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.
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Performs Parallel Analysis using Minimum Rank Factor Analysis (MRFA). |
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Performs Hull analysis for assessing the number of factors to retain. |
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Performs Minimum Rank Factor Analysis (MRFA) procedure. |
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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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ## 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")
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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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