EFA.MRFA-package: Dimensionality Assesment using Minimum Rank Factor Analysis...
In EFA.MRFA: Dimensionality Assessment Using Minimum Rank Factor Analysis

Description Details Value Author(s) References Examples

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.

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

`parallelMRFA`	Performs Parallel Analysis using Minimum Rank Factor Analysis (MRFA).
`hullEFA`	Performs Hull analysis for assessing the number of factors to retain.
`mrfa`	Performs Minimum Rank Factor Analysis (MRFA) procedure.
`GreaterLowerBound`	Estimates the communalities of the variables from a factor model.

David Navarro-Gonzalez

Urbano Lorenzo-Seva

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

## 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")

Computing PA. Time remaining  1 seconds                                                                  
Computing PA. Time remaining  1 seconds                                                                  
Computing PA. Time remaining  1 seconds                                                                  
Computing PA. Time remaining  1 seconds                                                                  
Computing PA. Time remaining  0 seconds                                                                  

                                                                                                    
Parallel Analysis (PA) based on Minimum Rank Factor Analysis

Adequacy of the Dispersion Matrix:

Determinant of the matrix     = 0.000475634672537
Bartlett's statistic          =   692.4 (df =   253; P = 0.000000)
Kaiser-Meyer-Olkin (KMO) test = 0.74909 (fair)

Implementation details:

  Correlation matrices analized:                Pearson correlation matrices
  Number of random correlation matrices:        5
  Method to obtain random correlation matrices: Permutation of the raw data

Item      Real-data        Mean of random   90 percentile of random
          % of variance    % of variance    % of variance

   1       28.02**           9.73            10.20
   2       11.89**           9.18             9.45
   3       10.20**           8.49             8.66
   4        7.60             7.83             7.93
   5        6.76             7.25             7.33
   6        5.28             6.79             6.87
   7        4.73             6.46             6.73
   8        4.17             6.02             6.15
   9        3.60             5.50             5.64
  10        3.31             4.90             5.10
  11        2.77             4.51             4.62
  12        2.69             4.33             4.37
  13        2.06             3.86             4.04
  14        1.65             3.52             3.56
  15        1.40             2.85             2.95
  16        1.28             2.43             2.71
  17        1.10             2.05             2.24
  18        0.73             1.75             1.90
  19        0.33             1.11             1.40
  20        0.18             0.80             1.04
  21        0.17             0.39             0.37
  22        0.09             0.25             0.25
  23        0.00             0.00             0.00

**  Advised number of factors:   3

HULL METHOD - CAF INDEX

        q      f          g       st
        0      0.2509   253       0.0000 
        1      0.4010   230       3.8330 
        2*     0.4371   208       
        3      0.4742   187       1.6631 
        4      0.4947   167       0.0000 

Number of advised dimensions: 1 
* Value outside the convex Hull 

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