Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:10 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level exploratory
factor analysis with both individual- and
cluster-level factor indicators
DATA: FILE = ex4.6.dat;
VARIABLE: NAMES = u1-u6 y1-y4 x1 x2 w clus;
USEVARIABLES = u1-u6 y1-y4;
CATEGORICAL = u1-u6;
CLUSTER = clus;
BETWEEN = y1-y4;
ANALYSIS: TYPE = TWOLEVEL EFA 1 2 UW 1 2 UB;
SAVEDATA: SWMATRIX = ex4.6sw.dat;
*** WARNING
One or more individual-level variables have no variation within a
cluster for the following clusters.
Variable Cluster IDs with no within-cluster variation
U1 2 5 7 8 11 16 19 24 25 26 29 31 33 34 35 36 42 48 50 73 82 97
U2 5 7 8 16 18 19 20 33 34 36 42 50 67 71 93 97
U3 5 7 8 14 18 24 26 32 34 36 40 47 48 50 51 71 76 82 93 97
U4 5 7 8 13 18 25 26 34 36 39 41 49 51 73 82 108
U5 5 7 8 17 18 24 27 28 32 34 36 39 42 50 51 77 82 93 97 108
U6 1 6 7 8 13 17 19 25 27 28 29 31 32 34 50 64 82 88 93 108
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a two-level exploratory
factor analysis with both individual- and
cluster-level factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
Variables with special functions
Cluster variable CLUS
Between variables
Y1 Y2 Y3 Y4
Estimator WLSMV
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 1000
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 10
Minimum value for logit thresholds -10
Minimum expected cell size for chi-square 0.100D-01
Optimization Specifications for the Exploratory Factor Analysis
Rotation Algorithm
Number of random starts 30
Maximum number of iterations 10000
Derivative convergence criterion 0.100D-04
Optimization algorithm EMA/FS
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 0
Adaptive quadrature ON
Link PROBIT
Cholesky ON
Input data file(s)
ex4.6.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
Average cluster size 9.091
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
U1 0.415 U2 0.370 U3 0.410
U4 0.371 U5 0.407 U6 0.381
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.476 476.000
Category 2 0.524 524.000
U2
Category 1 0.447 447.000
Category 2 0.553 553.000
U3
Category 1 0.473 473.000
Category 2 0.527 527.000
U4
Category 1 0.479 479.000
Category 2 0.521 521.000
U5
Category 1 0.490 490.000
Category 2 0.510 510.000
U6
Category 1 0.513 513.000
Category 2 0.487 487.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 0.081 0.033 -2.262 0.91% -0.812 -0.265 0.000
110.000 0.843 -0.369 2.325 0.91% 0.313 0.988
Y2 -0.040 0.120 -2.676 0.91% -0.853 -0.369 -0.111
110.000 1.009 -0.391 2.426 0.91% 0.236 0.837
Y3 -0.024 -0.239 -2.973 0.91% -0.933 -0.223 0.030
110.000 0.997 0.034 2.374 0.91% 0.191 0.789
Y4 0.009 0.545 -2.488 0.91% -0.839 -0.382 -0.132
110.000 1.143 0.489 3.467 0.91% 0.264 0.774
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EIGENVALUES FOR WITHIN LEVEL SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
3.089 1.552 0.439 0.357 0.322
EIGENVALUES FOR WITHIN LEVEL SAMPLE CORRELATION MATRIX
6
________
0.241
EIGENVALUES FOR BETWEEN LEVEL SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
6.263 1.442 0.589 0.539 0.470
EIGENVALUES FOR BETWEEN LEVEL SAMPLE CORRELATION MATRIX
6 7 8 9 10
________ ________ ________ ________ ________
0.285 0.158 0.142 0.066 0.047
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 36
Chi-Square Test of Model Fit
Value 534.471*
Degrees of Freedom 44
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.106
90 Percent C.I. 0.098 0.114
Probability RMSEA <= .05 0.000
CFI/TLI
CFI 0.438
TLI 0.234
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.211
Value for Between 0.111
MINIMUM ROTATION FUNCTION VALUE 2.91667
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.661*
U2 0.634*
U3 0.727*
U4 0.739*
U5 0.715*
U6 0.701*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.564 0.598 0.472 0.454 0.488
ESTIMATED RESIDUAL VARIANCES
U6
________
0.509
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.039
U2 0.038
U3 0.030
U4 0.037
U5 0.035
U6 0.034
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.052 0.048 0.043 0.055 0.050
S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
0.048
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 16.806
U2 16.852
U3 24.388
U4 19.759
U5 20.508
U6 20.669
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
10.855 12.511 10.879 8.213 9.784
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
10.713
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MINIMUM ROTATION FUNCTION VALUE 5.73490
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.826*
U2 0.841*
U3 0.870*
U4 0.970*
U5 0.835*
U6 0.815*
Y1 0.540*
Y2 0.570*
Y3 0.536*
Y4 0.618*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.318 0.292 0.243 0.060 0.303
ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.335 0.708 0.675 0.713 0.618
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.056
U2 0.051
U3 0.053
U4 0.033
U5 0.051
U6 0.053
Y1 0.071
Y2 0.067
Y3 0.076
Y4 0.063
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.092 0.086 0.092 0.064 0.085
S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.086 0.076 0.077 0.082 0.077
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 14.868
U2 16.362
U3 16.384
U4 29.409
U5 16.368
U6 15.446
Y1 7.643
Y2 8.481
Y3 7.015
Y4 9.872
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
3.468 3.382 2.628 0.935 3.565
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
3.899 9.288 8.793 8.719 7.974
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 41
Chi-Square Test of Model Fit
Value 111.446*
Degrees of Freedom 39
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.043
90 Percent C.I. 0.034 0.053
Probability RMSEA <= .05 0.880
CFI/TLI
CFI 0.917
TLI 0.872
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.021
Value for Between 0.111
MINIMUM ROTATION FUNCTION VALUE 0.16062
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.821* -0.076
U2 0.746* 0.011
U3 0.854* 0.005
U4 -0.063 0.876*
U5 0.006 0.818*
U6 0.012 0.801*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.425* 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.373 0.436 0.268 0.275 0.327
ESTIMATED RESIDUAL VARIANCES
U6
________
0.350
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.058 0.065
U2 0.049 0.055
U3 0.045 0.019
U4 0.063 0.054
U5 0.019 0.044
U6 0.046 0.043
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.059 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.058 0.069 0.072 0.067
S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
0.058
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 14.188 -1.159
U2 15.185 0.195
U3 19.095 0.267
U4 -0.994 16.218
U5 0.304 18.464
U6 0.254 18.565
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 7.207 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
5.167 7.581 3.858 3.825 4.882
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
6.034
FACTOR STRUCTURE
1 2
________ ________
U1 0.789 0.273
U2 0.751 0.328
U3 0.856 0.368
U4 0.310 0.850
U5 0.353 0.821
U6 0.352 0.806
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 1 BETWEEN FACTOR(S):
MINIMUM ROTATION FUNCTION VALUE 5.73491
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.826*
U2 0.841*
U3 0.870*
U4 0.970*
U5 0.835*
U6 0.815*
Y1 0.540*
Y2 0.570*
Y3 0.536*
Y4 0.618*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.318 0.292 0.243 0.060 0.303
ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.335 0.708 0.675 0.713 0.618
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.056
U2 0.051
U3 0.053
U4 0.033
U5 0.051
U6 0.053
Y1 0.071
Y2 0.067
Y3 0.076
Y4 0.063
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.092 0.086 0.092 0.064 0.085
S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.086 0.076 0.077 0.082 0.077
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 14.868
U2 16.362
U3 16.384
U4 29.409
U5 16.368
U6 15.446
Y1 7.643
Y2 8.481
Y3 7.015
Y4 9.872
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
3.468 3.382 2.628 0.935 3.565
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
3.899 9.288 8.793 8.719 7.974
EXPLORATORY FACTOR ANALYSIS WITH UNRESTRICTED WITHIN COVARIANCE AND 1 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 30
Chi-Square Test of Model Fit
Value 107.993*
Degrees of Freedom 35
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.046
90 Percent C.I. 0.036 0.056
Probability RMSEA <= .05 0.753
CFI/TLI
CFI 0.916
TLI 0.857
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.000
Value for Between 0.111
MINIMUM ROTATION FUNCTION VALUE 5.73490
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.826*
U2 0.841*
U3 0.870*
U4 0.970*
U5 0.835*
U6 0.815*
Y1 0.540*
Y2 0.570*
Y3 0.536*
Y4 0.618*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.318 0.292 0.243 0.060 0.303
ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.335 0.708 0.675 0.713 0.618
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.056
U2 0.051
U3 0.053
U4 0.033
U5 0.051
U6 0.053
Y1 0.071
Y2 0.067
Y3 0.076
Y4 0.063
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.092 0.086 0.092 0.064 0.085
S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.086 0.076 0.077 0.082 0.077
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 14.868
U2 16.362
U3 16.384
U4 29.409
U5 16.368
U6 15.446
Y1 7.643
Y2 8.481
Y3 7.015
Y4 9.872
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
3.468 3.382 2.628 0.935 3.565
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
3.899 9.288 8.793 8.719 7.974
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 2 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 45
Chi-Square Test of Model Fit
Value 518.313*
Degrees of Freedom 35
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.118
90 Percent C.I. 0.109 0.127
Probability RMSEA <= .05 0.000
CFI/TLI
CFI 0.446
TLI 0.051
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.211
Value for Between 0.036
MINIMUM ROTATION FUNCTION VALUE 2.91667
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.661*
U2 0.634*
U3 0.727*
U4 0.739*
U5 0.715*
U6 0.701*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.564 0.598 0.472 0.454 0.488
ESTIMATED RESIDUAL VARIANCES
U6
________
0.509
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.039
U2 0.038
U3 0.030
U4 0.037
U5 0.035
U6 0.034
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.052 0.048 0.043 0.055 0.050
S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
0.048
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 16.806
U2 16.852
U3 24.388
U4 19.759
U5 20.508
U6 20.669
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
10.855 12.511 10.879 8.213 9.784
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
10.713
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND 2 BETWEEN FACTOR(S):
MINIMUM ROTATION FUNCTION VALUE 0.57654
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.898* 0.002
U2 0.949* -0.024
U3 0.806* 0.136
U4 0.745* 0.297*
U5 0.862* 0.050
U6 0.951* -0.059
Y1 -0.002 0.681*
Y2 0.073 0.621*
Y3 -0.058 0.751*
Y4 0.014 0.771*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.590* 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.193 0.125 0.203 0.095 0.203
ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.158 0.538 0.555 0.483 0.392
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.042 0.011
U2 0.087 0.124
U3 0.087 0.109
U4 0.100 0.123
U5 0.096 0.147
U6 0.107 0.149
Y1 0.023 0.063
Y2 0.103 0.095
Y3 0.128 0.117
Y4 0.096 0.088
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.115 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.062 0.074 0.056 0.066
S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.077 0.083 0.084 0.101 0.087
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 21.372 0.139
U2 10.879 -0.194
U3 9.307 1.244
U4 7.473 2.414
U5 9.019 0.338
U6 8.872 -0.396
Y1 -0.087 10.742
Y2 0.712 6.523
Y3 -0.448 6.434
Y4 0.151 8.733
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 5.133 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
2.666 2.037 2.734 1.710 3.078
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
2.050 6.482 6.622 4.769 4.524
FACTOR STRUCTURE
1 2
________ ________
U1 0.899 0.531
U2 0.935 0.536
U3 0.886 0.611
U4 0.921 0.737
U5 0.892 0.558
U6 0.916 0.502
Y1 0.400 0.680
Y2 0.440 0.665
Y3 0.386 0.717
Y4 0.469 0.780
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 2 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 50
Chi-Square Test of Model Fit
Value 32.018*
Degrees of Freedom 30
P-Value 0.3667
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.008
90 Percent C.I. 0.000 0.026
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 0.998
TLI 0.995
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.021
Value for Between 0.036
MINIMUM ROTATION FUNCTION VALUE 0.16062
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.821* -0.076
U2 0.746* 0.011
U3 0.854* 0.005
U4 -0.063 0.876*
U5 0.006 0.818*
U6 0.012 0.801*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.425* 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.373 0.436 0.268 0.275 0.327
ESTIMATED RESIDUAL VARIANCES
U6
________
0.350
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.058 0.065
U2 0.049 0.055
U3 0.045 0.019
U4 0.063 0.054
U5 0.019 0.044
U6 0.046 0.043
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.059 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.058 0.069 0.072 0.067
S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
0.058
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 14.188 -1.159
U2 15.185 0.195
U3 19.095 0.267
U4 -0.994 16.218
U5 0.304 18.464
U6 0.254 18.565
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 7.207 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
5.167 7.581 3.858 3.825 4.882
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
6.034
FACTOR STRUCTURE
1 2
________ ________
U1 0.789 0.273
U2 0.751 0.328
U3 0.856 0.368
U4 0.310 0.850
U5 0.353 0.821
U6 0.352 0.806
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND 2 BETWEEN FACTOR(S):
MINIMUM ROTATION FUNCTION VALUE 0.57653
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.898* 0.002
U2 0.949* -0.024
U3 0.806* 0.136
U4 0.745* 0.297*
U5 0.862* 0.050
U6 0.951* -0.059
Y1 -0.002 0.681*
Y2 0.073 0.621*
Y3 -0.058 0.751*
Y4 0.014 0.771*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.590* 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.193 0.125 0.203 0.095 0.203
ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.158 0.538 0.555 0.483 0.392
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.042 0.011
U2 0.087 0.124
U3 0.087 0.109
U4 0.100 0.123
U5 0.096 0.147
U6 0.107 0.149
Y1 0.023 0.063
Y2 0.103 0.095
Y3 0.128 0.117
Y4 0.096 0.088
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.115 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.062 0.074 0.056 0.066
S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.077 0.083 0.084 0.101 0.087
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 21.372 0.139
U2 10.879 -0.194
U3 9.307 1.244
U4 7.473 2.414
U5 9.019 0.338
U6 8.872 -0.396
Y1 -0.087 10.743
Y2 0.712 6.523
Y3 -0.448 6.434
Y4 0.151 8.733
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 5.133 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
2.665 2.037 2.734 1.710 3.078
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
2.050 6.482 6.622 4.769 4.524
FACTOR STRUCTURE
1 2
________ ________
U1 0.899 0.531
U2 0.935 0.536
U3 0.886 0.611
U4 0.921 0.737
U5 0.892 0.558
U6 0.916 0.502
Y1 0.400 0.680
Y2 0.440 0.665
Y3 0.386 0.717
Y4 0.469 0.780
EXPLORATORY FACTOR ANALYSIS WITH UNRESTRICTED WITHIN COVARIANCE AND 2 BETWEEN FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 39
Chi-Square Test of Model Fit
Value 26.424*
Degrees of Freedom 26
P-Value 0.4400
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.004
90 Percent C.I. 0.000 0.025
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 1.000
TLI 0.999
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.000
Value for Between 0.036
MINIMUM ROTATION FUNCTION VALUE 0.57653
BETWEEN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.898* 0.002
U2 0.949* -0.024
U3 0.806* 0.136
U4 0.745* 0.297*
U5 0.862* 0.050
U6 0.951* -0.059
Y1 -0.002 0.681*
Y2 0.073 0.621*
Y3 -0.058 0.751*
Y4 0.014 0.771*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.590* 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.193 0.125 0.203 0.095 0.203
ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.158 0.538 0.555 0.483 0.392
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.042 0.011
U2 0.087 0.124
U3 0.087 0.109
U4 0.100 0.123
U5 0.096 0.147
U6 0.107 0.149
Y1 0.023 0.063
Y2 0.103 0.095
Y3 0.128 0.117
Y4 0.096 0.088
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.115 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.062 0.074 0.056 0.066
S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
0.077 0.083 0.084 0.101 0.087
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 21.372 0.139
U2 10.879 -0.194
U3 9.307 1.244
U4 7.473 2.414
U5 9.019 0.338
U6 8.872 -0.396
Y1 -0.087 10.742
Y2 0.712 6.523
Y3 -0.449 6.434
Y4 0.151 8.733
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 5.133 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
2.666 2.037 2.734 1.710 3.078
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6 Y1 Y2 Y3 Y4
________ ________ ________ ________ ________
2.050 6.482 6.622 4.769 4.524
FACTOR STRUCTURE
1 2
________ ________
U1 0.899 0.531
U2 0.935 0.536
U3 0.886 0.611
U4 0.921 0.737
U5 0.892 0.558
U6 0.916 0.502
Y1 0.400 0.680
Y2 0.440 0.665
Y3 0.386 0.717
Y4 0.469 0.780
EXPLORATORY FACTOR ANALYSIS WITH 1 WITHIN FACTOR(S) AND UNRESTRICTED BETWEEN COVARIANCE:
MODEL FIT INFORMATION
Number of Free Parameters 16
Chi-Square Test of Model Fit
Value 268.038*
Degrees of Freedom 9
P-Value 0.0000
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.170
90 Percent C.I. 0.152 0.187
Probability RMSEA <= .05 0.000
CFI/TLI
CFI 0.703
TLI 0.000
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.211
Value for Between 0.000
MINIMUM ROTATION FUNCTION VALUE 2.91667
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U1 0.661*
U2 0.634*
U3 0.727*
U4 0.739*
U5 0.715*
U6 0.701*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.564 0.598 0.472 0.454 0.488
ESTIMATED RESIDUAL VARIANCES
U6
________
0.509
S.E. GEOMIN ROTATED LOADINGS
1
________
U1 0.039
U2 0.038
U3 0.030
U4 0.037
U5 0.035
U6 0.034
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.052 0.048 0.043 0.055 0.050
S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
0.048
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U1 16.806
U2 16.852
U3 24.388
U4 19.759
U5 20.508
U6 20.669
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
10.855 12.511 10.879 8.213 9.784
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
10.713
EXPLORATORY FACTOR ANALYSIS WITH 2 WITHIN FACTOR(S) AND UNRESTRICTED BETWEEN COVARIANCE:
MODEL FIT INFORMATION
Number of Free Parameters 21
Chi-Square Test of Model Fit
Value 4.924*
Degrees of Freedom 4
P-Value 0.2952
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.015
90 Percent C.I. 0.000 0.052
Probability RMSEA <= .05 0.936
CFI/TLI
CFI 0.999
TLI 0.984
Chi-Square Test of Model Fit for the Baseline Model
Value 932.834
Degrees of Freedom 60
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.021
Value for Between 0.000
MINIMUM ROTATION FUNCTION VALUE 0.16062
WITHIN LEVEL RESULTS
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U1 0.821* -0.076
U2 0.746* 0.011
U3 0.854* 0.005
U4 -0.063 0.876*
U5 0.006 0.818*
U6 0.012 0.801*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 0.425* 1.000
ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.373 0.436 0.268 0.275 0.327
ESTIMATED RESIDUAL VARIANCES
U6
________
0.350
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 0.058 0.065
U2 0.049 0.055
U3 0.045 0.019
U4 0.063 0.054
U5 0.019 0.044
U6 0.046 0.043
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.059 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
0.072 0.058 0.069 0.072 0.067
S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
0.058
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U1 14.188 -1.159
U2 15.185 0.195
U3 19.096 0.267
U4 -0.994 16.218
U5 0.304 18.464
U6 0.254 18.565
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 7.207 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U1 U2 U3 U4 U5
________ ________ ________ ________ ________
5.167 7.581 3.858 3.825 4.882
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U6
________
6.034
FACTOR STRUCTURE
1 2
________ ________
U1 0.789 0.273
U2 0.751 0.328
U3 0.856 0.368
U4 0.310 0.850
U5 0.353 0.821
U6 0.352 0.806
SAVEDATA INFORMATION
Within and between sample statistics with Weight matrix
Save file
ex4.6sw.dat
Save format Free
Beginning Time: 23:10:59
Ending Time: 23:11:07
Elapsed Time: 00:00:08
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen
Back to examples