Mplus VERSION 8.6
MUTHEN & MUTHEN
07/20/2021 6:04 PM
OUTPUT SECTIONS
INPUT INSTRUCTIONS
TITLE: 7.7 Modèle quadratique 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 s q | C1@0 C2@1 C3@2 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
7.7 Modèle quadratique 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 S Q
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:
5.9316 9
5.9316 11
5.9316 1
5.9316 16
5.9316 3
5.9316 12
5.9316 20
5.9316 2
5.9316 10
5.9316 17
5.9316 8
5.9316 5
5.9316 13
5.9316 6
5.9316 14
5.9316 7
5.9316 unperturbed
5.9316 18
5.9316 19
5.9316 4
5.9316 15
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE.
THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED
VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES.
CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE C1.
MODEL FIT INFORMATION
Number of Free Parameters 12
Loglikelihood
H0 Value -1164.382
H0 Scaling Correction Factor 1.8456
for MLR
H1 Value -1161.416
H1 Scaling Correction Factor 1.7889
for MLR
Information Criteria
Akaike (AIC) 2352.764
Bayesian (BIC) 2384.145
Sample-Size Adjusted BIC 2346.244
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 4.094*
Degrees of Freedom 2
P-Value 0.1292
Scaling Correction Factor 1.4490
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 0.102
90 Percent C.I. 0.000 0.245
Probability RMSEA <= .05 0.196
CFI/TLI
CFI 0.943
TLI 0.830
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 0.063
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 2.000 0.000 999.000 999.000
C4 3.000 0.000 999.000 999.000
Q |
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
S WITH
I -51.600 23.814 -2.167 0.030
Q WITH
I 9.931 5.118 1.940 0.052
S -9.386 4.440 -2.114 0.035
Means
I 10.196 0.619 16.472 0.000
S -0.379 0.757 -0.501 0.616
Q -0.595 0.219 -2.719 0.007
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 63.911 26.017 2.456 0.014
S 46.274 20.963 2.207 0.027
Q 2.004 0.955 2.100 0.036
Residual Variances
C1 -18.327 19.056 -0.962 0.336
C2 27.402 7.821 3.504 0.000
C3 18.839 5.197 3.625 0.000
C4 0.000 0.000 999.000 999.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.645E-06
(ratio of smallest to largest eigenvalue)
STANDARDIZED MODEL RESULTS
STDYX Standardization
Two-Tailed
Estimate S.E. Est./S.E. P-Value
I |
C1 1.184 0.159 7.466 0.000
C2 1.306 0.187 6.988 0.000
C3 1.675 0.393 4.266 0.000
C4 3.566 0.971 3.674 0.000
S |
C1 0.000 0.000 999.000 999.000
C2 1.111 0.199 5.578 0.000
C3 2.850 0.693 4.112 0.000
C4 9.103 2.664 3.417 0.001
Q |
C1 0.000 0.000 999.000 999.000
C2 0.231 0.048 4.775 0.000
C3 1.186 0.283 4.185 0.000
C4 5.683 1.761 3.227 0.001
S WITH
I -0.949 0.054 -17.718 0.000
Q WITH
I 0.877 0.136 6.471 0.000
S -0.975 0.023 -42.279 0.000
Means
I 1.275 0.254 5.027 0.000
S -0.056 0.111 -0.501 0.617
Q -0.420 0.179 -2.352 0.019
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
S 1.000 0.000 999.000 999.000
Q 1.000 0.000 999.000 999.000
Residual Variances
C1 -0.402 999.000 999.000 999.000
C2 0.731 0.078 9.369 0.000
C3 0.827 0.072 11.435 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 Undefined 0.14020E+01
C2 0.269 0.078 3.446 0.001
C3 0.173 0.072 2.394 0.017
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 S Q
________ ________ ________
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 S Q
________ ________ ________
4 5 6
BETA
I S Q
________ ________ ________
I 0 0 0
S 0 0 0
Q 0 0 0
PSI
I S Q
________ ________ ________
I 7
S 8 9
Q 10 11 12
STARTING VALUES
NU
C1 C2 C3 C4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S Q
________ ________ ________
C1 1.000 0.000 0.000
C2 1.000 1.000 1.000
C3 1.000 2.000 4.000
C4 1.000 3.000 9.000
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 S Q
________ ________ ________
10.646 -0.542 -0.616
BETA
I S Q
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.000
Q 0.000 0.000 0.000
PSI
I S Q
________ ________ ________
I 48.323
S 0.000 51.306
Q 0.000 0.000 3.748
TECHNICAL 4 OUTPUT
ESTIMATES DERIVED FROM THE MODEL
ESTIMATED MEANS FOR THE LATENT VARIABLES
I S Q
________ ________ ________
10.196 -0.379 -0.595
S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S Q
________ ________ ________
0.619 0.757 0.219
EST./S.E. FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S Q
________ ________ ________
16.472 -0.501 -2.719
TWO-TAILED P-VALUE FOR ESTIMATED MEANS FOR THE LATENT VARIABLES
I S Q
________ ________ ________
0.000 0.616 0.007
ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 63.911
S -51.600 46.274
Q 9.931 -9.386 2.004
S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 26.017
S 23.814 20.963
Q 5.118 4.440 0.955
EST./S.E. FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 2.456
S -2.167 2.207
Q 1.940 -2.114 2.100
TWO-TAILED P-VALUE FOR ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 0.014
S 0.030 0.027
Q 0.052 0.035 0.036
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 1.000
S -0.949 1.000
Q 0.877 -0.975 1.000
S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 0.000
S 0.054 0.000
Q 0.136 0.023 0.000
EST./S.E. FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 999.000
S -17.718 999.000
Q 6.471 -42.279 999.000
TWO-TAILED P-VALUE FOR ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
I S Q
________ ________ ________
I 0.000
S 0.000 0.000
Q 0.000 0.000 0.000
SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES
SAMPLE STATISTICS
Means
I I_SE S S_SE Q
________ ________ ________ ________ ________
10.196 0.000 -0.379 0.000 -0.595
Means
Q_SE
________
0.000
Covariances
I I_SE S S_SE Q
________ ________ ________ ________ ________
I 92.908
I_SE 0.000 0.000
S -75.775 0.000 62.871
S_SE 0.000 0.000 0.000 0.000
Q 14.768 0.000 -12.232 0.000 2.416
Q_SE 0.000 0.000 0.000 0.000 0.000
Covariances
Q_SE
________
Q_SE 0.000
Correlations
I I_SE S S_SE Q
________ ________ ________ ________ ________
I 1.000
I_SE 999.000 1.000
S -0.991 999.000 1.000
S_SE 999.000 999.000 999.000 1.000
Q 0.986 999.000 -0.993 999.000 1.000
Q_SE 999.000 999.000 999.000 999.000 999.000
Correlations
Q_SE
________
Q_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\script7.7.dgm
Beginning Time: 18:04:55
Ending Time: 18:04:56
Elapsed Time: 00:00:01
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