Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:23 PM
INPUT INSTRUCTIONS
title: this is an example of a CFA with continuous factor indicators
montecarlo:
names = y1-y6;
nobs = 500;
nreps = 1;
save = ex5.20.dat;
model montecarlo:
f1 by y1@1 y2-y3*1;
f2 by y4@1 y5-y6*.8;
y1-y3*.5; ! reliability 0.67
y4-y6*.32; ! reliability 0.67
f1-f2*1;
model:
f1 by y1
y2-y3(lam2-lam3);
f2 by y4
y5-y6*.8 (lam5-lam6);
f1*1 (vf1);
f2*1 (vf2);
y1-y3*.5 (ve1-ve3); ! reliability 0.67
y4-y6*.32 (ve4-ve6); ! reliability 0.67
model constraint:
new(rel2*.67 rel5*.67 stan3*.82 stan6*.82);
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:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a CFA with continuous factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 0
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
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.019 0.015 0.022 -0.018 -0.015
Means
Y6
________
0.022
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.478
Y2 1.009 1.477
Y3 0.950 1.011 1.458
Y4 -0.001 -0.042 -0.015 1.353
Y5 -0.025 -0.049 -0.044 0.812 0.988
Y6 0.014 -0.024 0.024 0.755 0.657
Covariances
Y6
________
Y6 0.949
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.683 1.000
Y3 0.647 0.689 1.000
Y4 -0.001 -0.030 -0.011 1.000
Y5 -0.021 -0.040 -0.037 0.702 1.000
Y6 0.012 -0.020 0.021 0.666 0.679
Correlations
Y6
________
Y6 1.000
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value
Mean -3898.949
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3898.949 -3898.949
0.980 0.000 -3898.949 -3898.949
0.950 0.000 -3898.949 -3898.949
0.900 0.000 -3898.949 -3898.949
0.800 0.000 -3898.949 -3898.949
0.700 0.000 -3898.949 -3898.949
0.500 0.000 -3898.949 -3898.949
0.300 0.000 -3898.949 -3898.949
0.200 0.000 -3898.949 -3898.949
0.100 0.000 -3898.949 -3898.949
0.050 0.000 -3898.949 -3898.949
0.020 0.000 -3898.949 -3898.949
0.010 0.000 -3898.949 -3898.949
H1 Value
Mean -3896.904
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3896.904 -3896.904
0.980 0.000 -3896.904 -3896.904
0.950 0.000 -3896.904 -3896.904
0.900 0.000 -3896.904 -3896.904
0.800 0.000 -3896.904 -3896.904
0.700 0.000 -3896.904 -3896.904
0.500 0.000 -3896.904 -3896.904
0.300 0.000 -3896.904 -3896.904
0.200 0.000 -3896.904 -3896.904
0.100 0.000 -3896.904 -3896.904
0.050 0.000 -3896.904 -3896.904
0.020 0.000 -3896.904 -3896.904
0.010 0.000 -3896.904 -3896.904
Information Criteria
Akaike (AIC)
Mean 7831.898
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7831.898 7831.898
0.980 0.000 7831.898 7831.898
0.950 0.000 7831.898 7831.898
0.900 0.000 7831.898 7831.898
0.800 0.000 7831.898 7831.898
0.700 0.000 7831.898 7831.898
0.500 0.000 7831.898 7831.898
0.300 0.000 7831.898 7831.898
0.200 0.000 7831.898 7831.898
0.100 0.000 7831.898 7831.898
0.050 0.000 7831.898 7831.898
0.020 0.000 7831.898 7831.898
0.010 0.000 7831.898 7831.898
Bayesian (BIC)
Mean 7903.547
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7903.547 7903.547
0.980 0.000 7903.547 7903.547
0.950 0.000 7903.547 7903.547
0.900 0.000 7903.547 7903.547
0.800 0.000 7903.547 7903.547
0.700 0.000 7903.547 7903.547
0.500 0.000 7903.547 7903.547
0.300 0.000 7903.547 7903.547
0.200 0.000 7903.547 7903.547
0.100 0.000 7903.547 7903.547
0.050 0.000 7903.547 7903.547
0.020 0.000 7903.547 7903.547
0.010 0.000 7903.547 7903.547
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 7849.588
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 7849.588 7849.588
0.980 0.000 7849.588 7849.588
0.950 0.000 7849.588 7849.588
0.900 0.000 7849.588 7849.588
0.800 0.000 7849.588 7849.588
0.700 0.000 7849.588 7849.588
0.500 0.000 7849.588 7849.588
0.300 0.000 7849.588 7849.588
0.200 0.000 7849.588 7849.588
0.100 0.000 7849.588 7849.588
0.050 0.000 7849.588 7849.588
0.020 0.000 7849.588 7849.588
0.010 0.000 7849.588 7849.588
Chi-Square Test of Model Fit
Degrees of freedom 10
Mean 4.090
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 2.558 4.090
0.980 1.000 3.059 4.090
0.950 1.000 3.940 4.090
0.900 0.000 4.865 4.090
0.800 0.000 6.179 4.090
0.700 0.000 7.267 4.090
0.500 0.000 9.342 4.090
0.300 0.000 11.781 4.090
0.200 0.000 13.442 4.090
0.100 0.000 15.987 4.090
0.050 0.000 18.307 4.090
0.020 0.000 21.161 4.090
0.010 0.000 23.209 4.090
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 1.000
CFI/TLI
CFI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
TLI
Mean 1.000
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 0.000
0.980 0.000
0.950 0.000
0.900 0.000
0.800 0.000
0.700 0.000
0.500 0.000
0.300 0.000
0.200 0.000
0.100 0.000
0.050 0.000
0.020 0.000
0.010 0.000
SRMR (Standardized Root Mean Square Residual)
Mean 0.012
Std Dev 0.000
Number of successful computations 1
Cumulative Distribution Function
Value Function Value
0.990 1.000
0.980 1.000
0.950 1.000
0.900 1.000
0.800 1.000
0.700 1.000
0.500 1.000
0.300 1.000
0.200 1.000
0.100 1.000
0.050 1.000
0.020 1.000
0.010 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
F1 BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0602 0.0000 0.0521 0.0036 1.000 1.000
Y3 1.000 0.9983 0.0000 0.0507 0.0000 1.000 1.000
F2 BY
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.800 0.8756 0.0000 0.0411 0.0057 1.000 1.000
Y6 0.800 0.8132 0.0000 0.0395 0.0002 1.000 1.000
F2 WITH
F1 0.000 -0.0241 0.0000 0.0486 0.0006 1.000 0.000
Intercepts
Y1 0.000 -0.0193 0.0000 0.0542 0.0004 1.000 0.000
Y2 0.000 0.0145 0.0000 0.0542 0.0002 1.000 0.000
Y3 0.000 0.0224 0.0000 0.0538 0.0005 1.000 0.000
Y4 0.000 -0.0182 0.0000 0.0522 0.0003 1.000 0.000
Y5 0.000 -0.0152 0.0000 0.0446 0.0002 1.000 0.000
Y6 0.000 0.0217 0.0000 0.0437 0.0005 1.000 0.000
Variances
F1 1.000 0.9421 0.0000 0.0921 0.0033 1.000 1.000
F2 1.000 0.9370 0.0000 0.0871 0.0040 1.000 1.000
Residual Variances
Y1 0.500 0.5287 0.0000 0.0483 0.0008 1.000 1.000
Y2 0.500 0.4078 0.0000 0.0368 0.0085 0.000 1.000
Y3 0.500 0.5093 0.0000 0.0390 0.0001 1.000 1.000
Y4 0.320 0.4237 0.0000 0.0418 0.0107 0.000 1.000
Y5 0.320 0.2767 0.0000 0.0248 0.0019 1.000 1.000
Y6 0.320 0.3361 0.0000 0.0255 0.0003 1.000 1.000
New/Additional Parameters
REL2 0.670 0.7220 0.0000 0.0240 0.0027 0.000 1.000
REL5 0.670 0.7220 0.0000 0.0240 0.0027 0.000 1.000
STAN3 0.820 0.8052 0.0000 0.0153 0.0002 1.000 1.000
STAN6 0.820 0.8052 0.0000 0.0153 0.0002 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.205E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6
________
6
LAMBDA
F1 F2
________ ________
Y1 0 0
Y2 7 0
Y3 8 0
Y4 0 0
Y5 0 9
Y6 0 10
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 11
Y2 0 12
Y3 0 0 13
Y4 0 0 0 14
Y5 0 0 0 0 15
Y6 0 0 0 0 0
THETA
Y6
________
Y6 16
ALPHA
F1 F2
________ ________
0 0
BETA
F1 F2
________ ________
F1 0 0
F2 0 0
PSI
F1 F2
________ ________
F1 17
F2 18 19
PARAMETER SPECIFICATION FOR THE ADDITIONAL PARAMETERS
New/Additional Parameters
REL2 REL5 STAN3 STAN6
________ ________ ________ ________
20 21 22 23
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 1.065 0.000
Y3 1.003 0.000
Y4 0.000 1.000
Y5 0.000 0.800
Y6 0.000 0.800
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.320
Y5 0.000 0.000 0.000 0.000 0.320
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.320
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 THE ADDITIONAL PARAMETERS
New/Additional Parameters
REL2 REL5 STAN3 STAN6
________ ________ ________ ________
0.670 0.670 0.820 0.820
POPULATION VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y6
________
0.000
LAMBDA
F1 F2
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 0.000 1.000
Y5 0.000 0.800
Y6 0.000 0.800
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.500
Y2 0.000 0.500
Y3 0.000 0.000 0.500
Y4 0.000 0.000 0.000 0.320
Y5 0.000 0.000 0.000 0.000 0.320
Y6 0.000 0.000 0.000 0.000 0.000
THETA
Y6
________
Y6 0.320
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 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
Y6
Save file
ex5.20.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:23:05
Ending Time: 22:23:05
Elapsed Time: 00:00:00
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