Mplus VERSION 8.6
MUTHEN & MUTHEN
07/20/2021 6:20 PM
OUTPUT SECTIONS
INPUT INSTRUCTIONS
TITLE: 7.12 M4. Modèle linéaire covariables invariantes
DATA:
FILE = Cortisol.dat ;
LISTWISE = ON ;
VARIABLE:
NAMES =
SID C1 C2 C3 C4
SEXE TTT CREVEIL
T1 T2 T3 T4
TC1 TC2 TC3 TC4
FCT ;
USEVARIABLES = C1 C2 C3 C4
SEXE TTT CREVEIL ;
ANALYSIS:
ESTIMATOR = MLR ;
STARTS = 20 ;
MODEL:
i s | C1@0 C2@1 C3@4 C4@9 ;
i s ON SEXE TTT CREVEIL ;
C4@0 ; !fixer la variance résiduelle à zéro
OUTPUT:
SAMPSTAT STDYX TECH1 TECH4 ;
PLOT:
TYPE = PLOT3 ;
SERIES = C1 (0) C2 (1) C3 (4) C4 (9) ;
INPUT READING TERMINATED NORMALLY
7.12 M4. Modèle linéaire covariables invariantes
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 101
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 2
Observed dependent variables
Continuous
C1 C2 C3 C4
Observed independent variables
SEXE TTT CREVEIL
Continuous latent variables
I S
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Random Starts Specifications
Number of random starts 20
Random starts scale 0.500D+01
Input data file(s)
Cortisol.dat
Input data format FREE
SAMPLE STATISTICS
SAMPLE STATISTICS
Means
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
10.412 10.189 6.393 3.706 0.327
Means
TTT CREVEIL
________ ________
0.574 0.505
Covariances
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
C1 45.592
C2 22.137 36.375
C3 0.437 3.455 22.701
C4 -1.599 0.641 3.507 5.026
SEXE 0.308 0.663 -0.418 -0.222 0.220
TTT -0.064 -0.359 0.044 0.088 -0.049
CREVEIL -0.936 -0.075 0.158 0.205 -0.007
Covariances
TTT CREVEIL
________ ________
TTT 0.244
CREVEIL -0.003 0.250
Correlations
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
C1 1.000
C2 0.544 1.000
C3 0.014 0.120 1.000
C4 -0.106 0.047 0.328 1.000
SEXE 0.097 0.234 -0.187 -0.211 1.000
TTT -0.019 -0.120 0.019 0.080 -0.211
CREVEIL -0.277 -0.025 0.066 0.183 -0.028
Correlations
TTT CREVEIL
________ ________
TTT 1.000
CREVEIL -0.011 1.000
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
C1 10.412 1.383 1.205 0.99% 4.540 7.500 9.168
101.000 45.592 2.806 36.490 0.99% 10.490 15.275
C2 10.189 1.502 1.380 0.99% 5.190 6.885 8.637
101.000 36.375 2.786 33.265 0.99% 10.520 14.420
C3 6.393 2.088 1.825 0.99% 3.225 4.150 4.635
101.000 22.701 4.553 27.110 0.99% 5.155 8.620
C4 3.706 2.704 1.370 0.99% 2.170 2.880 3.123
101.000 5.026 9.698 15.955 0.99% 3.335 4.630
SEXE 0.327 0.739 0.000 67.33% 0.000 0.000 0.000
101.000 0.220 -1.454 1.000 32.67% 0.000 1.000
TTT 0.574 -0.300 0.000 42.57% 0.000 0.000 1.000
101.000 0.244 -1.910 1.000 57.43% 1.000 1.000
CREVEIL 0.505 -0.020 0.000 49.50% 0.000 0.000 1.000
101.000 0.250 -2.000 1.000 50.50% 1.000 1.000
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST FIT FUNCTION VALUES
Fit function values at local maxima and random start numbers:
39.5078 4
39.5078 9
39.5078 6
39.5078 15
39.5078 13
39.5078 3
39.5078 10
39.5078 5
39.5078 unperturbed
39.5078 17
39.5078 2
39.5078 12
39.5078 11
39.5078 20
39.5078 7
39.5078 14
39.5078 8
39.5078 16
39.5078 18
39.5078 19
39.5078 1
MODEL FIT INFORMATION
Number of Free Parameters 14
Loglikelihood
H0 Value -1167.103
H0 Scaling Correction Factor 1.5972
for MLR
H1 Value -1147.349
H1 Scaling Correction Factor 1.3795
for MLR
Information Criteria
Akaike (AIC) 2362.205
Bayesian (BIC) 2398.817
Sample-Size Adjusted BIC 2354.599
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 35.098*
Degrees of Freedom 12
P-Value 0.0005
Scaling Correction Factor 1.1256
for MLR
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.138
90 Percent C.I. 0.086 0.192
Probability RMSEA <= .05 0.005
CFI/TLI
CFI 0.623
TLI 0.434
Chi-Square Test of Model Fit for the Baseline Model
Value 79.264
Degrees of Freedom 18
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.116
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
C1 1.000 0.000 999.000 999.000
C2 1.000 0.000 999.000 999.000
C3 1.000 0.000 999.000 999.000
C4 1.000 0.000 999.000 999.000
S |
C1 0.000 0.000 999.000 999.000
C2 1.000 0.000 999.000 999.000
C3 4.000 0.000 999.000 999.000
C4 9.000 0.000 999.000 999.000
I ON
SEXE 1.542 1.070 1.441 0.150
TTT -0.539 0.952 -0.566 0.571
CREVEIL -1.685 1.118 -1.507 0.132
S ON
SEXE -0.276 0.120 -2.299 0.021
TTT 0.080 0.115 0.698 0.485
CREVEIL 0.276 0.132 2.087 0.037
S WITH
I -1.759 0.659 -2.669 0.008
Intercepts
C1 0.000 0.000 999.000 999.000
C2 0.000 0.000 999.000 999.000
C3 0.000 0.000 999.000 999.000
C4 0.000 0.000 999.000 999.000
I 11.045 1.000 11.044 0.000
S -0.837 0.118 -7.116 0.000
Residual Variances
C1 24.762 7.511 3.297 0.001
C2 19.694 6.421 3.067 0.002
C3 22.366 6.016 3.718 0.000
C4 0.000 0.000 999.000 999.000
I 16.255 5.962 2.726 0.006
S 0.247 0.075 3.296 0.001
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.398E-04
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
C1 0.645 0.104 6.194 0.000
C2 0.725 0.124 5.831 0.000
C3 0.785 0.103 7.597 0.000
C4 1.875 0.495 3.789 0.000
S |
C1 0.000 0.000 999.000 999.000
C2 0.092 0.014 6.661 0.000
C3 0.401 0.042 9.615 0.000
C4 2.154 0.436 4.936 0.000
I ON
SEXE 0.172 0.110 1.558 0.119
TTT -0.063 0.111 -0.570 0.569
CREVEIL -0.200 0.115 -1.747 0.081
S ON
SEXE -0.241 0.096 -2.519 0.012
TTT 0.074 0.106 0.695 0.487
CREVEIL 0.257 0.103 2.495 0.013
S WITH
I -0.877 0.053 -16.632 0.000
Intercepts
C1 0.000 0.000 999.000 999.000
C2 0.000 0.000 999.000 999.000
C3 0.000 0.000 999.000 999.000
C4 0.000 0.000 999.000 999.000
I 2.628 0.433 6.071 0.000
S -1.561 0.250 -6.244 0.000
Residual Variances
C1 0.584 0.134 4.340 0.000
C2 0.585 0.141 4.137 0.000
C3 0.780 0.051 15.225 0.000
C4 0.000 999.000 999.000 999.000
I 0.920 0.068 13.562 0.000
S 0.860 0.082 10.525 0.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
C1 0.416 0.134 3.097 0.002
C2 0.415 0.141 2.933 0.003
C3 0.220 0.051 4.284 0.000
C4 1.000 999.000 999.000 999.000
Latent Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
I 0.080 0.068 1.180 0.238
S 0.140 0.082 1.717 0.086
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
0 0 0 0 0
NU
TTT CREVEIL
________ ________
0 0
LAMBDA
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
C1 0 0 0 0 0
C2 0 0 0 0 0
C3 0 0 0 0 0
C4 0 0 0 0 0
SEXE 0 0 0 0 0
TTT 0 0 0 0 0
CREVEIL 0 0 0 0 0
THETA
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
C1 1
C2 0 2
C3 0 0 3
C4 0 0 0 0
SEXE 0 0 0 0 0
TTT 0 0 0 0 0
CREVEIL 0 0 0 0 0
THETA
TTT CREVEIL
________ ________
TTT 0
CREVEIL 0 0
ALPHA
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
4 5 0 0 0
BETA
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 0 0 6 7 8
S 0 0 9 10 11
SEXE 0 0 0 0 0
TTT 0 0 0 0 0
CREVEIL 0 0 0 0 0
PSI
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 12
S 13 14
SEXE 0 0 0
TTT 0 0 0 0
CREVEIL 0 0 0 0 0
STARTING VALUES
NU
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
TTT CREVEIL
________ ________
0.000 0.000
LAMBDA
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
C1 1.000 0.000 0.000 0.000 0.000
C2 1.000 1.000 0.000 0.000 0.000
C3 1.000 4.000 0.000 0.000 0.000
C4 1.000 9.000 0.000 0.000 0.000
SEXE 0.000 0.000 1.000 0.000 0.000
TTT 0.000 0.000 0.000 1.000 0.000
CREVEIL 0.000 0.000 0.000 0.000 1.000
THETA
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
C1 22.796
C2 0.000 18.188
C3 0.000 0.000 11.350
C4 0.000 0.000 0.000 0.000
SEXE 0.000 0.000 0.000 0.000 0.000
TTT 0.000 0.000 0.000 0.000 0.000
CREVEIL 0.000 0.000 0.000 0.000 0.000
THETA
TTT CREVEIL
________ ________
TTT 0.000
CREVEIL 0.000 0.000
ALPHA
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
10.413 -0.782 0.327 0.574 0.505
BETA
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 0.000 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000 0.000
SEXE 0.000 0.000 0.000 0.000 0.000
TTT 0.000 0.000 0.000 0.000 0.000
CREVEIL 0.000 0.000 0.000 0.000 0.000
PSI
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 29.375
S 0.000 0.576
SEXE 0.000 0.000 0.220
TTT 0.000 0.000 -0.049 0.244
CREVEIL 0.000 0.000 -0.007 -0.003 0.250
TECHNICAL 4 OUTPUT
ESTIMATES DERIVED FROM THE MODEL
ESTIMATED MEANS FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
10.389 -0.743 0.327 0.574 0.505
S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
0.546 0.066 0.047 0.049 0.050
EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
19.023 -11.203 7.001 11.672 10.150
TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 17.668
S -1.998 0.288
SEXE 0.377 -0.066 0.220
TTT -0.203 0.032 -0.049 0.244
CREVEIL -0.430 0.070 -0.007 -0.003 0.250
S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 6.788
S 0.768 0.090
SEXE 0.260 0.030 0.016
TTT 0.261 0.031 0.023 0.007
CREVEIL 0.284 0.034 0.023 0.025 0.000
EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 2.603
S -2.602 3.189
SEXE 1.446 -2.241 13.602
TTT -0.776 1.027 -2.122 33.459
CREVEIL -1.516 2.077 -0.282 -0.116 507.494
TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 0.009
S 0.009 0.001
SEXE 0.148 0.025 0.000
TTT 0.438 0.304 0.034 0.000
CREVEIL 0.130 0.038 0.778 0.908 0.000
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 1.000
S -0.886 1.000
SEXE 0.191 -0.264 1.000
TTT -0.097 0.122 -0.211 1.000
CREVEIL -0.204 0.263 -0.028 -0.011 1.000
S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 0.000
S 0.049 0.000
SEXE 0.121 0.106 0.000
TTT 0.124 0.118 0.099 0.000
CREVEIL 0.116 0.106 0.099 0.099 0.000
EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 999.000
S -17.972 999.000
SEXE 1.574 -2.481 999.000
TTT -0.788 1.031 -2.143 999.000
CREVEIL -1.761 2.484 -0.282 -0.116 999.000
TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S SEXE TTT CREVEIL
________ ________ ________ ________ ________
I 0.000
S 0.000 0.000
SEXE 0.115 0.013 0.000
TTT 0.431 0.303 0.032 0.000
CREVEIL 0.078 0.013 0.778 0.908 0.000
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
I I_SE S S_SE
________ ________ ________ ________
10.389 2.532 -0.743 0.281
Covariances
I I_SE S S_SE
________ ________ ________ ________
I 11.257
I_SE 0.000 0.000
S -1.285 0.000 0.209
S_SE 0.000 0.000 0.000 0.000
Correlations
I I_SE S S_SE
________ ________ ________ ________
I 1.000
I_SE 999.000 1.000
S -0.839 999.000 1.000
S_SE 999.000 999.000 999.000 1.000
PLOT INFORMATION
The following plots are available:
Histograms (sample values, estimated factor scores, estimated values, residuals)
Scatterplots (sample values, estimated factor scores, estimated values, residuals)
Sample means
Estimated means
Sample and estimated means
Adjusted estimated means
Latent variable distribution plots
Observed individual values
Estimated individual values
DIAGRAM INFORMATION
Use View Diagram under the Diagram menu in the Mplus Editor to view the diagram.
If running Mplus from the Mplus Diagrammer, the diagram opens automatically.
Diagram output
c:\project\mpluslivre\stx\chapitres\chapitre_07\script7.12.dgm
Beginning Time: 18:20:02
Ending Time: 18:20:02
Elapsed Time: 00:00:00
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