Mplus VERSION 8.6
MUTHEN & MUTHEN
07/20/2021 6:20 PM
OUTPUT SECTIONS
INPUT INSTRUCTIONS
TITLE: 7.12b M5. Modèle piecewise 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 s1 | C1@0 C2@1 C3@4 C4@4 ;
i s2 | C1@0 C2@0 C3@0 C4@9 ;
i s1 s2 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
7.12b M5. Modèle piecewise 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 3
Observed dependent variables
Continuous
C1 C2 C3 C4
Observed independent variables
SEXE TTT CREVEIL
Continuous latent variables
I S1 S2
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:
13.9437 19
13.9437 16
13.9437 9
13.9437 13
13.9437 18
13.9437 20
13.9437 3
13.9437 17
13.9437 8
13.9437 12
13.9437 7
13.9437 6
13.9437 4
13.9437 11
13.9437 15
13.9437 1
13.9437 5
13.9437 unperturbed
13.9437 14
13.9437 10
13.9437 2
MODEL FIT INFORMATION
Number of Free Parameters 21
Loglikelihood
H0 Value -1154.321
H0 Scaling Correction Factor 1.4489
for MLR
H1 Value -1147.349
H1 Scaling Correction Factor 1.3795
for MLR
Information Criteria
Akaike (AIC) 2350.641
Bayesian (BIC) 2405.559
Sample-Size Adjusted BIC 2339.231
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 12.811*
Degrees of Freedom 5
P-Value 0.0252
Scaling Correction Factor 1.0884
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 0.124
90 Percent C.I. 0.040 0.211
Probability RMSEA <= .05 0.066
CFI/TLI
CFI 0.873
TLI 0.541
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 0.050
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
S1 |
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 4.000 0.000 999.000 999.000
S2 |
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 9.000 0.000 999.000 999.000
I ON
SEXE 2.241 1.206 1.858 0.063
TTT -0.389 1.125 -0.346 0.729
CREVEIL -2.716 1.384 -1.962 0.050
S1 ON
SEXE -0.983 0.367 -2.679 0.007
TTT 0.026 0.385 0.068 0.946
CREVEIL 0.885 0.433 2.044 0.041
S2 ON
SEXE 0.083 0.093 0.893 0.372
TTT 0.052 0.104 0.497 0.619
CREVEIL -0.003 0.104 -0.031 0.976
S1 WITH
I -6.036 2.401 -2.514 0.012
S2 WITH
I -0.235 0.248 -0.944 0.345
S1 -0.135 0.244 -0.553 0.580
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 11.599 1.184 9.797 0.000
S1 -1.207 0.389 -3.105 0.002
S2 -0.363 0.100 -3.635 0.000
Residual Variances
C1 16.166 6.773 2.387 0.017
C2 19.443 5.736 3.390 0.001
C3 11.941 7.975 1.497 0.134
C4 0.000 0.000 999.000 999.000
I 26.141 9.024 2.897 0.004
S1 2.012 0.833 2.416 0.016
S2 0.105 0.103 1.018 0.309
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.793E-05
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
C1 0.803 0.090 8.918 0.000
C2 0.892 0.108 8.276 0.000
C3 1.134 0.242 4.677 0.000
C4 2.414 0.598 4.038 0.000
S1 |
C1 0.000 0.000 999.000 999.000
C2 0.257 0.043 5.920 0.000
C3 1.308 0.256 5.103 0.000
C4 2.784 0.699 3.981 0.000
S2 |
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 1.313 0.727 1.806 0.071
I ON
SEXE 0.194 0.103 1.889 0.059
TTT -0.036 0.103 -0.347 0.729
CREVEIL -0.251 0.109 -2.292 0.022
S1 ON
SEXE -0.295 0.104 -2.828 0.005
TTT 0.008 0.122 0.068 0.946
CREVEIL 0.284 0.131 2.166 0.030
S2 ON
SEXE 0.119 0.119 1.003 0.316
TTT 0.078 0.161 0.484 0.629
CREVEIL -0.005 0.160 -0.030 0.976
S1 WITH
I -0.832 0.113 -7.387 0.000
S2 WITH
I -0.142 0.182 -0.779 0.436
S1 -0.293 0.353 -0.830 0.407
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 2.143 0.315 6.812 0.000
S1 -0.773 0.276 -2.799 0.005
S2 -1.109 0.520 -2.135 0.033
Residual Variances
C1 0.356 0.145 2.461 0.014
C2 0.528 0.106 4.961 0.000
C3 0.524 0.321 1.632 0.103
C4 0.000 999.000 999.000 999.000
I 0.893 0.068 13.058 0.000
S1 0.827 0.096 8.631 0.000
S2 0.984 0.034 28.562 0.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
C1 0.644 0.145 4.459 0.000
C2 0.472 0.106 4.432 0.000
C3 0.476 0.321 1.482 0.138
C4 1.000 999.000 999.000 999.000
Latent Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
I 0.107 0.068 1.571 0.116
S1 0.173 0.096 1.811 0.070
S2 0.016 0.034 0.476 0.634
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
C1 C2 C3 C4 SEXE
________ ________ ________ ________ ________
0 0 0 0 0
NU
TTT CREVEIL
________ ________
0 0
LAMBDA
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
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
LAMBDA
CREVEIL
________
C1 0
C2 0
C3 0
C4 0
SEXE 0
TTT 0
CREVEIL 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 S1 S2 SEXE TTT
________ ________ ________ ________ ________
4 5 6 0 0
ALPHA
CREVEIL
________
0
BETA
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 0 0 0 7 8
S1 0 0 0 10 11
S2 0 0 0 13 14
SEXE 0 0 0 0 0
TTT 0 0 0 0 0
CREVEIL 0 0 0 0 0
BETA
CREVEIL
________
I 9
S1 12
S2 15
SEXE 0
TTT 0
CREVEIL 0
PSI
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 16
S1 17 18
S2 19 20 21
SEXE 0 0 0 0
TTT 0 0 0 0 0
CREVEIL 0 0 0 0 0
PSI
CREVEIL
________
CREVEIL 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 S1 S2 SEXE TTT
________ ________ ________ ________ ________
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 4.000 9.000 0.000 0.000
SEXE 0.000 0.000 0.000 1.000 0.000
TTT 0.000 0.000 0.000 0.000 1.000
CREVEIL 0.000 0.000 0.000 0.000 0.000
LAMBDA
CREVEIL
________
C1 0.000
C2 0.000
C3 0.000
C4 0.000
SEXE 0.000
TTT 0.000
CREVEIL 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 S1 S2 SEXE TTT
________ ________ ________ ________ ________
10.938 -1.450 7.675 0.327 0.574
ALPHA
CREVEIL
________
0.505
BETA
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 0.000 0.000 0.000 0.000 0.000
S1 0.000 0.000 0.000 0.000 0.000
S2 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
BETA
CREVEIL
________
I 0.000
S1 0.000
S2 0.000
SEXE 0.000
TTT 0.000
CREVEIL 0.000
PSI
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 40.607
S1 0.000 3.136
S2 0.000 0.000 10.428
SEXE 0.000 0.000 0.000 0.220
TTT 0.000 0.000 0.000 -0.049 0.244
CREVEIL 0.000 0.000 0.000 -0.007 -0.003
PSI
CREVEIL
________
CREVEIL 0.250
TECHNICAL 4 OUTPUT
ESTIMATES DERIVED FROM THE MODEL
ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
10.736 -1.066 -0.308 0.327 0.574
ESTIMATED MEANS FOR THE LATENT VARIABLES
CREVEIL
________
0.505
S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
0.647 0.212 0.052 0.047 0.049
S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
CREVEIL
________
0.050
EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
16.586 -5.030 -5.919 7.001 11.672
EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
CREVEIL
________
10.150
TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
CREVEIL
________
0.000
ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 29.286
S1 -7.175 2.435
S2 -0.199 -0.151 0.107
SEXE 0.530 -0.223 0.016 0.220
TTT -0.197 0.052 0.009 -0.049 0.244
CREVEIL -0.693 0.228 -0.001 -0.007 -0.003
ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 0.250
S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 10.200
S1 2.737 0.919
S2 0.288 0.252 0.104
SEXE 0.296 0.084 0.020 0.016
TTT 0.310 0.098 0.025 0.023 0.007
CREVEIL 0.350 0.111 0.026 0.023 0.025
S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 0.000
EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 2.871
S1 -2.622 2.650
S2 -0.691 -0.602 1.023
SEXE 1.791 -2.662 0.796 13.602
TTT -0.636 0.530 0.345 -2.122 33.459
CREVEIL -1.977 2.055 -0.057 -0.282 -0.116
EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 507.494
TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 0.004
S1 0.009 0.008
S2 0.490 0.547 0.306
SEXE 0.073 0.008 0.426 0.000
TTT 0.525 0.596 0.730 0.034 0.000
CREVEIL 0.048 0.040 0.955 0.778 0.908
TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 0.000
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 1.000
S1 -0.850 1.000
S2 -0.112 -0.297 1.000
SEXE 0.209 -0.305 0.103 1.000
TTT -0.074 0.067 0.053 -0.211 1.000
CREVEIL -0.256 0.292 -0.009 -0.028 -0.011
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 1.000
S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 0.000
S1 0.098 0.000
S2 0.184 0.324 0.000
SEXE 0.113 0.109 0.115 0.000
TTT 0.115 0.130 0.158 0.099 0.000
CREVEIL 0.111 0.133 0.162 0.099 0.099
S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 0.000
EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 999.000
S1 -8.714 999.000
S2 -0.609 -0.916 999.000
SEXE 1.848 -2.800 0.895 999.000
TTT -0.639 0.519 0.336 -2.143 999.000
CREVEIL -2.315 2.189 -0.056 -0.282 -0.116
EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 999.000
TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2 SEXE TTT
________ ________ ________ ________ ________
I 0.000
S1 0.000 0.000
S2 0.542 0.359 0.000
SEXE 0.065 0.005 0.371 0.000
TTT 0.523 0.604 0.737 0.032 0.000
CREVEIL 0.021 0.029 0.955 0.778 0.908
TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
CREVEIL
________
CREVEIL 0.000
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
I I_SE S1 S1_SE S2
________ ________ ________ ________ ________
10.736 2.775 -1.066 0.878 -0.308
Means
S2_SE
________
0.240
Covariances
I I_SE S1 S1_SE S2
________ ________ ________ ________ ________
I 21.585
I_SE 0.000 0.000
S1 -5.254 0.000 1.664
S1_SE 0.000 0.000 0.000 0.000
S2 -0.197 0.000 -0.022 0.000 0.049
S2_SE 0.000 0.000 0.000 0.000 0.000
Covariances
S2_SE
________
S2_SE 0.000
Correlations
I I_SE S1 S1_SE S2
________ ________ ________ ________ ________
I 1.000
I_SE 999.000 1.000
S1 -0.877 999.000 1.000
S1_SE 999.000 999.000 999.000 1.000
S2 -0.191 999.000 -0.078 999.000 1.000
S2_SE 999.000 999.000 999.000 999.000 999.000
Correlations
S2_SE
________
S2_SE 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\script7.12b.dgm
Beginning Time: 18:20:22
Ending Time: 18:20:22
Elapsed Time: 00:00:00
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