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 no measurement 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-f2@0];
MODEL g2: f1-f2 BY y1-y10 (*1);
[y1-y10];
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
this is an example of multiple-group EFA
with continuous factor indicators
with no measurement 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 CORRELATION
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 78
Loglikelihood
H0 Value -17300.588
H1 Value -17268.681
Information Criteria
Akaike (AIC) 34757.177
Bayesian (BIC) 35139.982
Sample-Size Adjusted BIC 34892.249
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 63.815
Degrees of Freedom 52
P-Value 0.1261
Chi-Square Contribution From Each Group
G1 33.275
G2 30.540
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.021
90 Percent C.I. 0.000 0.037
Probability RMSEA <= .05 0.999
CFI/TLI
CFI 0.994
TLI 0.990
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 0.019
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group G1
F1 BY
Y1 0.791 0.066 12.029 0.000
Y2 0.947 0.074 12.792 0.000
Y3 0.780 0.069 11.236 0.000
Y4 0.838 0.073 11.539 0.000
Y5 0.911 0.065 14.119 0.000
Y6 -0.032 0.072 -0.448 0.654
Y7 0.029 0.080 0.362 0.717
Y8 0.084 0.086 0.970 0.332
Y9 0.011 0.022 0.524 0.600
Y10 -0.085 0.078 -1.094 0.274
F2 BY
Y1 0.004 0.051 0.075 0.941
Y2 -0.125 0.076 -1.652 0.098
Y3 0.049 0.072 0.678 0.498
Y4 0.017 0.072 0.236 0.813
Y5 -0.005 0.044 -0.104 0.917
Y6 0.798 0.074 10.736 0.000
Y7 0.731 0.081 8.993 0.000
Y8 0.728 0.085 8.609 0.000
Y9 0.776 0.064 12.054 0.000
Y10 0.722 0.078 9.250 0.000
F2 WITH
F1 0.507 0.065 7.824 0.000
Means
F1 0.000 0.000 999.000 999.000
F2 0.000 0.000 999.000 999.000
Intercepts
Y1 0.907 0.057 15.907 0.000
Y2 1.113 0.057 19.407 0.000
Y3 1.040 0.055 18.775 0.000
Y4 0.949 0.059 16.085 0.000
Y5 1.041 0.059 17.678 0.000
Y6 0.959 0.055 17.432 0.000
Y7 1.032 0.058 17.872 0.000
Y8 1.091 0.060 18.112 0.000
Y9 0.987 0.056 17.543 0.000
Y10 1.008 0.056 17.915 0.000
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.996 0.075 13.217 0.000
Y2 0.852 0.075 11.349 0.000
Y3 0.884 0.068 12.936 0.000
Y4 1.024 0.079 12.967 0.000
Y5 0.910 0.076 12.029 0.000
Y6 0.901 0.078 11.528 0.000
Y7 1.110 0.086 12.853 0.000
Y8 1.214 0.093 13.113 0.000
Y9 0.973 0.081 12.047 0.000
Y10 1.118 0.086 12.999 0.000
Group G2
F1 BY
Y1 0.916 0.095 9.627 0.000
Y2 0.950 0.117 8.115 0.000
Y3 1.006 0.125 8.022 0.000
Y4 0.921 0.126 7.325 0.000
Y5 0.999 0.122 8.203 0.000
Y6 -0.041 0.117 -0.352 0.725
Y7 -0.055 0.117 -0.473 0.636
Y8 0.012 0.039 0.310 0.757
Y9 0.089 0.120 0.740 0.459
Y10 0.029 0.115 0.251 0.801
F2 BY
Y1 0.014 0.034 0.424 0.671
Y2 0.034 0.115 0.300 0.764
Y3 -0.103 0.128 -0.805 0.421
Y4 0.094 0.130 0.720 0.472
Y5 -0.077 0.124 -0.619 0.536
Y6 1.354 0.114 11.849 0.000
Y7 1.123 0.113 9.959 0.000
Y8 1.301 0.092 14.097 0.000
Y9 1.012 0.112 9.064 0.000
Y10 1.227 0.114 10.768 0.000
F2 WITH
F1 0.542 0.072 7.485 0.000
Means
F1 0.000 0.000 999.000 999.000
F2 0.000 0.000 999.000 999.000
Intercepts
Y1 1.263 0.077 16.394 0.000
Y2 1.319 0.075 17.597 0.000
Y3 1.303 0.079 16.530 0.000
Y4 1.349 0.079 17.180 0.000
Y5 1.333 0.077 17.214 0.000
Y6 1.673 0.086 19.526 0.000
Y7 1.603 0.083 19.387 0.000
Y8 1.624 0.086 18.964 0.000
Y9 1.528 0.080 19.048 0.000
Y10 1.603 0.086 18.742 0.000
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 2.115 0.164 12.880 0.000
Y2 1.872 0.154 12.135 0.000
Y3 2.197 0.178 12.361 0.000
Y4 2.131 0.166 12.839 0.000
Y5 2.077 0.170 12.211 0.000
Y6 1.894 0.167 11.359 0.000
Y7 2.224 0.169 13.176 0.000
Y8 1.958 0.166 11.793 0.000
Y9 2.089 0.154 13.571 0.000
Y10 2.112 0.168 12.548 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.291E-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
________ ________ ________ ________ ________
40 41 42 43 44
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
45 46 47 48 49
LAMBDA
F1 F2
________ ________
Y1 50 0
Y2 51 52
Y3 53 54
Y4 55 56
Y5 57 58
Y6 59 60
Y7 61 62
Y8 63 64
Y9 65 66
Y10 67 68
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 69
Y2 0 70
Y3 0 0 71
Y4 0 0 0 72
Y5 0 0 0 0 73
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 74
Y7 0 75
Y8 0 0 76
Y9 0 0 0 77
Y10 0 0 0 0 78
ALPHA
F1 F2
________ ________
0 0
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
________ ________ ________ ________ ________
42 43 44 45 46
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
47 48 49 50 51
LAMBDA
F1 F2
________ ________
Y1 52 53
Y2 54 55
Y3 56 57
Y4 58 59
Y5 60 61
Y6 62 63
Y7 64 65
Y8 66 67
Y9 68 69
Y10 70 71
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 72
Y2 0 73
Y3 0 0 74
Y4 0 0 0 75
Y5 0 0 0 0 76
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 77
Y7 0 78
Y8 0 0 79
Y9 0 0 0 80
Y10 0 0 0 0 81
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 0
F2 82 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: 23:11:20
Ending Time: 23:11:20
Elapsed Time: 00:00:00
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