omega.graph: Graph hierarchical factor structures

In psych: Procedures for Psychological, Psychometric, and Personality Research

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,flabels=NULL,cut=.2,
gcut=.2,simple=TRUE,  errors=FALSE, digits=1,e.size=.1,rsize=.15,side=3,
    main=NULL,cex=NULL,color.lines=TRUE,marg=c(.5,.5,1.5,.5),adj=2, ...) 
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
flabels	Labels for the factors (not counting g)
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
marg	The margins for the figure are set to be wider than normal by default
adj	Adjust the location of the factor loadings to vary as factor mod 4 + 1
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

Details

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

Value

clust.graph	A graph object
sem	A matrix suitable to be run throughe the sem function in the sem package.

Note

omega.graph requires rgraphviz. – omega requires GPArotation

Author(s)

https://personality-project.org/revelle.html
Maintainer: William Revelle [e-mail]

References

https://personality-project.org/r/r.omega.html

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

Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14, 57-74. (https://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. https://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

See Also

omega, make.hierarchical, ICLUST.rgraph

Examples

#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())}

psych documentation built on June 27, 2024, 5:07 p.m.