Parallel Analysis and Other Non Graphical Solutions to the Cattell Scree Test

Indices, heuristics and strategies to help determine the number of factors/components to retain: 1. Acceleration factor (af with or without Parallel Analysis); 2. Optimal Coordinates (noc with or without Parallel Analysis); 3. Parallel analysis (components, factors and bootstrap); 4. lambda > mean(lambda) (Kaiser, CFA and related); 5. Cattell-Nelson-Gorsuch (CNG); 6. Zoski and Jurs multiple regression (b, t and p); 7. Zoski and Jurs standard error of the regression coeffcient (sescree); 8. Nelson R2; 9. Bartlett khi-2; 10. Anderson khi-2; 11. Lawley khi-2 and 12. Bentler-Yuan khi-2.


    *                                                    *
    *  Changes and Developments in the nFactors Package  *
    *                                                    *

  • Changes in nFactors 2.3.3 (2011-12-16) -

Changes done because the functions mean() and sd() in the moreStats() function were depreciated with data.frames.

xMean <- sapply(x, mean) # mean(x) before change xSd <- sapply(x, sd) # sd(x) before change

  • Changes in nFactors 2.3.2 (2010-10-04) -

Changes in this version are stricly limited to orthographical correction of the documentation.

  • Changes in nFactors 2.3.1 (2009-14-10) -

o Two bugs were fixed inside the function structureSim. The first one, at line 21, is related to permutation analysis where the quantile paramater of the function call stayed fixed at 0.95 even if the value is different in the call. The variable quantile is now formally use in the call to eigenBootParallel. The second bug was realted to an error in the column names of the data.frame return from structureSim: the per and mean.eig columns were unfortunalely inrerchanged. Version 2.3.1 fixed it.

o Bug fixing was the occasion to introduce a new function used for a paper proposed to Behaviormetrika, studySim. But this function is useful for many other simulation settings.

  • Changes in nFactors 2.3 (2009-15-09) -

This version of nFactors is a major upgrade and so presents important additions and modifications. Care was taken to not modified parameters from version 2.2 calls so that functions and packages already requiring nFactors will yet operate correctly in the future. But like with all mojor upgrades, care must be taken and it is recommanded that developpers verify their results. All the future upgrades won't have this potentiel problems.

o Many new procedures to determine the number of components or factors to retain are added: permutation and bootstrap parallel analysis, CNG, Bentler and Yuan, Bartlett, Anderson, Lawley, Zosky and Jurs, etc.

o Care is taken to uniformise the labelling of new functions and new variables. According to the Java coding practice, with this labelling, the names begin with a small character, and capitals are used inside for added concepts.

o It is now possible to do most of the nfactors package analysis on a covariance matrix.

o It is now possible to do most of the nfactors package analysis in the CFA context.

o The permutation parallel analysis of Buja and Eyuboglu (1992) is added.

o It is now possible to bootstrap the eigenvalues from an empirical data matrix.

o New heuristic numerical indices are added to determine the number of components/factores to retain: CNG, Zoski and Jurs multiple regression, Joski and Jurs standard error of the scree, and Nelson R.

o Likelihood ratio tests are added: Bartlet, Anderson, Lawley, and Bentler and Yuan chi-squared.

o The eigenComputes function computes eigenvalues conditional of the class of the object from which data come from: eigenvalues from vector, correlation/covariance matrix, or data from a data.frame.

o The eigenFrom function determine the class of the object.

o The corFA function is added to insert commulalities in the diagonal of a correlation or a covariance matrix.

o The makeCor function creates a full correlation/covariance matrix from a matrix with lower part filled and upper part with zeros.

o Functions are added to generate a factor structure (generateStructure) and to simulate data and correlation matrices from a predefined factor structure (structureSim).

o A function, moreStats, is added to be computes additionnal statistics on a numeric data.frame.

o Utility functions for \code{nScree} class objects werw implemented: is.nScree, plot.nScree, plot.nScree and summary.nScree.

  • Changes in nFactors 2.2 (2009-02-06) -

o Considering the instabillity of the function factanal with ill conditionned correlation matrices, new functions for computing factor analysis are added: componentAxis, iteratePrincipalAxix, principalAxis and principalComponents.

o The diagReplace function replace the upper or the lower diagonal of a correlation matrix with the respective lower or lower diagonal.

o The rRecovery function is added for a verification of the quality of the recovery of an initial correlation matrix.

Reference manual

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2.4.1 by Gilles Raiche, 2 years ago

Browse source code at

Authors: Gilles Raiche (Universite du Quebec a Montreal) and David Magis (Universite de Liege)

Documentation:   PDF Manual  

Task views: Multivariate Statistics, Psychometric Models and Methods

GPL (>= 3.5.0) license

Imports stats, MASS, psych

Depends on lattice

Suggests testthat

Imported by whomds.

Depended on by BCSub,

Suggested by PCDimension, parameters, psycModel, see, sjPlot.

See at CRAN