nSeScree | R Documentation |
This function computes the seScree (S_{Y \bullet X}) indices (Zoski and Jurs, 1996) and the coefficient of determination indices of Nelson (2005) R^2 for determining the number of components/factors to retain.
nSeScree(x, cor = TRUE, model = "components", details = TRUE, r2limen = 0.75, ...)
x |
numeric: eigenvalues. |
cor |
logical: if |
model |
character: |
details |
logical: if |
r2limen |
numeric: criterion value retained for the coefficient of determination indices. |
... |
variable: additionnal parameters to give to the
|
The Zoski and Jurs S_{Y \bullet X} index is the standard error of the estimate (predicted) eigenvalues by the regression from the (k+1, …, p) subsequent ranks of the eigenvalues. The standard error is computed as:
(1) \qquad \qquad S_{Y \bullet X} = √{ \frac{(λ_k -
\hat{λ}_k)^2} {p-2} }
A value of 1/p is choosen as the criteria to determine the number of components or factors to retain, p corresponding to the number of variables.
The Nelson R^2 index is simply the multiple regresion coefficient of determination for the k+1, …, p eigenvalues. Note that Nelson didn't give formal prescriptions for the criteria for this index. He only suggested that a value of 0.75 or more must be considered. More is to be done to explore adequate values.
nFactors |
numeric: number of components/factors retained by the seScree procedure. |
details |
numeric: matrix of the details for each index. |
Gilles Raiche
Centre sur les Applications des Modeles de
Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca
Nasser, F. (2002). The performance of regression-based variations of the visual scree for determining the number of common factors. Educational and Psychological Measurement, 62(3), 397-419.
Nelson, L. R. (2005). Some observations on the scree test, and on coefficient alpha. Thai Journal of Educational Research and Measurement, 3(1), 1-17.
Raiche, G., Walls, T. A., Magis, D., Riopel, M. and Blais, J.-G. (2013). Non-graphical solutions for Cattell's scree test. Methodology, 9(1), 23-29.
Zoski, K. and Jurs, S. (1993). Using multiple regression to determine the number of factors to retain in factor analysis. Multiple Linear Regression Viewpoints, 20(1), 5-9.
Zoski, K. and Jurs, S. (1996). An objective counterpart to the visuel scree test for factor analysis: the standard error scree. Educational and Psychological Measurement, 56(3), 443-451.
plotuScree
, nScree
,
plotnScree
, plotParallel
## SIMPLE EXAMPLE OF SESCREE AND R2 ANALYSIS data(dFactors) eig <- dFactors$Raiche$eigenvalues results <- nSeScree(eig) results plotuScree(eig, main=paste(results$nFactors[1], " or ", results$nFactors[2], " factors retained by the sescree and R2 procedures", sep=""))
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