Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:12 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a second-order
factor analysis
DATA: FILE IS ex5.6.dat;
VARIABLE: NAMES ARE y1-y12;
MODEL: f1 BY y1-y3;
f2 BY y4-y6;
f3 BY y7-y9;
f4 BY y10-y12;
f5 BY f1-f4;
INPUT READING TERMINATED NORMALLY
this is an example of a second-order
factor analysis
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 12
Number of independent variables 0
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
Continuous latent variables
F1 F2 F3 F4 F5
Estimator ML
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Input data file(s)
ex5.6.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 0.011 -0.037 -3.873 0.20% -1.115 -0.330 0.018
500.000 1.725 -0.259 3.393 0.20% 0.309 1.172
Y2 0.028 0.005 -2.933 0.20% -0.829 -0.268 0.006
500.000 1.047 -0.184 2.750 0.20% 0.327 0.914
Y3 0.005 0.165 -2.221 0.20% -0.903 -0.307 0.011
500.000 0.936 -0.368 2.791 0.20% 0.274 0.805
Y4 0.100 -0.067 -3.912 0.20% -0.909 -0.273 0.043
500.000 1.815 0.032 4.194 0.20% 0.408 1.241
Y5 0.078 -0.119 -3.342 0.20% -0.802 -0.130 0.106
500.000 1.015 0.170 3.701 0.20% 0.323 0.913
Y6 0.076 0.162 -2.462 0.20% -0.754 -0.240 0.019
500.000 1.047 -0.210 2.953 0.20% 0.253 0.940
Y7 0.024 -0.060 -3.782 0.20% -1.153 -0.328 0.046
500.000 1.889 -0.130 4.158 0.20% 0.444 1.149
Y8 0.025 -0.107 -3.168 0.20% -0.942 -0.210 0.082
500.000 1.080 -0.039 2.993 0.20% 0.339 0.844
Y9 0.034 0.038 -2.979 0.20% -0.818 -0.263 -0.031
500.000 1.049 -0.203 2.925 0.20% 0.289 0.958
Y10 -0.016 0.005 -4.795 0.20% -1.218 -0.342 0.049
500.000 1.913 -0.055 3.946 0.20% 0.341 1.067
Y11 0.010 -0.005 -2.624 0.20% -0.901 -0.249 0.009
500.000 1.119 -0.168 3.460 0.20% 0.313 0.918
Y12 0.006 0.057 -3.178 0.20% -0.853 -0.232 -0.068
500.000 1.018 -0.082 2.882 0.20% 0.208 0.943
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 40
Loglikelihood
H0 Value -7211.373
H1 Value -7188.001
Information Criteria
Akaike (AIC) 14502.746
Bayesian (BIC) 14671.330
Sample-Size Adjusted BIC 14544.368
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 46.743
Degrees of Freedom 50
P-Value 0.6049
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.026
Probability RMSEA <= .05 1.000
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 4012.035
Degrees of Freedom 66
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
F1 BY
Y1 1.000 0.000 999.000 999.000
Y2 0.760 0.031 24.275 0.000
Y3 0.669 0.030 22.309 0.000
F2 BY
Y4 1.000 0.000 999.000 999.000
Y5 0.718 0.030 23.976 0.000
Y6 0.703 0.031 22.853 0.000
F3 BY
Y7 1.000 0.000 999.000 999.000
Y8 0.702 0.026 26.955 0.000
Y9 0.691 0.026 26.764 0.000
F4 BY
Y10 1.000 0.000 999.000 999.000
Y11 0.742 0.029 25.350 0.000
Y12 0.669 0.029 23.461 0.000
F5 BY
F1 1.000 0.000 999.000 999.000
F2 0.944 0.148 6.397 0.000
F3 1.168 0.179 6.516 0.000
F4 0.854 0.139 6.142 0.000
Intercepts
Y1 0.011 0.059 0.183 0.855
Y2 0.028 0.046 0.617 0.537
Y3 0.005 0.043 0.109 0.913
Y4 0.100 0.060 1.652 0.099
Y5 0.078 0.045 1.730 0.084
Y6 0.076 0.046 1.671 0.095
Y7 0.024 0.061 0.390 0.697
Y8 0.025 0.046 0.545 0.585
Y9 0.034 0.046 0.741 0.458
Y10 -0.016 0.062 -0.261 0.794
Y11 0.010 0.047 0.202 0.840
Y12 0.006 0.045 0.134 0.894
Variances
F5 0.464 0.100 4.657 0.000
Residual Variances
Y1 0.348 0.043 8.132 0.000
Y2 0.251 0.027 9.465 0.000
Y3 0.320 0.026 12.271 0.000
Y4 0.366 0.045 8.187 0.000
Y5 0.268 0.026 10.303 0.000
Y6 0.330 0.028 11.636 0.000
Y7 0.272 0.038 7.094 0.000
Y8 0.282 0.025 11.445 0.000
Y9 0.276 0.024 11.416 0.000
Y10 0.362 0.045 8.107 0.000
Y11 0.266 0.027 9.854 0.000
Y12 0.323 0.027 11.991 0.000
F1 0.913 0.103 8.855 0.000
F2 1.036 0.107 9.672 0.000
F3 0.984 0.119 8.237 0.000
F4 1.213 0.115 10.567 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.558E-02
(ratio of smallest to largest eigenvalue)
Beginning Time: 23:12:14
Ending Time: 23:12:15
Elapsed Time: 00:00:01
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