Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a CFA with parameter
constraints
DATA: FILE = ex5.20.dat;
VARIABLE: NAMES = y1-y6;
MODEL: f1 BY y1
y2-y3(lam2-lam3);
f2 BY y4
y5-y6(lam5-lam6);
f1 (vf1);
f2 (vf2);
y1-y3 (ve1-ve3);
y4-y6 (ve4-ve6);
MODEL CONSTRAINT:
NEW(rel2 rel5 stan3 stan6);
rel2 = lam2**2*vf1/(lam2**2*vf1 + ve2);
rel5 = lam5**2*vf2/(lam5**2*vf2 + ve5);
rel5 = rel2;
stan3 = lam3*SQRT(vf1)/SQRT(lam3**2*vf1 + ve3);
stan6 = lam6*SQRT(vf2)/SQRT(lam6**2*vf2 + ve6);
0 = stan6 - stan3;
ve2 > ve5;
ve4 > 0;
OUTPUT: STANDARDIZED;
INPUT READING TERMINATED NORMALLY
this is an example of a CFA with parameter
constraints
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 6
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Continuous latent variables
F1 F2
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)
ex5.20.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 -0.019 -0.050 -3.428 0.20% -1.070 -0.342 -0.034
500.000 1.478 -0.363 3.107 0.20% 0.284 1.074
Y2 0.015 -0.092 -3.996 0.20% -1.001 -0.307 0.017
500.000 1.477 -0.086 3.371 0.20% 0.364 1.043
Y3 0.022 0.187 -3.367 0.20% -1.093 -0.341 -0.033
500.000 1.458 -0.137 3.550 0.20% 0.333 1.080
Y4 -0.018 -0.016 -3.693 0.20% -0.903 -0.329 -0.055
500.000 1.353 0.246 3.484 0.20% 0.244 0.914
Y5 -0.015 -0.087 -2.991 0.20% -0.938 -0.269 -0.047
500.000 0.988 -0.241 3.220 0.20% 0.272 0.908
Y6 0.022 0.108 -3.093 0.20% -0.855 -0.298 -0.044
500.000 0.949 -0.230 2.987 0.20% 0.235 0.858
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value -3898.949
H1 Value -3896.904
Information Criteria
Akaike (AIC) 7831.898
Bayesian (BIC) 7903.547
Sample-Size Adjusted BIC 7849.588
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 4.090
Degrees of Freedom 10
P-Value 0.9432
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.000
90 Percent C.I. 0.000 0.009
Probability RMSEA <= .05 0.999
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 1418.024
Degrees of Freedom 15
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.012
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 1.000 0.000 999.000 999.000
Y2 1.060 0.052 20.334 0.000
Y3 0.998 0.051 19.670 0.000
F2 BY
Y4 1.000 0.000 999.000 999.000
Y5 0.876 0.041 21.322 0.000
Y6 0.813 0.040 20.574 0.000
F2 WITH
F1 -0.024 0.049 -0.495 0.621
Intercepts
Y1 -0.019 0.054 -0.355 0.723
Y2 0.015 0.054 0.268 0.789
Y3 0.022 0.054 0.416 0.677
Y4 -0.018 0.052 -0.349 0.727
Y5 -0.015 0.045 -0.340 0.734
Y6 0.022 0.044 0.497 0.619
Variances
F1 0.942 0.092 10.230 0.000
F2 0.937 0.087 10.755 0.000
Residual Variances
Y1 0.529 0.048 10.957 0.000
Y2 0.408 0.037 11.088 0.000
Y3 0.509 0.039 13.069 0.000
Y4 0.424 0.042 10.138 0.000
Y5 0.277 0.025 11.170 0.000
Y6 0.336 0.026 13.172 0.000
New/Additional Parameters
REL2 0.722 0.024 30.091 0.000
REL5 0.722 0.024 30.091 0.000
STAN3 0.805 0.015 52.744 0.000
STAN6 0.805 0.015 52.744 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.602E-04
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.800 0.022 36.300 0.000
Y2 0.850 0.014 60.183 0.000
Y3 0.805 0.015 52.744 0.000
F2 BY
Y4 0.830 0.020 40.981 0.000
Y5 0.850 0.014 60.183 0.000
Y6 0.805 0.015 52.744 0.000
F2 WITH
F1 -0.026 0.052 -0.495 0.620
Intercepts
Y1 -0.016 0.045 -0.355 0.723
Y2 0.012 0.045 0.268 0.789
Y3 0.019 0.045 0.416 0.677
Y4 -0.016 0.045 -0.349 0.727
Y5 -0.015 0.045 -0.340 0.734
Y6 0.022 0.045 0.497 0.619
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.359 0.035 10.186 0.000
Y2 0.278 0.024 11.589 0.000
Y3 0.352 0.025 14.305 0.000
Y4 0.311 0.034 9.265 0.000
Y5 0.278 0.024 11.589 0.000
Y6 0.352 0.025 14.305 0.000
STDY Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.800 0.022 36.300 0.000
Y2 0.850 0.014 60.183 0.000
Y3 0.805 0.015 52.744 0.000
F2 BY
Y4 0.830 0.020 40.981 0.000
Y5 0.850 0.014 60.183 0.000
Y6 0.805 0.015 52.744 0.000
F2 WITH
F1 -0.026 0.052 -0.495 0.620
Intercepts
Y1 -0.016 0.045 -0.355 0.723
Y2 0.012 0.045 0.268 0.789
Y3 0.019 0.045 0.416 0.677
Y4 -0.016 0.045 -0.349 0.727
Y5 -0.015 0.045 -0.340 0.734
Y6 0.022 0.045 0.497 0.619
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.359 0.035 10.186 0.000
Y2 0.278 0.024 11.589 0.000
Y3 0.352 0.025 14.305 0.000
Y4 0.311 0.034 9.265 0.000
Y5 0.278 0.024 11.589 0.000
Y6 0.352 0.025 14.305 0.000
STD Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 0.971 0.047 20.460 0.000
Y2 1.029 0.039 26.530 0.000
Y3 0.969 0.038 25.182 0.000
F2 BY
Y4 0.968 0.045 21.511 0.000
Y5 0.848 0.032 26.290 0.000
Y6 0.787 0.032 24.963 0.000
F2 WITH
F1 -0.026 0.052 -0.495 0.620
Intercepts
Y1 -0.019 0.054 -0.355 0.723
Y2 0.015 0.054 0.268 0.789
Y3 0.022 0.054 0.416 0.677
Y4 -0.018 0.052 -0.349 0.727
Y5 -0.015 0.045 -0.340 0.734
Y6 0.022 0.044 0.497 0.619
Variances
F1 1.000 0.000 999.000 999.000
F2 1.000 0.000 999.000 999.000
Residual Variances
Y1 0.529 0.048 10.957 0.000
Y2 0.408 0.037 11.088 0.000
Y3 0.509 0.039 13.069 0.000
Y4 0.424 0.042 10.138 0.000
Y5 0.277 0.025 11.170 0.000
Y6 0.336 0.026 13.172 0.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
Y1 0.641 0.035 18.150 0.000
Y2 0.722 0.024 30.091 0.000
Y3 0.648 0.025 26.372 0.000
Y4 0.689 0.034 20.491 0.000
Y5 0.722 0.024 30.091 0.000
Y6 0.648 0.025 26.372 0.000
Beginning Time: 23:11:18
Ending Time: 23:11:18
Elapsed Time: 00:00:00
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