotation to apply. The default for factors is oblimin. Unlike the normal call to pca where the default is varimax, in bassAckward the default for pca is oblimin.
What factor scoring algorithm should be used. The default is "tenBerge", other possibilities include "regression", or "bartlett"
If using any other scoring proceure that "tenBerge" should we adjust the correlations for the lack of factor score fit?
By default draw a bassAckward diagram
How to treat missing data. Use='pairwise" finds pairwise complete correlations.
What kind of correlation to find. The default is Pearson.
Should cases be weighted? Default, no.
If finding tetrachoric or polychoric correlations, what correction should be applied to empty cells (defaults to .5)
The object returned by bassAckward
Number of digits to display on each path
Values greater than the abs(cut) will be displayed in a path diagram.
Labels may be taken from the output of the bassAckward function or can be specified as a list.
Margins are set to be slightly bigger than normal to allow for a cleaner diagram
The main title for the figure
if TRUE, show the items associated with the factors
if TRUE, sort the items by factor loadings
Should the graphic be drawn left to right or top to bottom
Should we show the correlations between factors at the same level
Rename and sort the factors at two lowest levels for a more pleasing figure
Other graphic parameters (e.g., cex)
Echo the call
Echos the factor method used
A list of the factor correlations at each level
The factors at each level
Summary of the factor names
Factor labels including items for each level
The correlation matrix analyzed
The factor correlations at each level
The factor analysis loadings at each level, now includes Phi values
This is essentially a wrapper to the fa and pca combined with the faCor functions. They are called repeatedly and then the weights from the resulting solutions are used to find the factor/component correlations.
Although the default is do all factor solutions from 1 to the nfactors, this can be simplified by specifying just some of the factor solutions. Thus, for the 135 items of the spi, it is more reasonable to ask for 3,5, and 27 item solutions.
The function bassAckward.diagram may be called using the diagram function or may be called directly.
The output from bassAckward.diagram is the sorted factor structure suitable for using fa.lookup.
Although not particularly pretty, it is possible to do Schmid-Leiman rotations at each level. Specify the rotation as rotate="schmid".
Goldberg, L.R. (2006) Doing it all Bass-Ackwards: The development of hierarchical factor structures from the top down. Journal of Research in Personality, 40, 4, 347-358.
Gorsuch, Richard, (1983) Factor Analysis. Lawrence Erlebaum Associates.
Revelle, William. (in prep) An introduction to psychometric theory with applications in R. Springer. Working draft available at https://personality-project.org/r/book/
Waller, N. (2007), A general method for computing hierarchical component structures by Goldberg's Bass-Ackwards method, Journal of Research in Personality, 41, 4, 745-752, DOI: 10.1016/j.jrp.2006.08.005
fa, pca, omega and iclust for alternative hierarchical solutions.
# NOT RUN {
bassAckward(Thurstone,4,main="Thurstone data set")
print(bassAckward(psychTools::bfi[1:25],c(2,3,5),main="bfi data set"),short=FALSE)
#do pca instead of factors just summarize, don't plot
summary(bassAckward(psychTools::bfi[1:25],c(1,3,5,7),fm="pca",main="Components",plot=FALSE))
##not run, but useful example
#sp5 <- bassAckward(psychTools::spi[11:145], c(3,4,5,27))
# }
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