Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of multiple-group EFA
with continuous factor indicators
with intercept and loading measurement invariance
and factor covariance matrix invariance
DATA: FILE IS ex5.27.dat;
VARIABLE: NAMES ARE y1-y10 group;
GROUPING IS group (1 = g1 2 = g2);
MODEL: f1-f2 by y1-y10 (*1);
f1 WITH f2 (1);
f1-f2@1;
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
this is an example of multiple-group EFA
with continuous factor indicators
with intercept and loading measurement invariance
and factor covariance matrix invariance
SUMMARY OF ANALYSIS
Number of groups 2
Number of observations
Group G1 500
Group G2 500
Total sample size 1000
Number of dependent variables 10
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10
Continuous latent variables
EFA factors
*1: F1 F2
Variables with special functions
Grouping variable GROUP
Estimator ML
Rotation GEOMIN
Row standardization COVARIANCE
Type of rotation OBLIQUE
Epsilon value Varies
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
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
Input data file(s)
ex5.27.dat
Input data format FREE
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS FOR G1
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 0.907 0.041 -2.225 0.20% -0.188 0.544 0.936
500.000 1.624 -0.354 4.581 0.20% 1.224 1.951
Y2 1.113 0.199 -2.431 0.20% 0.077 0.741 1.063
500.000 1.644 0.021 5.295 0.20% 1.372 2.178
Y3 1.040 -0.087 -1.979 0.20% -0.048 0.725 1.103
500.000 1.533 -0.452 4.595 0.20% 1.431 2.120
Y4 0.949 -0.024 -3.828 0.20% -0.087 0.593 0.943
500.000 1.741 0.196 4.948 0.20% 1.271 2.036
Y5 1.041 -0.040 -2.560 0.20% -0.064 0.692 1.073
500.000 1.735 -0.103 4.768 0.20% 1.361 2.170
Y6 0.959 -0.001 -2.231 0.20% -0.099 0.644 0.930
500.000 1.513 -0.118 4.448 0.20% 1.243 2.003
Y7 1.032 0.023 -2.702 0.20% -0.031 0.649 0.988
500.000 1.667 -0.195 4.603 0.20% 1.283 2.166
Y8 1.091 0.033 -3.161 0.20% 0.067 0.757 1.036
500.000 1.813 0.135 5.084 0.20% 1.371 2.257
Y9 0.987 0.065 -3.713 0.20% 0.003 0.617 0.884
500.000 1.584 0.167 4.787 0.20% 1.178 2.044
Y10 1.008 0.000 -2.306 0.20% -0.101 0.721 1.029
500.000 1.584 -0.318 4.498 0.20% 1.350 2.067
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS FOR G2
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 1.263 -0.042 -3.567 0.20% -0.089 0.785 1.237
500.000 2.969 -0.140 5.766 0.20% 1.768 2.735
Y2 1.319 -0.017 -4.329 0.20% 0.002 0.933 1.267
500.000 2.811 0.234 6.995 0.20% 1.630 2.713
Y3 1.303 0.143 -3.874 0.20% -0.135 0.790 1.220
500.000 3.107 0.034 6.828 0.20% 1.671 2.812
Y4 1.349 -0.103 -4.199 0.20% -0.176 0.869 1.409
500.000 3.083 -0.181 5.859 0.20% 1.790 2.979
Y5 1.333 -0.080 -3.284 0.20% -0.076 0.922 1.352
500.000 2.998 -0.145 7.012 0.20% 1.812 2.819
Y6 1.673 -0.034 -3.885 0.20% -0.024 1.205 1.710
500.000 3.668 -0.092 7.465 0.20% 2.162 3.317
Y7 1.603 0.072 -3.738 0.20% 0.059 1.138 1.617
500.000 3.419 0.314 9.503 0.20% 2.019 3.175
Y8 1.624 -0.210 -4.974 0.20% 0.018 1.168 1.728
500.000 3.667 0.278 7.736 0.20% 2.164 3.233
Y9 1.528 -0.119 -4.847 0.20% 0.003 1.053 1.589
500.000 3.219 -0.031 6.640 0.20% 2.143 3.046
Y10 1.603 -0.071 -4.084 0.20% 0.024 1.114 1.571
500.000 3.656 0.078 7.899 0.20% 2.086 3.159
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 51
Loglikelihood
H0 Value -17342.092
H1 Value -17268.681
Information Criteria
Akaike (AIC) 34786.184
Bayesian (BIC) 35036.479
Sample-Size Adjusted BIC 34874.500
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 146.822
Degrees of Freedom 79
P-Value 0.0000
Chi-Square Contribution From Each Group
G1 73.660
G2 73.162
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.041
90 Percent C.I. 0.031 0.052
Probability RMSEA <= .05 0.911
CFI/TLI
CFI 0.968
TLI 0.963
Chi-Square Test of Model Fit for the Baseline Model
Value 2205.576
Degrees of Freedom 90
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.082
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group G1
F1 BY
Y1 0.834 0.065 12.928 0.000
Y2 0.955 0.064 14.973 0.000
Y3 0.855 0.050 17.002 0.000
Y4 0.874 0.066 13.268 0.000
Y5 0.948 0.060 15.786 0.000
Y6 -0.037 0.077 -0.478 0.632
Y7 0.007 0.010 0.756 0.450
Y8 0.066 0.080 0.825 0.410
Y9 0.046 0.076 0.606 0.544
Y10 -0.049 0.077 -0.636 0.525
F2 BY
Y1 0.037 0.068 0.543 0.587
Y2 -0.070 0.068 -1.029 0.304
Y3 0.009 0.020 0.441 0.659
Y4 0.074 0.070 1.054 0.292
Y5 -0.020 0.059 -0.346 0.729
Y6 1.061 0.068 15.666 0.000
Y7 0.914 0.052 17.559 0.000
Y8 0.970 0.071 13.610 0.000
Y9 0.891 0.067 13.296 0.000
Y10 0.961 0.069 13.935 0.000
F1 WITH
F2 0.524 0.058 9.086 0.000
Means
F1 0.000 0.000 999.000 999.000
F2 0.000 0.000 999.000 999.000
Intercepts
Y1 0.925 0.055 16.959 0.000
Y2 1.092 0.055 19.721 0.000
Y3 1.033 0.054 19.311 0.000
Y4 0.971 0.057 17.067 0.000
Y5 1.039 0.057 18.362 0.000
Y6 0.980 0.060 16.365 0.000
Y7 1.033 0.058 17.832 0.000
Y8 1.058 0.062 17.140 0.000
Y9 0.979 0.057 17.305 0.000
Y10 1.013 0.059 17.275 0.000
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.992 0.074 13.353 0.000
Y2 0.868 0.073 11.922 0.000
Y3 0.871 0.068 12.886 0.000
Y4 1.021 0.078 13.139 0.000
Y5 0.914 0.074 12.277 0.000
Y6 0.866 0.074 11.648 0.000
Y7 1.096 0.082 13.333 0.000
Y8 1.200 0.090 13.344 0.000
Y9 0.994 0.076 13.130 0.000
Y10 1.099 0.084 13.156 0.000
Group G2
F1 BY
Y1 0.834 0.065 12.928 0.000
Y2 0.955 0.064 14.973 0.000
Y3 0.855 0.050 17.002 0.000
Y4 0.874 0.066 13.268 0.000
Y5 0.948 0.060 15.786 0.000
Y6 -0.037 0.077 -0.478 0.632
Y7 0.007 0.010 0.756 0.450
Y8 0.066 0.080 0.825 0.410
Y9 0.046 0.076 0.606 0.544
Y10 -0.049 0.077 -0.636 0.525
F2 BY
Y1 0.037 0.068 0.543 0.587
Y2 -0.070 0.068 -1.029 0.304
Y3 0.009 0.020 0.441 0.659
Y4 0.074 0.070 1.054 0.292
Y5 -0.020 0.059 -0.346 0.729
Y6 1.061 0.068 15.666 0.000
Y7 0.914 0.052 17.559 0.000
Y8 0.970 0.071 13.610 0.000
Y9 0.891 0.067 13.296 0.000
Y10 0.961 0.069 13.935 0.000
F1 WITH
F2 0.524 0.058 9.086 0.000
Means
F1 0.329 0.077 4.261 0.000
F2 0.620 0.076 8.177 0.000
Intercepts
Y1 0.925 0.055 16.959 0.000
Y2 1.092 0.055 19.721 0.000
Y3 1.033 0.054 19.311 0.000
Y4 0.971 0.057 17.067 0.000
Y5 1.039 0.057 18.362 0.000
Y6 0.980 0.060 16.365 0.000
Y7 1.033 0.058 17.832 0.000
Y8 1.058 0.062 17.140 0.000
Y9 0.979 0.057 17.305 0.000
Y10 1.013 0.059 17.275 0.000
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 2.138 0.155 13.794 0.000
Y2 1.863 0.145 12.892 0.000
Y3 2.268 0.164 13.821 0.000
Y4 2.131 0.157 13.569 0.000
Y5 2.078 0.157 13.209 0.000
Y6 2.002 0.163 12.316 0.000
Y7 2.256 0.166 13.608 0.000
Y8 2.090 0.162 12.875 0.000
Y9 2.079 0.153 13.619 0.000
Y10 2.230 0.169 13.204 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.236E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION
PARAMETER SPECIFICATION FOR G1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
F1 F2
________ ________
Y1 11 0
Y2 12 13
Y3 14 15
Y4 16 17
Y5 18 19
Y6 20 21
Y7 22 23
Y8 24 25
Y9 26 27
Y10 28 29
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 30
Y2 0 31
Y3 0 0 32
Y4 0 0 0 33
Y5 0 0 0 0 34
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 35
Y7 0 36
Y8 0 0 37
Y9 0 0 0 38
Y10 0 0 0 0 39
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 0 0
PARAMETER SPECIFICATION FOR G2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
F1 F2
________ ________
Y1 11 0
Y2 12 13
Y3 14 15
Y4 16 17
Y5 18 19
Y6 20 21
Y7 22 23
Y8 24 25
Y9 26 27
Y10 28 29
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 40
Y2 0 41
Y3 0 0 42
Y4 0 0 0 43
Y5 0 0 0 0 44
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 45
Y7 0 46
Y8 0 0 47
Y9 0 0 0 48
Y10 0 0 0 0 49
ALPHA
F1 F2
________ ________
50 51
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 0 0
STARTING VALUES FOR G1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.907 1.113 1.040 0.949 1.041
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.959 1.032 1.091 0.987 1.008
LAMBDA
F1 F2
________ ________
Y1 0.793 0.000
Y2 0.883 0.112
Y3 0.805 -0.039
Y4 0.847 -0.011
Y5 0.908 0.008
Y6 0.375 -0.686
Y7 0.402 -0.629
Y8 0.455 -0.626
Y9 0.407 -0.667
Y10 0.283 -0.622
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.996
Y2 0.000 0.852
Y3 0.000 0.000 0.884
Y4 0.000 0.000 0.000 1.024
Y5 0.000 0.000 0.000 0.000 0.910
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.901
Y7 0.000 1.111
Y8 0.000 0.000 1.214
Y9 0.000 0.000 0.000 0.973
Y10 0.000 0.000 0.000 0.000 1.118
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
STARTING VALUES FOR G2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.907 1.113 1.040 0.949 1.041
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.959 1.032 1.091 0.987 1.008
LAMBDA
F1 F2
________ ________
Y1 0.924 0.000
Y2 0.969 0.016
Y3 0.948 -0.099
Y4 0.973 0.067
Y5 0.956 -0.077
Y6 0.706 1.129
Y7 0.564 0.937
Y8 0.730 1.084
Y9 0.648 0.843
Y10 0.706 1.022
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 2.115
Y2 0.000 1.871
Y3 0.000 0.000 2.198
Y4 0.000 0.000 0.000 2.131
Y5 0.000 0.000 0.000 0.000 2.077
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 1.894
Y7 0.000 2.223
Y8 0.000 0.000 1.958
Y9 0.000 0.000 0.000 2.089
Y10 0.000 0.000 0.000 0.000 2.112
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION
PARAMETER SPECIFICATION FOR G1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
F1 F2
________ ________
Y1 11 12
Y2 13 14
Y3 15 16
Y4 17 18
Y5 19 20
Y6 21 22
Y7 23 24
Y8 25 26
Y9 27 28
Y10 29 30
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 31
Y2 0 32
Y3 0 0 33
Y4 0 0 0 34
Y5 0 0 0 0 35
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 36
Y7 0 37
Y8 0 0 38
Y9 0 0 0 39
Y10 0 0 0 0 40
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 41 0
PARAMETER SPECIFICATION FOR G2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
LAMBDA
F1 F2
________ ________
Y1 11 12
Y2 13 14
Y3 15 16
Y4 17 18
Y5 19 20
Y6 21 22
Y7 23 24
Y8 25 26
Y9 27 28
Y10 29 30
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 42
Y2 0 43
Y3 0 0 44
Y4 0 0 0 45
Y5 0 0 0 0 46
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 47
Y7 0 48
Y8 0 0 49
Y9 0 0 0 50
Y10 0 0 0 0 51
ALPHA
F1 F2
________ ________
52 53
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 41 0
STARTING VALUES FOR G1
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.907 1.113 1.040 0.949 1.041
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.959 1.032 1.091 0.987 1.008
LAMBDA
F1 F2
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
Y5 0.000 0.000
Y6 0.000 0.000
Y7 0.000 0.000
Y8 0.000 0.000
Y9 0.000 0.000
Y10 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.812
Y2 0.000 0.822
Y3 0.000 0.000 0.767
Y4 0.000 0.000 0.000 0.871
Y5 0.000 0.000 0.000 0.000 0.868
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.757
Y7 0.000 0.834
Y8 0.000 0.000 0.906
Y9 0.000 0.000 0.000 0.792
Y10 0.000 0.000 0.000 0.000 0.792
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
STARTING VALUES FOR G2
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.907 1.113 1.040 0.949 1.041
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
0.959 1.032 1.091 0.987 1.008
LAMBDA
F1 F2
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
Y5 0.000 0.000
Y6 0.000 0.000
Y7 0.000 0.000
Y8 0.000 0.000
Y9 0.000 0.000
Y10 0.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.812
Y2 0.000 0.822
Y3 0.000 0.000 0.767
Y4 0.000 0.000 0.000 0.871
Y5 0.000 0.000 0.000 0.000 0.868
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.757
Y7 0.000 0.834
Y8 0.000 0.000 0.906
Y9 0.000 0.000 0.000 0.792
Y10 0.000 0.000 0.000 0.000 0.792
ALPHA
F1 F2
________ ________
0.000 0.000
BETA
F1 F2
________ ________
F1 0.000 0.000
F2 0.000 0.000
PSI
F1 F2
________ ________
F1 1.000
F2 0.000 1.000
Beginning Time: 23:11:21
Ending Time: 23:11:21
Elapsed Time: 00:00:00
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