The Very Simple Structure criterion ( `VSS`

) for estimating the optimal number of factors is plotted as a function of the increasing complexity and increasing number of factors.

`VSS.plot(x, title = "Very Simple Structure", line = FALSE)`

x

output from VSS

title

any title

line

connect different complexities

A plot window showing the VSS criterion varying as the number of factors and the complexity of the items.

Item-factor models differ in their "complexity". Complexity 1 means that all except the greatest (absolute) loading for an item are ignored. Basically a cluster model (e.g., `ICLUST`

). Complexity 2 implies all except the greatest two, etc.

Different complexities can suggest different number of optimal number of factors to extract. For personality items, complexity 1 and 2 are probably the most meaningful.

The Very Simple Structure criterion will tend to peak at the number of factors that are most interpretable for a given level of complexity. Note that some problems, the most interpretable number of factors will differ as a function of complexity. For instance, when doing the Harman 24 psychological variable problems, an unrotated solution of complexity one suggests one factor (g), while a complexity two solution suggests that a four factor solution is most appropriate. This latter probably reflects a bi-factor structure.

For examples of VSS.plot output, see https://personality-project.org/r/r.vss.html

# NOT RUN { test.data <- Harman74.cor$cov my.vss <- VSS(test.data) #suggests that 4 factor complexity two solution is optimal VSS.plot(my.vss,title="VSS of Holzinger-Harmon problem") #see the graphics window # }

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