Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of an EFA with covariates (MIMIC)
with continuous factor indicators and direct effects
DATA: FILE IS ex5.24.dat;
VARIABLE: NAMES ARE y1-y8 x1 x2;
MODEL: f1-f2 BY y1-y8(*1);
f1-f2 ON x1-x2;
y1 ON x1;
y8 ON x2;
OUTPUT: TECH1;
INPUT READING TERMINATED NORMALLY
this is an example of an EFA with covariates (MIMIC)
with continuous factor indicators and direct effects
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 8
Number of independent variables 2
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8
Observed independent variables
X1 X2
Continuous latent variables
EFA factors
*1: F1 F2
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)
ex5.24.dat
Input data format FREE
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 -0.008 -0.087 -3.466 0.20% -1.184 -0.317 0.024
500.000 1.592 -0.462 3.176 0.20% 0.347 1.076
Y2 -0.034 -0.001 -3.615 0.20% -0.904 -0.351 -0.097
500.000 1.254 0.135 3.413 0.20% 0.188 0.906
Y3 0.019 0.011 -3.101 0.20% -0.944 -0.250 0.063
500.000 1.258 -0.152 3.495 0.20% 0.303 0.989
Y4 -0.024 0.059 -3.188 0.20% -1.105 -0.306 -0.027
500.000 1.623 -0.243 3.787 0.20% 0.211 1.078
Y5 0.020 -0.001 -4.000 0.20% -1.081 -0.320 0.032
500.000 1.635 0.051 3.809 0.20% 0.380 1.016
Y6 0.077 -0.019 -3.845 0.20% -1.149 -0.300 0.042
500.000 2.072 -0.222 4.079 0.20% 0.392 1.346
Y7 0.023 0.052 -3.638 0.20% -1.149 -0.354 0.013
500.000 1.928 -0.156 4.340 0.20% 0.324 1.240
Y8 0.109 0.092 -4.588 0.20% -1.218 -0.430 0.004
500.000 2.677 -0.130 4.554 0.20% 0.468 1.465
X1 -0.073 0.041 -2.518 0.20% -0.928 -0.356 -0.050
500.000 0.990 -0.354 2.797 0.20% 0.175 0.743
X2 0.127 0.256 -2.012 0.20% -0.657 -0.155 0.061
500.000 0.945 -0.004 3.176 0.20% 0.300 0.938
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 37
Loglikelihood
H0 Value -4630.127
H1 Value -4614.993
Information Criteria
Akaike (AIC) 9334.254
Bayesian (BIC) 9490.194
Sample-Size Adjusted BIC 9372.754
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 30.268
Degrees of Freedom 23
P-Value 0.1419
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.025
90 Percent C.I. 0.000 0.047
Probability RMSEA <= .05 0.970
CFI/TLI
CFI 0.998
TLI 0.997
Chi-Square Test of Model Fit for the Baseline Model
Value 4254.549
Degrees of Freedom 44
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.010
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.754 0.040 18.906 0.000
Y2 0.861 0.049 17.435 0.000
Y3 0.820 0.043 19.182 0.000
Y4 0.855 0.049 17.572 0.000
Y5 0.773 0.049 15.653 0.000
Y6 -0.010 0.041 -0.247 0.805
Y7 0.003 0.022 0.125 0.900
Y8 0.009 0.040 0.226 0.821
F2 BY
Y1 0.000 0.021 0.003 0.997
Y2 -0.054 0.039 -1.375 0.169
Y3 -0.004 0.025 -0.162 0.871
Y4 0.118 0.039 3.031 0.002
Y5 0.177 0.040 4.423 0.000
Y6 0.861 0.045 19.061 0.000
Y7 0.840 0.038 21.823 0.000
Y8 0.786 0.044 17.951 0.000
F1 ON
X1 0.537 0.055 9.768 0.000
X2 0.271 0.050 5.390 0.000
F2 ON
X1 0.946 0.061 15.571 0.000
X2 0.556 0.056 9.914 0.000
Y1 ON
X1 0.387 0.039 9.855 0.000
Y8 ON
X2 0.577 0.039 14.800 0.000
F2 WITH
F1 0.593 0.039 15.216 0.000
Intercepts
Y1 0.024 0.043 0.564 0.573
Y2 -0.029 0.046 -0.641 0.521
Y3 0.023 0.045 0.516 0.606
Y4 -0.020 0.049 -0.399 0.690
Y5 0.024 0.049 0.485 0.628
Y6 0.075 0.049 1.553 0.121
Y7 0.021 0.046 0.464 0.643
Y8 0.035 0.046 0.760 0.447
Residual Variances
Y1 0.339 0.026 12.942 0.000
Y2 0.345 0.029 12.037 0.000
Y3 0.342 0.028 12.421 0.000
Y4 0.328 0.027 11.926 0.000
Y5 0.393 0.030 13.086 0.000
Y6 0.425 0.039 10.851 0.000
Y7 0.335 0.034 9.956 0.000
Y8 0.415 0.036 11.577 0.000
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.255E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 1 2 3 4
NU
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
5 6 0 0 0
LAMBDA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 7 8 0 0 0
Y3 9 10 0 0 0
Y4 11 12 0 0 0
Y5 13 14 0 0 0
Y6 15 16 0 0 0
Y7 17 18 0 0 0
Y8 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
LAMBDA
X2
________
Y1 0
Y2 0
Y3 0
Y4 0
Y5 0
Y6 0
Y7 0
Y8 0
X1 0
X2 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0
Y2 0 19
Y3 0 0 20
Y4 0 0 0 21
Y5 0 0 0 0 22
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
Y6 23
Y7 0 24
Y8 0 0 0
X1 0 0 0 0
X2 0 0 0 0 0
ALPHA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
0 0 25 26 0
ALPHA
X2
________
0
BETA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 0 0 0 0 27
F2 0 0 0 0 29
Y1 31 0 0 0 32
Y8 33 34 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
BETA
X2
________
F1 28
F2 30
Y1 0
Y8 35
X1 0
X2 0
PSI
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 0
F2 0 0
Y1 0 0 36
Y8 0 0 0 37
X1 0 0 0 0 0
X2 0 0 0 0 0
PSI
X2
________
X2 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 -0.034 0.019 -0.024 0.020
NU
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
0.077 0.023 0.000 0.000 0.000
LAMBDA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.932 0.195 0.000 0.000 0.000
Y3 0.943 0.133 0.000 0.000 0.000
Y4 1.138 0.053 0.000 0.000 0.000
Y5 1.118 -0.006 0.000 0.000 0.000
Y6 1.049 -0.720 0.000 0.000 0.000
Y7 1.038 -0.745 0.000 0.000 0.000
Y8 0.000 0.000 0.000 1.000 0.000
X1 0.000 0.000 0.000 0.000 1.000
X2 0.000 0.000 0.000 0.000 0.000
LAMBDA
X2
________
Y1 0.000
Y2 0.000
Y3 0.000
Y4 0.000
Y5 0.000
Y6 0.000
Y7 0.000
Y8 0.000
X1 0.000
X2 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.348
Y3 0.000 0.000 0.351
Y4 0.000 0.000 0.000 0.326
Y5 0.000 0.000 0.000 0.000 0.385
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
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
Y6 0.452
Y7 0.000 0.296
Y8 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
ALPHA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
0.000 0.000 -0.008 0.109 -0.073
ALPHA
X2
________
0.127
BETA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000 0.000
Y1 1.079 0.000 0.000 0.000 0.000
Y8 1.142 -0.825 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
BETA
X2
________
F1 0.000
F2 0.000
Y1 0.000
Y8 0.000
X1 0.000
X2 0.000
PSI
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
Y1 0.000 0.000 0.427
Y8 0.000 0.000 0.000 0.691
X1 0.000 0.000 0.000 0.000 0.990
X2 0.000 0.000 0.000 0.000 0.070
PSI
X2
________
X2 0.945
TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 1 2 3 4
NU
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
5 6 0 0 0
LAMBDA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 7 8 0 0 0
Y3 9 10 0 0 0
Y4 11 12 0 0 0
Y5 13 14 0 0 0
Y6 15 16 0 0 0
Y7 17 18 0 0 0
Y8 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
LAMBDA
X2
________
Y1 0
Y2 0
Y3 0
Y4 0
Y5 0
Y6 0
Y7 0
Y8 0
X1 0
X2 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0
Y2 0 19
Y3 0 0 20
Y4 0 0 0 21
Y5 0 0 0 0 22
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
THETA
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
Y6 23
Y7 0 24
Y8 0 0 0
X1 0 0 0 0
X2 0 0 0 0 0
ALPHA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
0 0 25 26 0
ALPHA
X2
________
0
BETA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 0 0 0 0 27
F2 0 0 0 0 29
Y1 31 32 0 0 33
Y8 34 35 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
BETA
X2
________
F1 28
F2 30
Y1 0
Y8 36
X1 0
X2 0
PSI
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 0
F2 37 0
Y1 0 0 38
Y8 0 0 0 39
X1 0 0 0 0 0
X2 0 0 0 0 0
PSI
X2
________
X2 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 -0.034 0.019 -0.024 0.020
NU
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
0.077 0.023 0.000 0.000 0.000
LAMBDA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
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 1.000 0.000
X1 0.000 0.000 0.000 0.000 1.000
X2 0.000 0.000 0.000 0.000 0.000
LAMBDA
X2
________
Y1 0.000
Y2 0.000
Y3 0.000
Y4 0.000
Y5 0.000
Y6 0.000
Y7 0.000
Y8 0.000
X1 0.000
X2 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.627
Y3 0.000 0.000 0.629
Y4 0.000 0.000 0.000 0.812
Y5 0.000 0.000 0.000 0.000 0.817
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
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 X1 X2
________ ________ ________ ________ ________
Y6 1.036
Y7 0.000 0.964
Y8 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
ALPHA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
0.000 0.000 -0.008 0.109 -0.073
ALPHA
X2
________
0.127
BETA
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
BETA
X2
________
F1 0.000
F2 0.000
Y1 0.000
Y8 0.000
X1 0.000
X2 0.000
PSI
F1 F2 Y1 Y8 X1
________ ________ ________ ________ ________
F1 1.000
F2 0.000 1.000
Y1 0.000 0.000 0.796
Y8 0.000 0.000 0.000 1.338
X1 0.000 0.000 0.000 0.000 0.990
X2 0.000 0.000 0.000 0.000 0.070
PSI
X2
________
X2 0.945
Beginning Time: 23:11:19
Ending Time: 23:11:19
Elapsed Time: 00:00:00
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