R function aimed to identify the number of components/factors starting by a raw data matrix by using the principles of Horn's Parallel Analysis.
parallel(x, iter = 1000, ordinal = FALSE, method = c("perm", "random"),
alpha = 0.05, standard = FALSE, plot = TRUE, fn = eigen, ...)
-
x
Data frame or matrix of raw data. -
iter
Number of iterations. -
ordinal
If TRUE, the function uses the polychoric/tetrachoric correlation instead of the Pearson's index (very slow).} -
method
Method for random data generation. When method isperm
, random permutations of observed data are used (permutation is performed within each column independently). When method israndom
, random data normally distributed are generated. -
alpha
Alpha threshold to select the number of components/factors. -
standard
If TRUE, the analysis is performed on standardized data. -
plot
Shows the scree plot overlapping the observed eigen values. -
fn
Function to calculate eigenvalues. The defaulteigen
uses the principal component analysis with eigen decomposition, whilepsych::fa
calculates eigenvalues according to factor analysis. -
...
Further arguments for the functionfn
.
The function returns an object of S3 class parallel
listing elements:
-
correlation
type of correlation index used. -
method
method of data generation (random or permutations). -
synthetic.eigen
matrix of eigen values from iterations of parallel analysis. -
pca.eigen
estimated eigenvalues from observed data. -
parallel.CI
averages and confidence intervals of eigen values estimated by parallel analysis. -
parallel.quantiles
quantiles of eigenvalues estimated by parallel analysis. -
suggest.ncomp
suggested number of components/factors.
The plot
method returns the scree plot overlapping parallel quantiles (gray points and bars).
The basic functionalities are stand-alone, but the package psych
is required to run analyses for ordinal data.
Buja A., Eyuboglu N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509-540.
Crawford A.V., Green S.B., Levy R., Lo W.J. Scott L., Svetina D., Thompson M.S. (2010). Evaluation of parallel analysis methods for determining the number of factors. Educational and Psychological Measurement, 70(6), 885-901.
Horn J.L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30, 179-185.
Franklin S.B., Gibson D.J., Robertson P.A., Pohlmann J.T., Fralish, J.S. (1995). Parallel analysis: a method for determining significant principal components. Journal of Vegetation Science, 6(1), 99-106.
Peres-Neto P.R., Jackson D.A., Somers K.M. (2005). How many principal components? Stopping rules for determining the number of non-trivial axes revisited. Computational Statistics and Data Analysis, 49, 974-997.
Weng L.J., Cheng C.P. (2005). Parallel analysis with unidimensional binary data. Educational and Psychological Measurement, 65(5), 697-716.