xF A C T O R
Unrestricted Factor Analysis
Release Version 12.04.01 x64bits
May, 2023
Rovira i Virgili University
Tarragona, SPAIN
Programming:
Urbano Lorenzo-Seva
Mathematical Specification:
Urbano Lorenzo-Seva
Pere J. Ferrando
Date: Thursday, August 31, 2023
Time: 13:59:43
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DETAILS OF ANALYSIS
Participants' variance/covariance data file : E:\ARTICULOS\RESAC\
extoperassinacq.dat
Number of participants : 7
Number of variables : 7
Variables included in the analysis : ALL
Variables excluded in the analysis : NONE
Number of factors : 1
Number of second order factors : 0
Procedure for determining the number of dimensions : Minimum Average Partial
(MAP) (Velicer, 1976)
Dispersion matrix : User defined
Robust analyses based on bootstrap : None
Method for factor extraction : Robust MORGANA factor
analysis
Correction for Chi square : LOSEFER empirical correction
(Lorenzo-Seva & Ferrando, 2023)
Rotation to achieve factor simplicity : Promin (Lorenzo-Seva, 1999)
Clever rotation start : Weighted Varimax
Number of random starts : 100
Maximum mumber of iterations : 1000
Convergence value : 0.00001000
Factor scores estimates : Estimates based on linear
model
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DISPERSION MATRIX (USER DEFINED)
Variable 1 2 3 4 5 6 7
V 1 1.000
V 2 -0.045 1.000
V 3 0.023 -0.006 1.000
V 4 0.016 0.095 0.034 1.000
V 5 0.022 0.160 0.032 0.174 1.000
V 6 0.026 0.133 0.021 0.126 0.206 1.000
V 7 0.034 0.015 0.071 0.049 0.065 0.057 1.000
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ADEQUACY OF THE USER DEFINED COVARIANCE MATRIX
Determinant of the matrix = 0.867217612209106
Bartlett's statistic = 0.4 (df = 21; P = 1.000000)
Kaiser-Meyer-Olkin (KMO) test = 0.61719 (mediocre)
NORMED ITEM-MSA INDICES
Items Normed MSA
1 0.50161
2 0.62573
3 0.56638
4 0.64469
5 0.60443
6 0.62405
7 0.61653
Number of items proposed to be removed: NONE
Values of MSA below .50 suggest that the item does not measure the same domain as
the remaining items in the pool, and so that it should be removed.
Lorenzo-Seva, U. & Ferrando, P.J. (2021) MSA: the forgotten index for identifying
inappropriate items
before computing exploratory item factor analysis. Methodology, in
press.
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EXPLAINED VARIANCE BASED ON EIGENVALUES
Variable Eigenvalue Proportion of Cumulative Proportion
Variance of Variance
1 1.47986 0.21141 0.21141
2 1.08773 0.15539
3 0.98837 0.14120
4 0.92579 0.13226
5 0.89109 0.12730
6 0.84778 0.12111
7 0.77938 0.11134
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MINIMUM AVERAGE PARTIAL TEST (MAP)
Velicer (1976)
Dimensions Averaged Partial
1 0.03118*
2 0.14423
3 1.00000
* Advised number of dimensions: 1
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GOODNESS OF FIT STATISTICS
Goodness of Fit Index (GFI) = 0.996
Adjusted Goodness of Fit Index (AGFI) = 0.993
Goodness of Fit Index without diagonal values (GFI) = 0.905
Adjusted Goodness of Fit Index without diagonal values(AGFI) = 0.833
EIGENVALUES OF THE REDUCED CORRELATION MATRIX
Variable Eigenvalue
1 0.632418571
2 0.112475363
3 0.030355449
4 -0.004802063
5 -0.051057931
6 -0.064486053
7 -0.066565765
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UNROTATED LOADING MATRIX
Variable F 1 Communality
V 1 0.029 0.001
V 2 0.319 0.102
V 3 0.054 0.003
V 4 0.241 0.058
V 5 0.444 0.197
V 6 0.459 0.211
V 7 0.128 0.016
EXPLAINED VARIANCE AND RELIABILITY
Mislevy & Bock (1990)
Factor Variance Reliability estimate
1 0.588 0.415
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ESTIMATED RESIDUAL CORRELATION BETWEEN PAIRS OF VARIABLES ESTIMATED BY MORGANA
FACTOR ANALYSIS
Ferrando & Lorenzo, 2023)
PAIRS OF VARIABLES
PAIR: V 4 -- V 5
ESTIMATED RESIDUAL CORRELATION VALUE OF THE PAIR: 0.076
PAIR: V 3 -- V 7
ESTIMATED RESIDUAL CORRELATION VALUE OF THE PAIR: 0.065
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DISTRIBUTION OF RESIDUALS
Number of Residuals = 21
Summary Statistics for Fitted Residuals
Smallest Fitted Residual = -0.0539
Median Fitted Residual = 0.0082
Largest Fitted Residual = 0.0304
Mean Fitted Residual = 0.0033
Variance Fitted Residual = 0.0004
Root Mean Square of Residuals (RMSR) = 0.0193
Expected mean value of RMSR for an acceptable model = 0.4082 (Kelley's criterion)
(Kelley, 1935,page 13; see also Harman, 1962, page 21 of the 2nd edition)
Histogram for fitted residuals
Value Freq
|
-0.0539 1 | ****
-0.0399 0 |
-0.0258 2 | ********
-0.0118 1 | ****
0.0023 9 | ****************************************
0.0163 7 | *******************************
0.0304 1 | ****
+-----------+---------+---------+-----------+
0 2.2 4.5 6.8 9.0
Summary Statistics for Standardized Residuals
Smallest Standardized Residual = -0.13
Median Standardized Residual = 0.02
Largest Standardized Residual = 0.07
Mean Standardized Residual = 0.01
Stemleaf Plot for Standardized Residuals
-0 | 111
0 | 000000000000000111
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References
Harman, H. H. (1962). Modern Factor Analysis, 2nd Edition. University of Chicago
Press, Chicago.
Kelley, T. L. (1935). Essential Traits of Mental Life, Harvard Studies in
Education, vol. 26. Harvard University Press, Cambridge.
Lorenzo-Seva, U., & Ferrando, P.J. (2023). A simulation-based scaled test statistic
for assessing model-data fit in least-squares unrestricted factor-analysis
solutions. Methodology, 19, 96-115. doi:10.5964/meth.9839
McDonald, R.P. (1999). Test theory: A unified treatment. Mahwah, NJ: Lawrence
Erlbaum.
Mardia, K. V. (1970). Measures of multivariate skewnees and kurtosis with
applications. Biometrika, 57, 519-530. doi:10.2307/2334770
Mislevy, R.J., & Bock, R.D. (1990). BILOG 3 Item analysis and test scoring with
binary logistic models. Mooresville: Scientific Software.
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. doi:10.1007/bf02293900
Ten Berge, J.M.F., & Socan, G. (2004). The greatest lower bound to the reliability
of a test and the hypothesis of unidimensionality. Psychometrika, 69, 613-625.
doi:10.1007/bf02289858
Velicer, W. F. (1976). Determining the number of components from the matrix of
partial correlations. Psychometrika, 41, 321-327. doi:10.1007/bf02293557
Woodhouse, B. & Jackson, P.H. (1977). Lower bounds to the reliability of the total
score on a test composed of nonhomogeneous items: II. A search procedure to locate
the greatest lower bound. Psychometrika, 42, 579-591. doi:10.1007/bf02295980
FACTOR is based on CLAPACK.
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du
Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., & Sorensen, D. (1999).
LAPACK Users' Guide. Society for Industrial and Applied Mathematics. Philadelphia,
PA
FACTOR can be refered as:
Ferrando, P.J., & Lorenzo-Seva, U. (2017). Program FACTOR at 10: origins,
development and future directions. Psicothema, 29(2), 236-241. doi:
10.7334/psicothema2016.304
Lorenzo-Seva, U., & Ferrando, P.J. (2013). FACTOR 9.2 A comprehensive program for
fitting exploratory and semiconfirmatory factor analysis and IRT models. Applied
Psychological Measurement, 37(6), 497-498. doi:10.1177/0146621613487794
Lorenzo-Seva, U., & Ferrando, P.J. (2006). FACTOR: A computer program to fit the
exploratory factor analysis model. Behavioral Research Methods, 38(1), 88-91.
10.3758/bf03192753
For further information and new releases go to:
psico.fcep.urv.cat/utilitats/factor
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FACTOR completed
Computing time : 0.00000000 minutes.
Matrices generated : 29331
Our last advice: Distrust 5% of statistics, and 95% of statisticians. (Cal
desconfiar un 5% de l'estadistica, i un 95% de l'estadistic.)
