Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
title: this is an example of a linear growth
model for a categorical outcome.
this is the same example as in section 9.2 of
Mplus Web Note #4, page 18, using 4-category
outcomes
montecarlo:
names = u11-u14;
generate = u11-u14(3);
categorical = u11 - u14;
nobs = 500;
nreps = 1;
save = ex6.5.dat;
analysis:
parameterization = theta;
model population:
i s | u11@0 u12@1 u13@2 u14@3;
[u11$1-u14$1*-.7];
[u11$2-u14$2*0];
[u11$3-u14$3*.7];
u11*.5 u12*.6 u13*.9 u14*1.4;
[i@0 s*-.5];
i*.5; s*.1; i with s*0;
model:
i s | u11@0 u12@1 u13@2 u14@3;
[u11$1-u14$1*-.7] (1);
[u11$2-u14$2*0] (2);
[u11$3-u14$3*.7] (3);
u11@.5 u12*.6 u13*.9 u14*1.4;
! in the theta parameterization used here,
! the residual variance needs to be fixed for
! one time point for identification purposes.
! here, it is fixed at the true value for the first
! time point (.5), although in the real-data
! analysis the default is fixed at 1 which makes
! the estimates come out in a different metric
[i@0 s*-.5];
i*.5; s*.1; i with s*0;
output:
tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a linear growth
model for a categorical outcome.
this is the same example as in section 9.2 of
Mplus Web Note #4, page 18, using 4-category
outcomes
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 4
Number of independent variables 0
Number of continuous latent variables 2
Observed dependent variables
Binary and ordered categorical (ordinal)
U11 U12 U13 U14
Continuous latent variables
I S
Estimator WLSMV
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Parameterization THETA
Link PROBIT
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means/Intercepts/Thresholds
U11$1 U11$2 U11$3 U12$1 U12$2
________ ________ ________ ________ ________
-0.719 -0.040 0.668 -0.285 0.440
Means/Intercepts/Thresholds
U12$3 U13$1 U13$2 U13$3 U14$1
________ ________ ________ ________ ________
0.986 0.238 0.595 1.136 0.457
Means/Intercepts/Thresholds
U14$2 U14$3
________ ________
0.849 1.237
Covariances/Correlations/Residual Correlations
U11 U12 U13 U14
________ ________ ________ ________
U11
U12 0.506
U13 0.397 0.541
U14 0.303 0.427 0.515
MODEL FIT INFORMATION
Number of Free Parameters 10
Chi-Square Test of Model Fit
Degrees of freedom 8
Mean 12.014
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 1.646 12.014
0.980 1.000 2.032 12.014
0.950 1.000 2.733 12.014
0.900 1.000 3.490 12.014
0.800 1.000 4.594 12.014
0.700 1.000 5.527 12.014
0.500 1.000 7.344 12.014
0.300 1.000 9.524 12.014
0.200 1.000 11.030 12.014
0.100 0.000 13.362 12.014
0.050 0.000 15.507 12.014
0.020 0.000 18.168 12.014
0.010 0.000 20.090 12.014
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.032
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 0.000
0.010 0.000
CFI/TLI
CFI
Mean 0.992
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 0.994
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 0.021
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 0.000
0.010 0.000
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
I |
U11 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U13 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U14 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
S |
U11 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U12 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U13 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U14 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
I WITH
S 0.000 -0.0236 0.0000 0.0590 0.0006 1.000 0.000
Means
I 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
S -0.500 -0.5462 0.0000 0.0760 0.0021 1.000 1.000
Thresholds
U11$1 -0.700 -0.8090 0.0000 0.1075 0.0119 1.000 1.000
U11$2 0.000 -0.0502 0.0000 0.0549 0.0025 1.000 0.000
U11$3 0.700 0.7076 0.0000 0.1011 0.0001 1.000 1.000
U12$1 -0.700 -0.8090 0.0000 0.1075 0.0119 1.000 1.000
U12$2 0.000 -0.0502 0.0000 0.0549 0.0025 1.000 0.000
U12$3 0.700 0.7076 0.0000 0.1011 0.0001 1.000 1.000
U13$1 -0.700 -0.8090 0.0000 0.1075 0.0119 1.000 1.000
U13$2 0.000 -0.0502 0.0000 0.0549 0.0025 1.000 0.000
U13$3 0.700 0.7076 0.0000 0.1011 0.0001 1.000 1.000
U14$1 -0.700 -0.8090 0.0000 0.1075 0.0119 1.000 1.000
U14$2 0.000 -0.0502 0.0000 0.0549 0.0025 1.000 0.000
U14$3 0.700 0.7076 0.0000 0.1011 0.0001 1.000 1.000
Variances
I 0.500 0.7253 0.0000 0.2501 0.0507 1.000 1.000
S 0.100 0.1565 0.0000 0.0677 0.0032 1.000 1.000
Residual Variances
U11 0.500 0.5000 0.0000 0.0000 0.0000 1.000 0.000
U12 0.600 0.6666 0.0000 0.2042 0.0044 1.000 1.000
U13 0.900 1.2082 0.0000 0.3439 0.0950 1.000 1.000
U14 1.400 1.6644 0.0000 0.5026 0.0699 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.298E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL OUTPUT
PARAMETER SPECIFICATION
TAU
U11$1 U11$2 U11$3 U12$1 U12$2
________ ________ ________ ________ ________
1 2 3 1 2
TAU
U12$3 U13$1 U13$2 U13$3 U14$1
________ ________ ________ ________ ________
3 1 2 3 1
TAU
U14$2 U14$3
________ ________
2 3
NU
U11 U12 U13 U14
________ ________ ________ ________
0 0 0 0
LAMBDA
I S
________ ________
U11 0 0
U12 0 0
U13 0 0
U14 0 0
THETA
U11 U12 U13 U14
________ ________ ________ ________
U11 0
U12 0 4
U13 0 0 5
U14 0 0 0 6
ALPHA
I S
________ ________
0 7
BETA
I S
________ ________
I 0 0
S 0 0
PSI
I S
________ ________
I 8
S 9 10
STARTING VALUES
TAU
U11$1 U11$2 U11$3 U12$1 U12$2
________ ________ ________ ________ ________
-0.700 0.000 0.700 -0.700 0.000
TAU
U12$3 U13$1 U13$2 U13$3 U14$1
________ ________ ________ ________ ________
0.700 -0.700 0.000 0.700 -0.700
TAU
U14$2 U14$3
________ ________
0.000 0.700
NU
U11 U12 U13 U14
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S
________ ________
U11 1.000 0.000
U12 1.000 1.000
U13 1.000 2.000
U14 1.000 3.000
THETA
U11 U12 U13 U14
________ ________ ________ ________
U11 0.500
U12 0.000 0.600
U13 0.000 0.000 0.900
U14 0.000 0.000 0.000 1.400
ALPHA
I S
________ ________
0.000 -0.500
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 0.500
S 0.000 0.100
POPULATION VALUES
TAU
U11$1 U11$2 U11$3 U12$1 U12$2
________ ________ ________ ________ ________
-0.700 0.000 0.700 -0.700 0.000
TAU
U12$3 U13$1 U13$2 U13$3 U14$1
________ ________ ________ ________ ________
0.700 -0.700 0.000 0.700 -0.700
TAU
U14$2 U14$3
________ ________
0.000 0.700
NU
U11 U12 U13 U14
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
I S
________ ________
U11 1.000 0.000
U12 1.000 1.000
U13 1.000 2.000
U14 1.000 3.000
THETA
U11 U12 U13 U14
________ ________ ________ ________
U11 0.500
U12 0.000 0.600
U13 0.000 0.000 0.900
U14 0.000 0.000 0.000 1.400
ALPHA
I S
________ ________
0.000 -0.500
BETA
I S
________ ________
I 0.000 0.000
S 0.000 0.000
PSI
I S
________ ________
I 0.500
S 0.000 0.100
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U11
U12
U13
U14
Save file
ex6.5.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:24:25
Ending Time: 22:24:26
Elapsed Time: 00:00:01
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