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psych (version 1.0-97)

omega.graph: Graph hierarchical factor structures

Description

Hierarchical factor structures represent the correlations between variables in terms of a smaller set of correlated factors which themselves can be represented by a higher order factor.

Two alternative solutions to such structures are found by the omega function. The correlated factors solutions represents the effect of the higher level, general factor, through its effect on the correlated factors. The other representation makes use of the Schmid Leiman transformation to find the direct effect of the general factor upon the original variables as well as the effect of orthogonal residual group factors upon the items.

Graphic presentations of these two alternatives are helpful in understanding the structure. omega.graph and omega.diagram draw both such structures. Graphs are drawn directly onto the graphics window or expressed in ``dot" commands for conversion to graphics using implementations of Graphviz (if using omega.graph).

Using Graphviz allows the user to clean up the Rgraphviz output. However, if Graphviz and Rgraphviz are not available, use omega.diagram.

See the other structural diagramming functions, fa.diagram and structure.diagram.

In addition

Usage

omega.diagram(om.results,sl=TRUE,sort=TRUE,labels=NULL,cut=.2,gcut,simple=TRUE,errors=FALSE, digits=1,e.size=.1,rsize=.15,side=3,main=NULL,cex=NULL,color.lines=TRUE, ...) 
omega.graph(om.results, out.file = NULL,  sl = TRUE, labels = NULL, size = c(8, 6), node.font = c("Helvetica", 14), edge.font = c("Helvetica", 10),  rank.direction=c("RL","TB","LR","BT"), digits = 1, title = "Omega", ...)

Arguments

om.results
The output from the omega function
out.file
Optional output file for off line analysis using Graphviz
sl
Orthogonal clusters using the Schmid-Leiman transform (sl=TRUE) or oblique clusters
labels
variable labels
size
size of graphics window
node.font
What font to use for the items
edge.font
What font to use for the edge labels
rank.direction
Defaults to left to right
digits
Precision of labels
cex
control font size
color.lines
Use black for positive, red for negative
title
Figure title
main
main figure caption
...
Other options to pass into the graphics packages
e.size
the size to draw the ellipses for the factors. This is scaled by the number of variables.
cut
Minimum path coefficient to draw
gcut
Minimum general factor path to draw
simple
draw just one path per item
sort
sort the solution before making the diagram
side
on which side should errors be drawn?
errors
show the error estimates
rsize
size of the rectangles

Value

  • clust.graphA graph object
  • semA matrix suitable to be run throughe the sem function in the sem package.

Details

While omega.graph requires the Rgraphviz package, omega.diagram does not. code{omega} requires the GPArotation package.

References

http://personality-project.org/r/r.omega.html Revelle, W. (in preparation) An Introduction to Psychometric Theory with applications in R. http://personality-project.org/r/book

Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14, 57-74. (http://personality-project.org/revelle/publications/iclust.pdf)

Zinbarg, R.E., Revelle, W., Yovel, I., & Li. W. (2005). Cronbach's Alpha, Revelle's Beta, McDonald's Omega: Their relations with each and two alternative conceptualizations of reliability. Psychometrika. 70, 123-133. http://personality-project.org/revelle/publications/zinbarg.revelle.pmet.05.pdf

Zinbarg, R., Yovel, I., Revelle, W. & McDonald, R. (2006). Estimating generalizability to a universe of indicators that all have one attribute in common: A comparison of estimators for omega. Applied Psychological Measurement, 30, 121-144. DOI: 10.1177/0146621605278814 http://apm.sagepub.com/cgi/reprint/30/2/121

See Also

omega, make.hierarchical, ICLUST.rgraph

Examples

Run this code
#24 mental tests from Holzinger-Swineford-Harman
if(require(GPArotation) ) {om24 <- omega(Harman74.cor$cov,4) } #run omega

#
#example hierarchical structure from Jensen and Weng
if(require(GPArotation) ) {jen.omega <- omega(make.hierarchical())}

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