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
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);
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
this is an example of multiple-group EFA
with continuous factor indicators
with intercept and loading 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 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 54
Loglikelihood
H0 Value -17309.844
H1 Value -17268.681
Information Criteria
Akaike (AIC) 34727.688
Bayesian (BIC) 34992.707
Sample-Size Adjusted BIC 34821.200
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 82.326
Degrees of Freedom 76
P-Value 0.2900
Chi-Square Contribution From Each Group
G1 41.995
G2 40.332
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.013
90 Percent C.I. 0.000 0.029
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 0.997
TLI 0.996
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 0.027
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group G1
F1 BY
Y1 0.786 0.062 12.697 0.000
Y2 0.891 0.063 14.233 0.000
Y3 0.815 0.053 15.518 0.000
Y4 0.823 0.063 13.006 0.000
Y5 0.900 0.060 14.898 0.000
Y6 -0.041 0.068 -0.598 0.550
Y7 0.011 0.016 0.717 0.473
Y8 0.059 0.074 0.799 0.424
Y9 0.053 0.070 0.763 0.445
Y10 -0.052 0.069 -0.747 0.455
F2 BY
Y1 0.036 0.051 0.699 0.485
Y2 -0.037 0.051 -0.718 0.473
Y3 0.005 0.017 0.301 0.763
Y4 0.066 0.052 1.254 0.210
Y5 -0.014 0.043 -0.329 0.742
Y6 0.837 0.057 14.675 0.000
Y7 0.701 0.047 14.925 0.000
Y8 0.753 0.060 12.498 0.000
Y9 0.678 0.057 11.866 0.000
Y10 0.755 0.056 13.381 0.000
F2 WITH
F1 0.483 0.068 7.106 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 0.053 17.447 0.000
Y2 1.091 0.054 20.217 0.000
Y3 1.034 0.052 19.828 0.000
Y4 0.971 0.055 17.630 0.000
Y5 1.040 0.055 18.866 0.000
Y6 0.978 0.052 18.632 0.000
Y7 1.035 0.052 19.964 0.000
Y8 1.058 0.055 19.286 0.000
Y9 0.981 0.050 19.459 0.000
Y10 1.011 0.052 19.290 0.000
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.994 0.074 13.364 0.000
Y2 0.878 0.073 12.034 0.000
Y3 0.869 0.068 12.834 0.000
Y4 1.022 0.078 13.153 0.000
Y5 0.914 0.075 12.247 0.000
Y6 0.877 0.074 11.891 0.000
Y7 1.119 0.082 13.565 0.000
Y8 1.214 0.090 13.556 0.000
Y9 1.024 0.076 13.419 0.000
Y10 1.103 0.083 13.307 0.000
Group G2
F1 BY
Y1 0.786 0.062 12.697 0.000
Y2 0.891 0.063 14.233 0.000
Y3 0.815 0.053 15.518 0.000
Y4 0.823 0.063 13.006 0.000
Y5 0.900 0.060 14.898 0.000
Y6 -0.041 0.068 -0.598 0.550
Y7 0.011 0.016 0.717 0.473
Y8 0.059 0.074 0.799 0.424
Y9 0.053 0.070 0.763 0.445
Y10 -0.052 0.069 -0.747 0.455
F2 BY
Y1 0.036 0.051 0.699 0.485
Y2 -0.037 0.051 -0.718 0.473
Y3 0.005 0.017 0.301 0.763
Y4 0.066 0.052 1.254 0.210
Y5 -0.014 0.043 -0.329 0.742
Y6 0.837 0.057 14.675 0.000
Y7 0.701 0.047 14.925 0.000
Y8 0.753 0.060 12.498 0.000
Y9 0.678 0.057 11.866 0.000
Y10 0.755 0.056 13.381 0.000
F2 WITH
F1 0.953 0.155 6.159 0.000
Means
F1 0.342 0.082 4.162 0.000
F2 0.798 0.103 7.719 0.000
Intercepts
Y1 0.925 0.053 17.447 0.000
Y2 1.091 0.054 20.217 0.000
Y3 1.034 0.052 19.828 0.000
Y4 0.971 0.055 17.630 0.000
Y5 1.040 0.055 18.866 0.000
Y6 0.978 0.052 18.632 0.000
Y7 1.035 0.052 19.964 0.000
Y8 1.058 0.055 19.286 0.000
Y9 0.981 0.050 19.459 0.000
Y10 1.011 0.052 19.290 0.000
Variances
F1 1.246 0.155 8.030 0.000
F2 2.612 0.316 8.274 0.000
Residual Variances
Y1 2.131 0.155 13.732 0.000
Y2 1.862 0.145 12.857 0.000
Y3 2.251 0.165 13.676 0.000
Y4 2.124 0.157 13.515 0.000
Y5 2.063 0.158 13.064 0.000
Y6 1.886 0.160 11.821 0.000
Y7 2.222 0.164 13.524 0.000
Y8 2.011 0.159 12.664 0.000
Y9 2.055 0.151 13.583 0.000
Y10 2.138 0.165 12.955 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.266E-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 52
F2 53 54
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 54
F2 55 56
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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