Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:24 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-part analysis
MONTECARLO: NAMES = u1-u4 y1-y4;
GENERATE = u1-u4(1);
CATEGORICAL = u1-u4;
MISSING = y1-y4;
NOBSERVATIONS = 500;
NREPS = 1;
! SAVE = intermediate.dat;
MODEL POPULATION:
! u part
iu su | u1@0 u2@1 u3@2 u4@3;
[u1$1-u4$1*-.5] (1);
[iu@0 su*.85];
iu*1.45;
! y part
iy sy | y1@0 y2@1 y3@2 y4@3;
[y1-y4@0];
y1-y4*.5;
[iy*.5 sy*1];
iy*1;
sy*.2;
iy WITH sy*.1;
iu WITH iy*0.9; ! corr = 0.75
MODEL MISSING:
[y1-y4@15]; ! Low logit intercepts give P(y missing) = 1 for u = 0
y1 ON u1@-30; ! if u1=1, P(y1 missing) = 0
y2 ON u2@-30; ! if u2=1, P(y2 missing) = 0
y3 ON u3@-30; ! if u3=1, P(y3 missing) = 0
y4 ON u4@-30; ! if u4=1, P(y4 missing) = 0
ANALYSIS:
ESTIMATOR = MLR;
MODEL:
! u part
iu su | u1@0 u2@1 u3@2 u4@3;
[u1$1-u4$1*-.5] (1);
[iu@0 su*.85];
iu*1.45;
su@0;
! y part
iy sy | y1@0 y2@1 y3@2 y4@3;
[y1-y4@0];
y1-y4*.5;
[iy*.5 sy*1];
iy*1;
sy*.2;
iy WITH sy*.1;
iu WITH iy*0.9; ! corr = 0.75
iu WITH sy@0;
OUTPUT:
TECH8;
*** WARNING in MODEL command
All continuous latent variable covariances involving SU have been fixed to 0
because the variance of SU is fixed at 0.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a two-part analysis
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 8
Number of independent variables 0
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Continuous latent variables
IU SU IY SY
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
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 1
Adaptive quadrature ON
Link LOGIT
Cholesky OFF
SUMMARY OF DATA FOR THE FIRST REPLICATION
Number of missing data patterns 16
Number of y missing data patterns 16
Number of u missing data patterns 1
SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION
MISSING DATA PATTERNS FOR Y (x = not missing)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Y1 x x x x x x x x
Y2 x x x x x x x x
Y3 x x x x x x x x
Y4 x x x x x x x x
MISSING DATA PATTERN FREQUENCIES FOR Y
Pattern Frequency Pattern Frequency Pattern Frequency
1 229 7 42 13 7
2 38 8 8 14 6
3 16 9 2 15 1
4 13 10 14 16 1
5 95 11 9
6 17 12 2
COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT FOR Y
Covariance Coverage
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 0.608
Y2 0.502 0.756
Y3 0.560 0.688 0.870
Y4 0.586 0.710 0.808 0.918
SAMPLE STATISTICS FOR THE FIRST REPLICATION
ESTIMATED SAMPLE STATISTICS
Means
Y1 Y2 Y3 Y4
________ ________ ________ ________
0.735 1.597 2.544 3.624
Covariances
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.282
Y2 1.033 1.934
Y3 0.994 1.725 2.606
Y4 1.083 2.061 2.676 3.893
Correlations
Y1 Y2 Y3 Y4
________ ________ ________ ________
Y1 1.000
Y2 0.656 1.000
Y3 0.544 0.769 1.000
Y4 0.485 0.751 0.840 1.000
MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -2408.279
MODEL FIT INFORMATION
Number of Free Parameters 13
Loglikelihood
H0 Value
Mean -3307.256
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -3307.256 -3307.256
0.980 0.000 -3307.256 -3307.256
0.950 0.000 -3307.256 -3307.256
0.900 0.000 -3307.256 -3307.256
0.800 0.000 -3307.256 -3307.256
0.700 0.000 -3307.256 -3307.256
0.500 0.000 -3307.256 -3307.256
0.300 0.000 -3307.256 -3307.256
0.200 0.000 -3307.256 -3307.256
0.100 0.000 -3307.256 -3307.256
0.050 0.000 -3307.256 -3307.256
0.020 0.000 -3307.256 -3307.256
0.010 0.000 -3307.256 -3307.256
Information Criteria
Akaike (AIC)
Mean 6640.511
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6640.511 6640.511
0.980 0.000 6640.511 6640.511
0.950 0.000 6640.511 6640.511
0.900 0.000 6640.511 6640.511
0.800 0.000 6640.511 6640.511
0.700 0.000 6640.511 6640.511
0.500 0.000 6640.511 6640.511
0.300 0.000 6640.511 6640.511
0.200 0.000 6640.511 6640.511
0.100 0.000 6640.511 6640.511
0.050 0.000 6640.511 6640.511
0.020 0.000 6640.511 6640.511
0.010 0.000 6640.511 6640.511
Bayesian (BIC)
Mean 6695.301
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6695.301 6695.301
0.980 0.000 6695.301 6695.301
0.950 0.000 6695.301 6695.301
0.900 0.000 6695.301 6695.301
0.800 0.000 6695.301 6695.301
0.700 0.000 6695.301 6695.301
0.500 0.000 6695.301 6695.301
0.300 0.000 6695.301 6695.301
0.200 0.000 6695.301 6695.301
0.100 0.000 6695.301 6695.301
0.050 0.000 6695.301 6695.301
0.020 0.000 6695.301 6695.301
0.010 0.000 6695.301 6695.301
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 6654.038
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 6654.038 6654.038
0.980 0.000 6654.038 6654.038
0.950 0.000 6654.038 6654.038
0.900 0.000 6654.038 6654.038
0.800 0.000 6654.038 6654.038
0.700 0.000 6654.038 6654.038
0.500 0.000 6654.038 6654.038
0.300 0.000 6654.038 6654.038
0.200 0.000 6654.038 6654.038
0.100 0.000 6654.038 6654.038
0.050 0.000 6654.038 6654.038
0.020 0.000 6654.038 6654.038
0.010 0.000 6654.038 6654.038
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 6.569
Std Dev 0.000
Degrees of freedom 12
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 3.571 6.569
0.980 1.000 4.178 6.569
0.950 1.000 5.226 6.569
0.900 1.000 6.304 6.569
0.800 0.000 7.807 6.569
0.700 0.000 9.034 6.569
0.500 0.000 11.340 6.569
0.300 0.000 14.011 6.569
0.200 0.000 15.812 6.569
0.100 0.000 18.549 6.569
0.050 0.000 21.026 6.569
0.020 0.000 24.054 6.569
0.010 0.000 26.217 6.569
Likelihood Ratio Chi-Square
Mean 5.938
Std Dev 0.000
Degrees of freedom 12
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 1.000 3.571 5.938
0.980 1.000 4.178 5.938
0.950 1.000 5.226 5.938
0.900 0.000 6.304 5.938
0.800 0.000 7.807 5.938
0.700 0.000 9.034 5.938
0.500 0.000 11.340 5.938
0.300 0.000 14.011 5.938
0.200 0.000 15.812 5.938
0.100 0.000 18.549 5.938
0.050 0.000 21.026 5.938
0.020 0.000 24.054 5.938
0.010 0.000 26.217 5.938
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
IU |
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
SU |
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
IY |
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
SY |
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 2.000 2.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 3.000 3.0000 0.0000 0.0000 0.0000 1.000 0.000
IY WITH
SY 0.100 0.0719 0.0000 0.0364 0.0008 1.000 1.000
IU 0.900 0.8031 0.0000 0.1313 0.0094 1.000 1.000
IU WITH
SY 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
IU 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
SU 0.850 0.8527 0.0000 0.0660 0.0000 1.000 1.000
IY 0.500 0.5545 0.0000 0.0601 0.0030 1.000 1.000
SY 1.000 1.0073 0.0000 0.0282 0.0001 1.000 1.000
Intercepts
Y1 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Thresholds
U1$1 -0.500 -0.6113 0.0000 0.1122 0.0124 1.000 1.000
U2$1 -0.500 -0.6113 0.0000 0.1122 0.0124 1.000 1.000
U3$1 -0.500 -0.6113 0.0000 0.1122 0.0124 1.000 1.000
U4$1 -0.500 -0.6113 0.0000 0.1122 0.0124 1.000 1.000
Variances
IU 1.450 1.6813 0.0000 0.3317 0.0535 1.000 1.000
SU 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
IY 1.000 1.0151 0.0000 0.1004 0.0002 1.000 1.000
SY 0.200 0.2289 0.0000 0.0252 0.0008 1.000 1.000
Residual Variances
Y1 0.500 0.3937 0.0000 0.0739 0.0113 1.000 1.000
Y2 0.500 0.4525 0.0000 0.0504 0.0023 1.000 1.000
Y3 0.500 0.4927 0.0000 0.0548 0.0001 1.000 1.000
Y4 0.500 0.4316 0.0000 0.0941 0.0047 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.371E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
13 13 13 13
NU
U1 U2 U3 U4 Y1
________ ________ ________ ________ ________
0 0 0 0 0
NU
Y2 Y3 Y4
________ ________ ________
0 0 0
LAMBDA
IU SU IY SY
________ ________ ________ ________
U1 0 0 0 0
U2 0 0 0 0
U3 0 0 0 0
U4 0 0 0 0
Y1 0 0 0 0
Y2 0 0 0 0
Y3 0 0 0 0
Y4 0 0 0 0
THETA
U1 U2 U3 U4 Y1
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
Y1 0 0 0 0 1
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
THETA
Y2 Y3 Y4
________ ________ ________
Y2 2
Y3 0 3
Y4 0 0 4
ALPHA
IU SU IY SY
________ ________ ________ ________
0 5 6 7
BETA
IU SU IY SY
________ ________ ________ ________
IU 0 0 0 0
SU 0 0 0 0
IY 0 0 0 0
SY 0 0 0 0
PSI
IU SU IY SY
________ ________ ________ ________
IU 8
SU 0 0
IY 9 0 10
SY 0 0 11 12
STARTING VALUES
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-0.500 -0.500 -0.500 -0.500
NU
U1 U2 U3 U4 Y1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y2 Y3 Y4
________ ________ ________
0.000 0.000 0.000
LAMBDA
IU SU IY SY
________ ________ ________ ________
U1 1.000 0.000 0.000 0.000
U2 1.000 1.000 0.000 0.000
U3 1.000 2.000 0.000 0.000
U4 1.000 3.000 0.000 0.000
Y1 0.000 0.000 1.000 0.000
Y2 0.000 0.000 1.000 1.000
Y3 0.000 0.000 1.000 2.000
Y4 0.000 0.000 1.000 3.000
THETA
U1 U2 U3 U4 Y1
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
Y1 0.000 0.000 0.000 0.000 0.500
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
THETA
Y2 Y3 Y4
________ ________ ________
Y2 0.500
Y3 0.000 0.500
Y4 0.000 0.000 0.500
ALPHA
IU SU IY SY
________ ________ ________ ________
0.000 0.850 0.500 1.000
BETA
IU SU IY SY
________ ________ ________ ________
IU 0.000 0.000 0.000 0.000
SU 0.000 0.000 0.000 0.000
IY 0.000 0.000 0.000 0.000
SY 0.000 0.000 0.000 0.000
PSI
IU SU IY SY
________ ________ ________ ________
IU 1.450
SU 0.000 0.000
IY 0.900 0.000 1.000
SY 0.000 0.000 0.100 0.200
POPULATION VALUES
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-0.500 -0.500 -0.500 -0.500
NU
U1 U2 U3 U4 Y1
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
Y2 Y3 Y4
________ ________ ________
0.000 0.000 0.000
LAMBDA
IU SU IY SY
________ ________ ________ ________
U1 1.000 0.000 0.000 0.000
U2 1.000 1.000 0.000 0.000
U3 1.000 2.000 0.000 0.000
U4 1.000 3.000 0.000 0.000
Y1 0.000 0.000 1.000 0.000
Y2 0.000 0.000 1.000 1.000
Y3 0.000 0.000 1.000 2.000
Y4 0.000 0.000 1.000 3.000
THETA
U1 U2 U3 U4 Y1
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.500
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
THETA
Y2 Y3 Y4
________ ________ ________
Y2 0.500
Y3 0.000 0.500
Y4 0.000 0.000 0.500
ALPHA
IU SU IY SY
________ ________ ________ ________
0.000 0.850 0.500 1.000
BETA
IU SU IY SY
________ ________ ________ ________
IU 0.000 0.000 0.000 0.000
SU 0.000 0.000 0.000 0.000
IY 0.000 0.000 0.000 0.000
SY 0.000 0.000 0.000 0.000
PSI
IU SU IY SY
________ ________ ________ ________
IU 1.450
SU 0.000 0.000
IY 0.900 0.000 1.000
SY 0.000 0.000 0.100 0.200
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.33107499D+04 0.0000000 0.0000000 EM
2 -0.33081490D+04 2.6008567 0.0007856 EM
3 -0.33079313D+04 0.2176608 0.0000658 EM
4 -0.33078112D+04 0.1201305 0.0000363 EM
5 -0.33077282D+04 0.0830191 0.0000251 EM
6 -0.33076639D+04 0.0643270 0.0000194 EM
7 -0.33076111D+04 0.0528066 0.0000160 EM
8 -0.33075664D+04 0.0446455 0.0000135 EM
9 -0.33075280D+04 0.0383676 0.0000116 EM
10 -0.33074947D+04 0.0333005 0.0000101 EM
11 -0.33074657D+04 0.0290859 0.0000088 EM
12 -0.33074401D+04 0.0255079 0.0000077 EM
13 -0.33074177D+04 0.0224261 0.0000068 EM
14 -0.33073980D+04 0.0197463 0.0000060 EM
15 -0.33073806D+04 0.0173991 0.0000053 EM
16 -0.33073652D+04 0.0153327 0.0000046 EM
17 -0.33073517D+04 0.0135084 0.0000041 EM
18 -0.33073398D+04 0.0118951 0.0000036 EM
19 -0.33073294D+04 0.0104684 0.0000032 EM
20 -0.33073202D+04 0.0092062 0.0000028 EM
21 -0.33073121D+04 0.0080902 0.0000024 EM
22 -0.33073050D+04 0.0071044 0.0000021 EM
23 -0.33072987D+04 0.0062338 0.0000019 EM
24 -0.33072933D+04 0.0054657 0.0000017 EM
25 -0.33072885D+04 0.0047899 0.0000014 EM
26 -0.33072843D+04 0.0041943 0.0000013 EM
27 -0.33072806D+04 0.0036704 0.0000011 EM
28 -0.33072774D+04 0.0032100 0.0000010 EM
29 -0.33072746D+04 0.0028059 0.0000008 EM
30 -0.33072721D+04 0.0024513 0.0000007 EM
31 -0.33072700D+04 0.0021405 0.0000006 EM
32 -0.33072681D+04 0.0018682 0.0000006 EM
33 -0.33072665D+04 0.0016299 0.0000005 EM
34 -0.33072651D+04 0.0014214 0.0000004 EM
35 -0.33072558D+04 0.0092719 0.0000028 FS
36 -0.33072556D+04 0.0002249 0.0000001 FS
Beginning Time: 22:24:16
Ending Time: 22:24:17
Elapsed Time: 00:00:01
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