Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:05 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level multiple
indicator growth model with categorical
outcomes using multiple imputation data
DATA: FILE = ex11.8implist.dat;
TYPE = IMPUTATION;
SWMATRIX = ex11.8swlist.dat;
VARIABLE: NAMES are u11 u21 u31 u12 u22 u32 u13 u23 u33 clus;
CATEGORICAL = u11-u33;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL;
ESTIMATOR = WLSMV;
PROCESSORS = 2;
MODEL: %WITHIN%
f1w BY u11
u21 (1)
u31 (2);
f2w BY u12
u22 (1)
u32 (2);
f3w BY u13
u23 (1)
u33 (2);
iw sw | f1w@0 f2w@1 f3w@2;
%BETWEEN%
f1b BY u11
u21 (1)
u31 (2);
f2b BY u12
u22 (1)
u32 (2);
f3b BY u13
u23 (1)
u33 (2);
[u11$1 u12$1 u13$1] (3);
[u21$1 u22$1 u23$1] (4);
[u31$1 u32$1 u33$1] (5);
u11-u33;
ib sb | f1b@0 f2b@1 f3b@2;
[f1b-f3b@0 ib@0 sb];
f1b-f3b (6);
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level multiple
indicator growth model with categorical
outcomes using multiple imputation data
SUMMARY OF ANALYSIS
Number of groups 1
Average number of observations 1000
Number of replications
Requested 5
Completed 5
Number of dependent variables 9
Number of independent variables 0
Number of continuous latent variables 10
Observed dependent variables
Binary and ordered categorical (ordinal)
U11 U21 U31 U12 U22 U32
U13 U23 U33
Continuous latent variables
F1W F2W F3W IW SW F1B
F2B F3B IB SB
Variables with special functions
Cluster variable CLUS
Estimator WLSMV
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 1000
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 10
Minimum value for logit thresholds -10
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm FS
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 0
Adaptive quadrature ON
Link PROBIT
Cholesky ON
Input data file(s)
Multiple data files from
ex11.8implist.dat
Input data format FREE
SUMMARY OF DATA FOR THE FIRST DATA SET
Number of clusters 20
Average cluster size 50.000
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
U11 0.292 U21 0.344 U31 0.318
U12 0.426 U22 0.437 U32 0.335
U13 0.318 U23 0.219 U33 0.224
UNIVARIATE PROPORTIONS FOR CATEGORICAL VARIABLES
NOTE: These are average results over 5 data sets.
U11
Category 1 0.511
Category 2 0.489
U21
Category 1 0.460
Category 2 0.540
U31
Category 1 0.602
Category 2 0.398
U12
Category 1 0.292
Category 2 0.708
U22
Category 1 0.221
Category 2 0.779
U32
Category 1 0.365
Category 2 0.635
U13
Category 1 0.228
Category 2 0.772
U23
Category 1 0.156
Category 2 0.844
U33
Category 1 0.317
Category 2 0.683
SAMPLE STATISTICS
NOTE: These are average results over 5 data sets.
ESTIMATED SAMPLE STATISTICS
MEANS/INTERCEPTS/THRESHOLDS
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
0.031 -0.148 0.329 -0.725 -1.035
MEANS/INTERCEPTS/THRESHOLDS
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
-0.416 -0.887 -1.139 -0.571
WITHIN LEVEL VARIANCE/COVARIANCE
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 0.610 1.000
U31 0.487 0.568 1.000
U12 0.346 0.439 0.384 1.000
U22 0.287 0.386 0.303 0.576 1.000
U32 0.297 0.368 0.331 0.619 0.598
U13 0.291 0.307 0.392 0.531 0.574
U23 0.178 0.244 0.245 0.550 0.533
U33 0.248 0.322 0.322 0.477 0.549
WITHIN LEVEL VARIANCE/COVARIANCE
U32 U13 U23 U33
________ ________ ________ ________
U32 1.000
U13 0.574 1.000
U23 0.527 0.751 1.000
U33 0.525 0.746 0.706 1.000
WITHIN LEVEL CORRELATION
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 0.610 1.000
U31 0.487 0.568 1.000
U12 0.346 0.439 0.384 1.000
U22 0.287 0.386 0.303 0.576 1.000
U32 0.297 0.368 0.331 0.619 0.598
U13 0.291 0.307 0.392 0.531 0.574
U23 0.178 0.244 0.245 0.550 0.533
U33 0.248 0.322 0.322 0.477 0.549
WITHIN LEVEL CORRELATION
U32 U13 U23 U33
________ ________ ________ ________
U32 1.000
U13 0.574 1.000
U23 0.527 0.751 1.000
U33 0.525 0.746 0.706 1.000
BETWEEN LEVEL VARIANCE/COVARIANCE
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 0.412
U21 0.226 0.524
U31 0.243 0.051 0.467
U12 0.305 0.311 0.351 0.613
U22 0.271 0.225 0.273 0.423 0.774
U32 0.136 0.095 0.152 0.279 0.221
U13 0.171 0.227 0.147 0.216 0.275
U23 0.176 0.129 0.116 0.156 0.291
U33 0.169 0.150 0.082 0.064 0.230
BETWEEN LEVEL VARIANCE/COVARIANCE
U32 U13 U23 U33
________ ________ ________ ________
U32 0.477
U13 0.017 0.446
U23 0.099 0.258 0.279
U33 0.070 0.266 0.249 0.385
BETWEEN LEVEL CORRELATION
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 0.486 1.000
U31 0.553 0.104 1.000
U12 0.607 0.549 0.656 1.000
U22 0.480 0.353 0.454 0.614 1.000
U32 0.307 0.190 0.322 0.517 0.364
U13 0.399 0.468 0.322 0.413 0.469
U23 0.519 0.337 0.322 0.377 0.625
U33 0.424 0.334 0.194 0.132 0.420
BETWEEN LEVEL CORRELATION
U32 U13 U23 U33
________ ________ ________ ________
U32 1.000
U13 0.036 1.000
U23 0.273 0.731 1.000
U33 0.163 0.643 0.761 1.000
MODEL FIT INFORMATION
Number of Free Parameters 25
Chi-Square Test of Model Fit
Degrees of freedom 65
Mean 57.060
Std Dev 1.635
Number of successful computations 5
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 41.444 55.581
0.980 1.000 43.779 55.581
0.950 1.000 47.450 55.581
0.900 1.000 50.883 55.581
0.800 1.000 55.262 55.581
0.700 0.200 58.573 55.581
0.500 0.000 64.335 55.937
0.300 0.000 70.462 56.544
0.200 0.000 74.351 57.072
0.100 0.000 79.973 57.072
0.050 0.000 84.821 57.072
0.020 0.000 90.501 57.072
0.010 0.000 94.422 57.072
RMSEA (Root Mean Square Error Of Approximation)
Mean 0.000
Std Dev 0.000
Number of successful computations 5
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 1.000
0.010 1.000
CFI/TLI
CFI
Mean 1.000
Std Dev 0.000
Number of successful computations 5
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 1.011
Std Dev 0.002
Number of successful computations 5
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) for the WITHIN level
Mean 0.048
Std Dev 0.005
Number of successful computations 5
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 0.600
0.020 0.000
0.010 0.000
SRMR (Standardized Root Mean Square Residual) for the BETWEEN level
Mean 0.140
Std Dev 0.012
Number of successful computations 5
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 0.000
0.050 0.000
0.020 0.000
0.010 0.000
MODEL RESULTS
Two-Tailed Rate of
Estimate S.E. Est./S.E. P-Value Missing
Within Level
IW |
F1W 1.000 0.000 999.000 999.000 0.000
F2W 1.000 0.000 999.000 999.000 0.000
F3W 1.000 0.000 999.000 999.000 0.000
SW |
F1W 0.000 0.000 999.000 999.000 0.000
F2W 1.000 0.000 999.000 999.000 0.000
F3W 2.000 0.000 999.000 999.000 0.000
F1W BY
U11 1.000 0.000 999.000 999.000 0.000
U21 1.057 0.162 6.522 0.000 0.309
U31 0.912 0.137 6.680 0.000 0.190
F2W BY
U12 1.000 0.000 999.000 999.000 0.000
U22 1.057 0.162 6.522 0.000 0.309
U32 0.912 0.137 6.680 0.000 0.190
F3W BY
U13 1.000 0.000 999.000 999.000 0.000
U23 1.057 0.162 6.522 0.000 0.309
U33 0.912 0.137 6.680 0.000 0.190
SW WITH
IW 0.003 0.162 0.017 0.986 0.467
Variances
IW 0.851 0.315 2.699 0.007 0.284
SW 0.456 0.195 2.340 0.019 0.293
Residual Variances
F1W 0.406 0.263 1.543 0.123 0.362
F2W 0.237 0.297 0.797 0.425 0.194
F3W 0.315 0.457 0.689 0.491 0.526
Between Level
IB |
F1B 1.000 0.000 999.000 999.000 0.000
F2B 1.000 0.000 999.000 999.000 0.000
F3B 1.000 0.000 999.000 999.000 0.000
SB |
F1B 0.000 0.000 999.000 999.000 0.000
F2B 1.000 0.000 999.000 999.000 0.000
F3B 2.000 0.000 999.000 999.000 0.000
F1B BY
U11 1.000 0.000 999.000 999.000 0.000
U21 1.057 0.162 6.522 0.000 0.309
U31 0.912 0.137 6.680 0.000 0.190
F2B BY
U12 1.000 0.000 999.000 999.000 0.000
U22 1.057 0.162 6.522 0.000 0.309
U32 0.912 0.137 6.680 0.000 0.190
F3B BY
U13 1.000 0.000 999.000 999.000 0.000
U23 1.057 0.162 6.522 0.000 0.309
U33 0.912 0.137 6.680 0.000 0.190
SB WITH
IB 0.099 0.132 0.752 0.452 0.043
Means
IB 0.000 0.000 999.000 999.000 0.000
SB 0.942 0.151 6.253 0.000 0.074
Intercepts
F1B 0.000 0.000 999.000 999.000 0.000
F2B 0.000 0.000 999.000 999.000 0.000
F3B 0.000 0.000 999.000 999.000 0.000
Thresholds
U11$1 0.024 0.237 0.102 0.919 0.001
U21$1 -0.407 0.227 -1.791 0.073 0.006
U31$1 0.428 0.201 2.127 0.033 0.037
U12$1 0.024 0.237 0.102 0.919 0.001
U22$1 -0.407 0.227 -1.791 0.073 0.006
U32$1 0.428 0.201 2.127 0.033 0.037
U13$1 0.024 0.237 0.102 0.919 0.001
U23$1 -0.407 0.227 -1.791 0.073 0.006
U33$1 0.428 0.201 2.127 0.033 0.037
Variances
IB 0.239 0.227 1.051 0.293 0.073
SB -0.038 0.109 -0.352 0.725 0.063
Residual Variances
U11 0.455 0.345 1.320 0.187 0.001
U21 0.731 0.603 1.211 0.226 0.003
U31 0.561 0.317 1.769 0.077 0.001
U12 0.918 0.841 1.092 0.275 0.052
U22 1.400 0.903 1.550 0.121 0.051
U32 0.560 0.358 1.564 0.118 0.014
U13 1.062 0.514 2.065 0.039 0.108
U23 0.417 0.370 1.126 0.260 0.085
U33 0.766 0.555 1.381 0.167 0.261
F1B 0.236 0.212 1.111 0.266 0.020
F2B 0.236 0.212 1.111 0.266 0.020
F3B 0.236 0.212 1.111 0.266 0.020
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.348E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
0 0 0 0 0
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
0 0 0 0
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0 0 0 0 0
NU
U32 U13 U23 U33
________ ________ ________ ________
0 0 0 0
LAMBDA
F1W F2W F3W IW SW
________ ________ ________ ________ ________
U11 0 0 0 0 0
U21 1 0 0 0 0
U31 2 0 0 0 0
U12 0 0 0 0 0
U22 0 1 0 0 0
U32 0 2 0 0 0
U13 0 0 0 0 0
U23 0 0 1 0 0
U33 0 0 2 0 0
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 0
U21 0 0
U31 0 0 0
U12 0 0 0 0
U22 0 0 0 0 0
U32 0 0 0 0 0
U13 0 0 0 0 0
U23 0 0 0 0 0
U33 0 0 0 0 0
THETA
U32 U13 U23 U33
________ ________ ________ ________
U32 0
U13 0 0
U23 0 0 0
U33 0 0 0 0
ALPHA
F1W F2W F3W IW SW
________ ________ ________ ________ ________
0 0 0 0 0
BETA
F1W F2W F3W IW SW
________ ________ ________ ________ ________
F1W 0 0 0 0 0
F2W 0 0 0 0 0
F3W 0 0 0 0 0
IW 0 0 0 0 0
SW 0 0 0 0 0
PSI
F1W F2W F3W IW SW
________ ________ ________ ________ ________
F1W 3
F2W 0 4
F3W 0 0 5
IW 0 0 0 6
SW 0 0 0 7 8
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
23 24 25 23 24
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
25 23 24 25
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0 0 0 0 0
NU
U32 U13 U23 U33
________ ________ ________ ________
0 0 0 0
LAMBDA
F1B F2B F3B IB SB
________ ________ ________ ________ ________
U11 0 0 0 0 0
U21 1 0 0 0 0
U31 2 0 0 0 0
U12 0 0 0 0 0
U22 0 1 0 0 0
U32 0 2 0 0 0
U13 0 0 0 0 0
U23 0 0 1 0 0
U33 0 0 2 0 0
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 9
U21 0 10
U31 0 0 11
U12 0 0 0 12
U22 0 0 0 0 13
U32 0 0 0 0 0
U13 0 0 0 0 0
U23 0 0 0 0 0
U33 0 0 0 0 0
THETA
U32 U13 U23 U33
________ ________ ________ ________
U32 14
U13 0 15
U23 0 0 16
U33 0 0 0 17
ALPHA
F1B F2B F3B IB SB
________ ________ ________ ________ ________
0 0 0 0 18
BETA
F1B F2B F3B IB SB
________ ________ ________ ________ ________
F1B 0 0 0 0 0
F2B 0 0 0 0 0
F3B 0 0 0 0 0
IB 0 0 0 0 0
SB 0 0 0 0 0
PSI
F1B F2B F3B IB SB
________ ________ ________ ________ ________
F1B 19
F2B 0 19
F3B 0 0 19
IB 0 0 0 20
SB 0 0 0 21 22
STARTING VALUES FOR WITHIN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U32 U13 U23 U33
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F1W F2W F3W IW SW
________ ________ ________ ________ ________
U11 1.000 0.000 0.000 0.000 0.000
U21 1.000 0.000 0.000 0.000 0.000
U31 1.000 0.000 0.000 0.000 0.000
U12 0.000 1.000 0.000 0.000 0.000
U22 0.000 1.000 0.000 0.000 0.000
U32 0.000 1.000 0.000 0.000 0.000
U13 0.000 0.000 1.000 0.000 0.000
U23 0.000 0.000 1.000 0.000 0.000
U33 0.000 0.000 1.000 0.000 0.000
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 0.000 1.000
U31 0.000 0.000 1.000
U12 0.000 0.000 0.000 1.000
U22 0.000 0.000 0.000 0.000 1.000
U32 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U33 0.000 0.000 0.000 0.000 0.000
THETA
U32 U13 U23 U33
________ ________ ________ ________
U32 1.000
U13 0.000 1.000
U23 0.000 0.000 1.000
U33 0.000 0.000 0.000 1.000
ALPHA
F1W F2W F3W IW SW
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1W F2W F3W IW SW
________ ________ ________ ________ ________
F1W 0.000 0.000 0.000 1.000 0.000
F2W 0.000 0.000 0.000 1.000 1.000
F3W 0.000 0.000 0.000 1.000 2.000
IW 0.000 0.000 0.000 0.000 0.000
SW 0.000 0.000 0.000 0.000 0.000
PSI
F1W F2W F3W IW SW
________ ________ ________ ________ ________
F1W 0.050
F2W 0.000 0.050
F3W 0.000 0.000 0.050
IW 0.000 0.000 0.000 0.050
SW 0.000 0.000 0.000 0.000 0.050
STARTING VALUES FOR BETWEEN
TAU
U11$1 U21$1 U31$1 U12$1 U22$1
________ ________ ________ ________ ________
-0.377 -0.567 -0.164 -0.377 -0.567
TAU
U32$1 U13$1 U23$1 U33$1
________ ________ ________ ________
-0.164 -0.377 -0.567 -0.164
NU
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
U32 U13 U23 U33
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
F1B F2B F3B IB SB
________ ________ ________ ________ ________
U11 1.000 0.000 0.000 0.000 0.000
U21 1.000 0.000 0.000 0.000 0.000
U31 1.000 0.000 0.000 0.000 0.000
U12 0.000 1.000 0.000 0.000 0.000
U22 0.000 1.000 0.000 0.000 0.000
U32 0.000 1.000 0.000 0.000 0.000
U13 0.000 0.000 1.000 0.000 0.000
U23 0.000 0.000 1.000 0.000 0.000
U33 0.000 0.000 1.000 0.000 0.000
THETA
U11 U21 U31 U12 U22
________ ________ ________ ________ ________
U11 1.000
U21 0.000 1.000
U31 0.000 0.000 1.000
U12 0.000 0.000 0.000 1.000
U22 0.000 0.000 0.000 0.000 1.000
U32 0.000 0.000 0.000 0.000 0.000
U13 0.000 0.000 0.000 0.000 0.000
U23 0.000 0.000 0.000 0.000 0.000
U33 0.000 0.000 0.000 0.000 0.000
THETA
U32 U13 U23 U33
________ ________ ________ ________
U32 1.000
U13 0.000 1.000
U23 0.000 0.000 1.000
U33 0.000 0.000 0.000 1.000
ALPHA
F1B F2B F3B IB SB
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1B F2B F3B IB SB
________ ________ ________ ________ ________
F1B 0.000 0.000 0.000 1.000 0.000
F2B 0.000 0.000 0.000 1.000 1.000
F3B 0.000 0.000 0.000 1.000 2.000
IB 0.000 0.000 0.000 0.000 0.000
SB 0.000 0.000 0.000 0.000 0.000
PSI
F1B F2B F3B IB SB
________ ________ ________ ________ ________
F1B 0.050
F2B 0.000 0.050
F3B 0.000 0.000 0.050
IB 0.000 0.000 0.000 0.050
SB 0.000 0.000 0.000 0.000 0.050
TECHNICAL 8 OUTPUT
Beginning Time: 23:05:57
Ending Time: 23:05:59
Elapsed Time: 00:00:02
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