Mplus VERSION 8.6
MUTHEN & MUTHEN
07/20/2021 6:15 PM
OUTPUT SECTIONS
INPUT INSTRUCTIONS
TITLE: 7.9 Modèle piecewise equidistant
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 ;
ANALYSIS:
ESTIMATOR = MLR ;
STARTS = 20 ;
MODEL:
i s1 | C1@0 C2@1 C3@2 C4@2 ;
i s2 | C1@0 C2@0 C3@0 C4@3 ;
C4@0 ; !fixer la variance résiduelle à zéro
OUTPUT:
SAMPSTAT STDYX TECH1 TECH4 ;
PLOT:
TYPE = PLOT3 ;
SERIES = C1 (0) C2 (1) C3 (2) C4 (3) ;
INPUT READING TERMINATED NORMALLY
7.9 Modèle piecewise equidistant
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 101
Number of dependent variables 4
Number of independent variables 0
Number of continuous latent variables 3
Observed dependent variables
Continuous
C1 C2 C3 C4
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
________ ________ ________ ________
10.412 10.189 6.393 3.706
Covariances
C1 C2 C3 C4
________ ________ ________ ________
C1 45.592
C2 22.137 36.375
C3 0.437 3.455 22.701
C4 -1.599 0.641 3.507 5.026
Correlations
C1 C2 C3 C4
________ ________ ________ ________
C1 1.000
C2 0.544 1.000
C3 0.014 0.120 1.000
C4 -0.106 0.047 0.328 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
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST FIT FUNCTION VALUES
Fit function values at local maxima and random start numbers:
10.9481 1
10.9481 19
10.9481 15
10.9481 18
10.9481 7
10.9481 14
10.9481 5
10.9481 9
10.9481 3
10.9481 16
10.9481 17
10.9481 12
10.9481 11
10.9481 6
10.9481 10
10.9481 unperturbed
10.9481 8
10.9481 20
10.9481 4
10.9481 2
10.9481 13
MODEL FIT INFORMATION
Number of Free Parameters 12
Loglikelihood
H0 Value -1166.890
H0 Scaling Correction Factor 1.8897
for MLR
H1 Value -1161.416
H1 Scaling Correction Factor 1.7889
for MLR
Information Criteria
Akaike (AIC) 2357.780
Bayesian (BIC) 2389.162
Sample-Size Adjusted BIC 2351.260
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 9.246*
Degrees of Freedom 2
P-Value 0.0098
Scaling Correction Factor 1.1841
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 0.189
90 Percent C.I. 0.079 0.320
Probability RMSEA <= .05 0.023
CFI/TLI
CFI 0.803
TLI 0.410
Chi-Square Test of Model Fit for the Baseline Model
Value 42.868
Degrees of Freedom 6
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value 0.086
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 2.000 0.000 999.000 999.000
C4 2.000 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 3.000 0.000 999.000 999.000
S1 WITH
I -21.468 8.686 -2.471 0.013
S2 WITH
I -0.700 0.925 -0.757 0.449
S1 0.047 0.713 0.066 0.947
Means
I 10.474 0.662 15.812 0.000
S1 -1.789 0.446 -4.013 0.000
S2 -1.064 0.178 -5.980 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
Variances
I 43.425 16.415 2.645 0.008
S1 11.920 4.605 2.588 0.010
S2 0.380 0.409 0.931 0.352
Residual Variances
C1 2.179 10.558 0.206 0.837
C2 26.324 7.069 3.724 0.000
C3 17.599 5.734 3.069 0.002
C4 0.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.254E-05
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
C1 0.976 0.120 8.115 0.000
C2 1.059 0.139 7.600 0.000
C3 1.379 0.310 4.448 0.000
C4 2.939 0.768 3.825 0.000
S1 |
C1 0.000 0.000 999.000 999.000
C2 0.555 0.084 6.643 0.000
C3 1.445 0.314 4.600 0.000
C4 3.080 0.789 3.901 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 0.825 0.489 1.689 0.091
S1 WITH
I -0.944 0.043 -21.796 0.000
S2 WITH
I -0.172 0.245 -0.703 0.482
S1 0.022 0.345 0.064 0.949
Means
I 1.589 0.299 5.313 0.000
S1 -0.518 0.156 -3.329 0.001
S2 -1.724 0.954 -1.807 0.071
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
Variances
I 1.000 0.000 999.000 999.000
S1 1.000 0.000 999.000 999.000
S2 1.000 0.000 999.000 999.000
Residual Variances
C1 0.048 0.235 0.204 0.839
C2 0.680 0.075 9.108 0.000
C3 0.771 0.142 5.426 0.000
C4 0.000 999.000 999.000 999.000
R-SQUARE
Observed Two-Tailed
Variable Estimate S.E. Est./S.E. P-Value
C1 0.952 0.235 4.058 0.000
C2 0.320 0.075 4.293 0.000
C3 0.229 0.142 1.614 0.107
C4 1.000 999.000 999.000 999.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
C1 C2 C3 C4
________ ________ ________ ________
0 0 0 0
LAMBDA
I S1 S2
________ ________ ________
C1 0 0 0
C2 0 0 0
C3 0 0 0
C4 0 0 0
THETA
C1 C2 C3 C4
________ ________ ________ ________
C1 1
C2 0 2
C3 0 0 3
C4 0 0 0 0
ALPHA
I S1 S2
________ ________ ________
4 5 6
BETA
I S1 S2
________ ________ ________
I 0 0 0
S1 0 0 0
S2 0 0 0
PSI
I S1 S2
________ ________ ________
I 7
S1 8 9
S2 10 11 12
STARTING VALUES
NU
C1 C2 C3 C4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S1 S2
________ ________ ________
C1 1.000 0.000 0.000
C2 1.000 1.000 0.000
C3 1.000 2.000 0.000
C4 1.000 2.000 3.000
THETA
C1 C2 C3 C4
________ ________ ________ ________
C1 22.796
C2 0.000 18.188
C3 0.000 0.000 11.350
C4 0.000 0.000 0.000 0.000
ALPHA
I S1 S2
________ ________ ________
11.306 -2.905 7.675
BETA
I S1 S2
________ ________ ________
I 0.000 0.000 0.000
S1 0.000 0.000 0.000
S2 0.000 0.000 0.000
PSI
I S1 S2
________ ________ ________
I 48.692
S1 0.000 14.219
S2 0.000 0.000 10.428
TECHNICAL 4 OUTPUT
ESTIMATES DERIVED FROM THE MODEL
ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
10.474 -1.789 -1.064
S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
0.662 0.446 0.178
EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
15.812 -4.013 -5.980
TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
0.000 0.000 0.000
ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 43.425
S1 -21.468 11.920
S2 -0.700 0.047 0.380
S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 16.415
S1 8.686 4.605
S2 0.925 0.713 0.409
EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 2.645
S1 -2.471 2.588
S2 -0.757 0.066 0.931
TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 0.008
S1 0.013 0.010
S2 0.449 0.947 0.352
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 1.000
S1 -0.944 1.000
S2 -0.172 0.022 1.000
S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 0.000
S1 0.043 0.000
S2 0.245 0.345 0.000
EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 999.000
S1 -21.796 999.000
S2 -0.703 0.064 999.000
TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S1 S2
________ ________ ________
I 0.000
S1 0.000 0.000
S2 0.482 0.949 0.000
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
I I_SE S1 S1_SE S2
________ ________ ________ ________ ________
10.474 1.425 -1.789 1.048 -1.064
Means
S2_SE
________
0.516
Covariances
I I_SE S1 S1_SE S2
________ ________ ________ ________ ________
I 41.393
I_SE 0.000 0.000
S1 -20.461 0.000 10.821
S1_SE 0.000 0.000 0.000 0.000
S2 -0.694 0.000 0.444 0.000 0.114
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 -0.967 999.000 1.000
S1_SE 999.000 999.000 999.000 1.000
S2 -0.319 999.000 0.400 999.000 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
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\script7.9.dgm
Beginning Time: 18:15:10
Ending Time: 18:15:10
Elapsed Time: 00:00:00
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2021 Muthen & Muthen