Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:25 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level growth model
for a categorical outcome (three-level analysis).
montecarlo:
names are u1-u4 x w;
generate = u1-u4(1);
categorical = u1-u4;
nobservations = 500;
ncsizes = 3;
csizes = 10 (5) 50 (3) 30 (10);
seed = 58459;
nreps = 1;
within = x;
between = w;
save = ex9.13.dat;
ANALYSIS:
TYPE = TWOLEVEL;
integration = 7;
MODEL POPULATION:
%WITHIN%
x@1;
iw sw | u1@0 u2@1 u3@2 u4@3;
iw ON x*1;
sw ON x*.2;
iw*1; sw*.5;
%BETWEEN%
w@1;
ib sb | u1@0 u2@1 u3@2 u4@3;
[u1$1-u4$1*0];
ib ON w*.5;
sb ON w*.2;
[ib@0 sb*.5];
ib*.5; sb*.3;
MODEL:
%WITHIN%
iw sw | u1@0 u2@1 u3@2 u4@3;
iw ON x*1;
sw ON x*.2;
iw*1; sw*.5;
%BETWEEN%
ib sb | u1@0 u2@1 u3@2 u4@3;
[u1$1-u4$1*0] (1);
ib ON w*.5;
sb ON w*.2;
[ib@0 sb*.5];
ib*.5; sb*.3;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level growth model
for a categorical outcome (three-level analysis).
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of replications
Requested 1
Completed 1
Value of seed 58459
Number of dependent variables 4
Number of independent variables 2
Number of continuous latent variables 4
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Observed independent variables
X W
Continuous latent variables
IW SW IB SB
Variables with special functions
Within variables
X
Between variables
W
Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 4
Adaptive quadrature ON
Link LOGIT
Cholesky ON
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Size (s) Number of clusters of Size s
3 50
5 10
10 30
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
X W
________ ________
0.030 0.068
Covariances
X W
________ ________
X 1.048
W 0.042 1.220
Correlations
X W
________ ________
X 1.000
W 0.037 1.000
MODEL FIT INFORMATION
Number of Free Parameters 12
Loglikelihood
H0 Value
Mean -1053.648
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1053.648 -1053.648
0.980 0.000 -1053.648 -1053.648
0.950 0.000 -1053.648 -1053.648
0.900 0.000 -1053.648 -1053.648
0.800 0.000 -1053.648 -1053.648
0.700 0.000 -1053.648 -1053.648
0.500 0.000 -1053.648 -1053.648
0.300 0.000 -1053.648 -1053.648
0.200 0.000 -1053.648 -1053.648
0.100 0.000 -1053.648 -1053.648
0.050 0.000 -1053.648 -1053.648
0.020 0.000 -1053.648 -1053.648
0.010 0.000 -1053.648 -1053.648
Information Criteria
Akaike (AIC)
Mean 2131.295
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2131.295 2131.295
0.980 0.000 2131.295 2131.295
0.950 0.000 2131.295 2131.295
0.900 0.000 2131.295 2131.295
0.800 0.000 2131.295 2131.295
0.700 0.000 2131.295 2131.295
0.500 0.000 2131.295 2131.295
0.300 0.000 2131.295 2131.295
0.200 0.000 2131.295 2131.295
0.100 0.000 2131.295 2131.295
0.050 0.000 2131.295 2131.295
0.020 0.000 2131.295 2131.295
0.010 0.000 2131.295 2131.295
Bayesian (BIC)
Mean 2181.871
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2181.871 2181.871
0.980 0.000 2181.871 2181.871
0.950 0.000 2181.871 2181.871
0.900 0.000 2181.871 2181.871
0.800 0.000 2181.871 2181.871
0.700 0.000 2181.871 2181.871
0.500 0.000 2181.871 2181.871
0.300 0.000 2181.871 2181.871
0.200 0.000 2181.871 2181.871
0.100 0.000 2181.871 2181.871
0.050 0.000 2181.871 2181.871
0.020 0.000 2181.871 2181.871
0.010 0.000 2181.871 2181.871
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 2143.782
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 2143.782 2143.782
0.980 0.000 2143.782 2143.782
0.950 0.000 2143.782 2143.782
0.900 0.000 2143.782 2143.782
0.800 0.000 2143.782 2143.782
0.700 0.000 2143.782 2143.782
0.500 0.000 2143.782 2143.782
0.300 0.000 2143.782 2143.782
0.200 0.000 2143.782 2143.782
0.100 0.000 2143.782 2143.782
0.050 0.000 2143.782 2143.782
0.020 0.000 2143.782 2143.782
0.010 0.000 2143.782 2143.782
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
IW |
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
SW |
U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
IW ON
X 1.000 1.1054 0.0000 0.1320 0.0111 1.000 1.000
SW ON
X 0.200 0.1053 0.0000 0.0815 0.0090 1.000 0.000
SW WITH
IW 0.000 0.2347 0.0000 0.0940 0.0551 0.000 1.000
Residual Variances
IW 1.000 0.4328 0.0000 0.2789 0.3218 0.000 0.000
SW 0.500 0.1963 0.0000 0.1154 0.0922 0.000 0.000
Between Level
IB |
U1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
SB |
U1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
U2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
U3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
U4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
IB ON
W 0.500 0.3456 0.0000 0.1124 0.0238 1.000 1.000
SB ON
W 0.200 0.3195 0.0000 0.0926 0.0143 1.000 1.000
SB WITH
IB 0.000 -0.1940 0.0000 0.1223 0.0376 1.000 0.000
Intercepts
IB 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SB 0.500 0.3516 0.0000 0.0932 0.0220 1.000 1.000
Thresholds
U1$1 0.000 -0.1330 0.0000 0.1292 0.0177 1.000 0.000
U2$1 0.000 -0.1330 0.0000 0.1292 0.0177 1.000 0.000
U3$1 0.000 -0.1330 0.0000 0.1292 0.0177 1.000 0.000
U4$1 0.000 -0.1330 0.0000 0.1292 0.0177 1.000 0.000
Residual Variances
IB 0.500 0.5119 0.0000 0.2311 0.0001 1.000 1.000
SB 0.300 0.3171 0.0000 0.1198 0.0003 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.122E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0 0 0 0
NU
U1 U2 U3 U4 X
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IW SW X
________ ________ ________
U1 0 0 0
U2 0 0 0
U3 0 0 0
U4 0 0 0
X 0 0 0
THETA
U1 U2 U3 U4 X
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
X 0 0 0 0 0
ALPHA
IW SW X
________ ________ ________
0 0 0
BETA
IW SW X
________ ________ ________
IW 0 0 1
SW 0 0 2
X 0 0 0
PSI
IW SW X
________ ________ ________
IW 3
SW 4 5
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
12 12 12 12
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB SB W
________ ________ ________
U1 0 0 0
U2 0 0 0
U3 0 0 0
U4 0 0 0
W 0 0 0
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
W 0 0 0 0 0
ALPHA
IB SB W
________ ________ ________
0 6 0
BETA
IB SB W
________ ________ ________
IB 0 0 7
SB 0 0 8
W 0 0 0
PSI
IB SB W
________ ________ ________
IB 9
SB 10 11
W 0 0 0
STARTING VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IW SW X
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 1.000 0.000
U3 1.000 2.000 0.000
U4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
X 0.000 0.000 0.000 0.000 0.000
ALPHA
IW SW X
________ ________ ________
0.000 0.000 0.000
BETA
IW SW X
________ ________ ________
IW 0.000 0.000 1.000
SW 0.000 0.000 0.200
X 0.000 0.000 0.000
PSI
IW SW X
________ ________ ________
IW 1.000
SW 0.000 0.500
X 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB W
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 1.000 0.000
U3 1.000 2.000 0.000
U4 1.000 3.000 0.000
W 0.000 0.000 1.000
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB W
________ ________ ________
0.000 0.500 0.000
BETA
IB SB W
________ ________ ________
IB 0.000 0.000 0.500
SB 0.000 0.000 0.200
W 0.000 0.000 0.000
PSI
IB SB W
________ ________ ________
IB 0.500
SB 0.000 0.300
W 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IW SW X
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 1.000 0.000
U3 1.000 2.000 0.000
U4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
ALPHA
IW SW X
________ ________ ________
0.000 0.000 0.000
BETA
IW SW X
________ ________ ________
IW 0.000 0.000 1.000
SW 0.000 0.000 0.200
X 0.000 0.000 0.000
PSI
IW SW X
________ ________ ________
IW 1.000
SW 0.000 0.500
X 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB W
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 1.000 0.000
U3 1.000 2.000 0.000
U4 1.000 3.000 0.000
W 0.000 0.000 1.000
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB W
________ ________ ________
0.000 0.500 0.000
BETA
IB SB W
________ ________ ________
IB 0.000 0.000 0.500
SB 0.000 0.000 0.200
W 0.000 0.000 0.000
PSI
IB SB W
________ ________ ________
IB 0.500
SB 0.000 0.300
W 0.000 0.000 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.10608231D+04 0.0000000 0.0000000 EM
2 -0.10583263D+04 2.4968106 0.0023537 FS
3 -0.10556395D+04 2.6868343 0.0025388 EM
4 -0.10546308D+04 1.0086982 0.0009555 EM
5 -0.10541687D+04 0.4620405 0.0004381 EM
6 -0.10539441D+04 0.2246450 0.0002131 EM
7 -0.10538286D+04 0.1155033 0.0001096 EM
8 -0.10537657D+04 0.0628311 0.0000596 EM
9 -0.10537295D+04 0.0362450 0.0000344 EM
10 -0.10537073D+04 0.0222341 0.0000211 EM
11 -0.10536927D+04 0.0145187 0.0000138 EM
12 -0.10536827D+04 0.0100653 0.0000096 EM
13 -0.10536753D+04 0.0073586 0.0000070 EM
14 -0.10536697D+04 0.0056200 0.0000053 EM
15 -0.10536653D+04 0.0044387 0.0000042 EM
16 -0.10536617D+04 0.0035926 0.0000034 EM
17 -0.10536587D+04 0.0029583 0.0000028 EM
18 -0.10536562D+04 0.0024648 0.0000023 EM
19 -0.10536542D+04 0.0020700 0.0000020 EM
20 -0.10536524D+04 0.0017478 0.0000017 EM
21 -0.10536509D+04 0.0014812 0.0000014 EM
22 -0.10536497D+04 0.0012583 0.0000012 EM
23 -0.10536486D+04 0.0010708 0.0000010 EM
24 -0.10536477D+04 0.0009124 0.0000009 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U1
U2
U3
U4
X
W
CLUSTER
Save file
ex9.13.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:25:45
Ending Time: 22:26:02
Elapsed Time: 00:00:17
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