omega.graph {psych}R Documentation

Graph hierarchical factor structures


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 draws both such structures. Graphs are drawn directly onto the graphics window or expressed in ``dot" commands for conversion to graphics using implementations of Graphviz.

Using Graphviz allows the user to clean up the Rgraphviz output.

In addition


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", ...)


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
title Figure title
... Other options to pass into the graphics packages


Requires the Rgraphviz package. omega requires the GPArotation package.


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


Requires rgraphviz. – omega requires GPArotation

Maintainer: William Revelle


Revelle, W. (in preparation) An Introduction to Psychometric Theory with applications in R.

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

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.

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


#24 mental tests from Holzinger-Swineford-Harman
if(require(GPArotation) ) {om24 <- omega(Harman74.cor$cov,4) } #run omega
if(require(Rgraphviz) ){om24pn <- omega.graph(om24,sl=FALSE)} #show the structure
#example hierarchical structure from Jensen and Weng
if(require(GPArotation) ) { <- omega(make.hierarchical())}
if(require(Rgraphviz) ) {om.jen <- omega.graph(,sl=FALSE) }

[Package psych version 1.0-68 Index]