EFA.MRFA-package {EFA.MRFA}

Dimensionality Assesment using Minimum Rank Factor Analysis (MRFA)

Description

Package for performing Parallel Analysis using Minimum Rank Factor Analysis (MRFA) . It also include a function to perform the MRFA only and another function to compute the Greater Lower Bound step for estimating the variables communalities.

Details

For more information about the methods used in each function, please go to each main page.

Value

\link{parallelMRFA}

Performs Parallel Analysis using Minimum Rank Factor Analysis (MRFA).

\link{hullEFA}

Performs Hull analysis for assessing the number of factors to retain.

\link{mrfa}

Performs Minimum Rank Factor Analysis (MRFA) procedure.

\link{GreaterLowerBound}

Estimates the communalities of the variables from a factor model.

Author(s)

David Navarro-Gonzalez

Urbano Lorenzo-Seva

References

Devlin, S. J., Gnanadesikan, R., & Kettenring, J. R. (1981). Robust estimation of dispersion matrices and principal components. Journal of the American Statistical Association, 76, 354-362. doi: 10.1080/01621459.1981.10477654

Lorenzo-Seva, U., Timmerman, M. E., & Kiers, H. A. (2011). The Hull Method for Selecting the Number of Common Factors. Multivariate Behavioral Research, 46(2), 340-364. doi: 10.1080/00273171.2011.564527

ten Berge, J. M. F., & Kiers, H. A. L. (1991). A numerical approach to the approximate and the exact minimum rank of a covariance matrix. Psychometrika, 56(2), 309-315. doi: 10.1007/BF02294464

Ten Berge, J.M.F., Snijders, T.A.B. & Zegers, F.E. (1981). Computational aspects of the greatest lower bound to reliability and constrained minimum trace factor analysis. Psychometrika, 46, 201-213.

Timmerman, M. E., & Lorenzo-Seva, U. (2011). Dimensionality assessment of ordered polytomous items with parallel analysis. Psychological Methods, 16(2), 209-220. doi: 10.1037/a0023353

Examples

## Example 1:

## perform a Parallel Analysis using an example Database with only 5 random data sets and
## using the 90th percentile of distribution of the random data
parallelMRFA(IDAQ, Ndatsets=5, percent=90)

## For speeding purposes, the number of datasets have been largely reduced. For a proper
## use of parallelMRFA, we recommend to use the default Ndatsets value (Ndatsets=500)

#Example 2:

## Perform the Hull method defining the maximum number of dimensions to be tested by the
## Parallel Analysis + 1 rule, with Maximum Likelihood factor extraction method and CAF
## as Hull index.
hullEFA(IDAQ, extr = "ML")