Parallel Analysis

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.

Usage

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 is perm, random permutations of observed data are used (permutation is performed within each column independently). When method is random, 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 default eigen uses the principal component analysis with eigen decomposition, while psych::fa calculates eigenvalues according to factor analysis.

• ... Further arguments for the function fn.

Output

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).

Dependencies

The basic functionalities are stand-alone, but the package psych is required to run analyses for ordinal data.

References

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.