Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 10:58 PM
INPUT INSTRUCTIONS
TITLE: Tables 7 & 8 internal
CACE estimation with a single continuous outcome with one covariate.
See Mplus manual for details of internal monte carlo simulations.
MONTECARLO:
names are u1 outcome trtment covariat;
nobs = 300;
nrep = 1000;
seed = 1234567;
classes = c(2);
genclasses = c(2);
categorical = u1;
generate = u1(1);
cutpoints = trtment(0.);
missing = u1;
ANALYSIS: type = mixture missing;
MODEL:
%OVERALL%
[outcome*1.5];
outcome ON trtment covariat;
outcome*1;
c#1 ON covariat*0;
[c#1*0];
%c#1%
[u1$1@15];
[outcome*1.5];
outcome ON trtment@0 covariat*0.0;
outcome*1.0;
%c#2%
[u1$1@-15];
outcome ON trtment*-0.5 covariat*0.0;
outcome*1.0;
MODEL MONTECARLO:
%OVERALL%
[trtment@0];
trtment@1;
[covariat@0];
covariat@1;
outcome ON trtment*0 ;
c#1 ON covariat*0;
[c#1*0];
%c#1%
[u1$1@15];
[outcome*1.5];
outcome ON trtment@0 covariat*0.0;
outcome*1.0;
%c#2%
[u1$1@-15];
[outcome*1.5];
outcome ON trtment*-0.5 covariat*0.0;
outcome*1.0;
MODEL MISSING:
%OVERALL%
[u1@15];
u1 ON trtment@-30;
*** WARNING in ANALYSIS command
Starting with Version 5, TYPE=MISSING is the default for all analyses.
To obtain listwise deletion, use LISTWISE=ON in the DATA command.
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
Tables 7 & 8 internal
CACE estimation with a single continuous outcome with one covariate.
See Mplus manual for details of internal monte carlo simulations.
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 300
Number of replications
Requested 1000
Completed 1000
Value of seed 1234567
Number of dependent variables 2
Number of independent variables 2
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Continuous
OUTCOME
Binary and ordered categorical (ordinal)
U1
Observed independent variables
TRTMENT COVARIAT
Categorical latent variables
C
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-06
Relative loglikelihood change 0.100D-06
Derivative 0.100D-05
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-05
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-05
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
Link LOGIT
SUMMARY OF DATA FOR THE FIRST REPLICATION
Number of missing data patterns 2
Number of y missing data patterns 1
Number of u missing data patterns 2
SUMMARY OF MISSING DATA PATTERNS FOR THE FIRST REPLICATION
MISSING DATA PATTERNS (x = not missing)
1 2
U1 x
OUTCOME x x
TRTMENT x x
COVARIAT x x
MISSING DATA PATTERN FREQUENCIES
Pattern Frequency Pattern Frequency
1 145 2 155
MISSING DATA PATTERNS FOR U (x = not missing)
1 2
U1 x
MISSING DATA PATTERN FREQUENCIES FOR U
Pattern Frequency Pattern Frequency
1 145 2 155
MISSING DATA PATTERNS FOR Y (x = not missing)
1
OUTCOME x
TRTMENT x
COVARIAT x
MISSING DATA PATTERN FREQUENCIES FOR Y
Pattern Frequency
1 300
COVARIANCE COVERAGE OF DATA FOR THE FIRST REPLICATION
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
U1 OUTCOME TRTMENT COVARIAT
________ ________ ________ ________
U1 0.517
OUTCOME 0.517 1.000
TRTMENT 0.517 1.000 1.000
COVARIAT 0.517 1.000 1.000 1.000
PROPORTION OF DATA PRESENT FOR U
Covariance Coverage
U1
________
U1 0.517
PROPORTION OF DATA PRESENT FOR Y
Covariance Coverage
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000
TRTMENT 1.000 1.000
COVARIAT 1.000 1.000 1.000
SAMPLE STATISTICS FOR THE FIRST REPLICATION
ESTIMATED SAMPLE STATISTICS
Means
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 1.259 0.517 -0.028
Covariances
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.012
TRTMENT -0.039 0.250
COVARIAT -0.022 -0.013 0.931
Correlations
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000
TRTMENT -0.078 1.000
COVARIAT -0.023 -0.027 1.000
MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -1058.917
TESTS OF MODEL FIT
Number of Free Parameters 9
Loglikelihood
H0 Value
Mean -524.287
Std Dev 14.191
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 -557.299 -558.227
0.980 0.981 -553.430 -552.888
0.950 0.959 -547.629 -546.449
0.900 0.905 -542.474 -542.088
0.800 0.798 -536.230 -536.357
0.700 0.685 -531.728 -532.522
0.500 0.507 -524.287 -524.119
0.300 0.293 -516.845 -517.031
0.200 0.188 -512.344 -513.040
0.100 0.100 -506.100 -506.197
0.050 0.051 -500.945 -500.861
0.020 0.023 -495.143 -494.485
0.010 0.015 -491.275 -489.250
Information Criteria
Akaike (AIC)
Mean 1066.574
Std Dev 28.381
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.985 1000.550 995.726
0.980 0.977 1008.287 1006.219
0.950 0.949 1019.889 1019.495
0.900 0.900 1030.200 1029.894
0.800 0.812 1042.688 1043.765
0.700 0.707 1051.690 1052.014
0.500 0.493 1066.574 1066.238
0.300 0.315 1081.457 1083.031
0.200 0.202 1090.459 1090.496
0.100 0.095 1102.947 1101.953
0.050 0.041 1113.258 1110.441
0.020 0.019 1124.860 1123.702
0.010 0.010 1132.597 1131.908
Bayesian (BIC)
Mean 1099.908
Std Dev 28.381
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.985 1033.884 1029.060
0.980 0.977 1041.621 1039.553
0.950 0.949 1053.223 1052.829
0.900 0.900 1063.534 1063.228
0.800 0.812 1076.022 1077.099
0.700 0.707 1085.025 1085.348
0.500 0.493 1099.908 1099.572
0.300 0.315 1114.791 1116.365
0.200 0.202 1123.793 1123.830
0.100 0.095 1136.281 1135.287
0.050 0.041 1146.592 1143.775
0.020 0.019 1158.194 1157.036
0.010 0.010 1165.931 1165.242
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1071.365
Std Dev 28.381
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.985 1005.342 1000.517
0.980 0.977 1013.078 1011.010
0.950 0.949 1024.681 1024.286
0.900 0.900 1034.991 1034.686
0.800 0.812 1047.479 1048.556
0.700 0.707 1056.482 1056.805
0.500 0.493 1071.365 1071.029
0.300 0.315 1086.248 1087.822
0.200 0.202 1095.251 1095.287
0.100 0.095 1107.739 1106.744
0.050 0.041 1118.049 1115.233
0.020 0.019 1129.652 1128.494
0.010 0.010 1137.388 1136.700
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Mean 0.011
Std Dev 0.024
Degrees of freedom 0
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.996 0.000 0.000
0.980 0.996 0.000 0.000
0.950 0.996 0.000 0.000
0.900 0.996 0.000 0.000
0.800 0.996 0.000 0.000
0.700 0.996 0.000 0.001
0.500 0.996 0.000 0.003
0.300 0.996 0.000 0.009
0.200 0.996 0.000 0.016
0.100 0.996 0.000 0.032
0.050 0.996 0.000 0.050
0.020 0.996 0.000 0.088
0.010 0.996 0.000 0.101
Likelihood Ratio Chi-Square
Mean 0.011
Std Dev 0.024
Degrees of freedom 0
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.996 0.000 0.000
0.980 0.996 0.000 0.000
0.950 0.996 0.000 0.000
0.900 0.996 0.000 0.000
0.800 0.996 0.000 0.000
0.700 0.996 0.000 0.001
0.500 0.996 0.000 0.003
0.300 0.996 0.000 0.009
0.200 0.996 0.000 0.016
0.100 0.996 0.000 0.032
0.050 0.996 0.000 0.050
0.020 0.996 0.000 0.088
0.010 0.996 0.000 0.101
Chi-Square Test for MCAR under the Unrestricted Latent Class Indicator Model
Pearson Chi-Square for MCAR
Mean 0.000
Std Dev 0.000
Degrees of freedom 0
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 0.000 0.000
0.980 0.000 0.000 0.000
0.950 0.000 0.000 0.000
0.900 0.000 0.000 0.000
0.800 0.000 0.000 0.000
0.700 0.000 0.000 0.000
0.500 0.000 0.000 0.000
0.300 0.000 0.000 0.000
0.200 0.000 0.000 0.000
0.100 0.000 0.000 0.000
0.050 0.000 0.000 0.000
0.020 0.000 0.000 0.000
0.010 0.000 0.000 0.000
Likelihood Ratio Chi-Square
Mean 0.000
Std Dev 0.000
Degrees of freedom 0
Number of successful computations 1000
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 0.000 0.000
0.980 0.000 0.000 0.000
0.950 0.000 0.000 0.000
0.900 0.000 0.000 0.000
0.800 0.000 0.000 0.000
0.700 0.000 0.000 0.000
0.500 0.000 0.000 0.000
0.300 0.000 0.000 0.000
0.200 0.000 0.000 0.000
0.100 0.000 0.000 0.000
0.050 0.000 0.000 0.000
0.020 0.000 0.000 0.000
0.010 0.000 0.000 0.000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 150.45440 0.50151
2 149.54560 0.49849
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 150.45442 0.50151
2 149.54558 0.49849
CLASSIFICATION QUALITY
Entropy 0.465
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 150 0.49957
2 150 0.50043
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.803 0.197
2 0.200 0.800
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
OUTCOME ON
TRTMENT 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
COVARIAT 0.000 -0.0055 0.1015 0.1014 0.0103 0.939 0.061
Intercepts
OUTCOME 1.500 1.4928 0.1151 0.1194 0.0133 0.921 0.999
Thresholds
U1$1 15.000 15.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
OUTCOME 1.000 0.9627 0.1441 0.1371 0.0221 0.888 0.998
Latent Class 2
OUTCOME ON
TRTMENT -0.500 -0.4971 0.2441 0.2454 0.0595 0.941 0.541
COVARIAT 0.000 0.0002 0.1011 0.1030 0.0102 0.949 0.051
Intercepts
OUTCOME 1.500 1.4999 0.2149 0.2150 0.0461 0.926 0.997
Thresholds
U1$1 -15.000 -15.0000 0.0000 0.0000 0.0000 1.000 0.000
Residual Variances
OUTCOME 1.000 0.9641 0.1377 0.1410 0.0202 0.910 0.997
Categorical Latent Variables
C#1 ON
COVARIAT 0.000 0.0091 0.1712 0.1705 0.0294 0.952 0.048
Intercepts
C#1 0.000 0.0062 0.1667 0.1658 0.0278 0.943 0.057
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.389E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 0 0 0
LAMBDA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0 0 0
TRTMENT 0 0 0
COVARIAT 0 0 0
THETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0
TRTMENT 0 0
COVARIAT 0 0 0
ALPHA
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 1 0 0
BETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0 0 2
TRTMENT 0 0 0
COVARIAT 0 0 0
PSI
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 3
TRTMENT 0 0
COVARIAT 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 0 0 0
LAMBDA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0 0 0
TRTMENT 0 0 0
COVARIAT 0 0 0
THETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0
TRTMENT 0 0
COVARIAT 0 0 0
ALPHA
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 4 0 0
BETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0 5 6
TRTMENT 0 0 0
COVARIAT 0 0 0
PSI
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 7
TRTMENT 0 0
COVARIAT 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1
________
1 0
TAU(U) FOR LATENT CLASS 2
U1$1
________
1 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 8 0
GAMMA(C)
TRTMENT COVARIAT
________ ________
C#1 0 9
C#2 0 0
STARTING VALUES FOR LATENT CLASS 1
NU
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000 0.000 0.000
TRTMENT 0.000 1.000 0.000
COVARIAT 0.000 0.000 1.000
THETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000
TRTMENT 0.000 0.000
COVARIAT 0.000 0.000 0.000
ALPHA
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 1.500 0.000 0.000
BETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000 0.000 0.000
TRTMENT 0.000 0.000 0.000
COVARIAT 0.000 0.000 0.000
PSI
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000
TRTMENT 0.000 0.500
COVARIAT 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000 0.000 0.000
TRTMENT 0.000 1.000 0.000
COVARIAT 0.000 0.000 1.000
THETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000
TRTMENT 0.000 0.000
COVARIAT 0.000 0.000 0.000
ALPHA
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 1.500 0.000 0.000
BETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000 -0.500 0.000
TRTMENT 0.000 0.000 0.000
COVARIAT 0.000 0.000 0.000
PSI
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000
TRTMENT 0.000 0.500
COVARIAT 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1
________
1 15.000
TAU(U) FOR LATENT CLASS 2
U1$1
________
1 -15.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0.000 0.000
GAMMA(C)
TRTMENT COVARIAT
________ ________
C#1 0.000 0.000
C#2 0.000 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000 0.000 0.000
TRTMENT 0.000 1.000 0.000
COVARIAT 0.000 0.000 1.000
THETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000
TRTMENT 0.000 0.000
COVARIAT 0.000 0.000 0.000
ALPHA
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 1.500 0.000 0.000
BETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000 0.000 0.000
TRTMENT 0.000 0.000 0.000
COVARIAT 0.000 0.000 0.000
PSI
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000
TRTMENT 0.000 1.000
COVARIAT 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000 0.000 0.000
TRTMENT 0.000 1.000 0.000
COVARIAT 0.000 0.000 1.000
THETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000
TRTMENT 0.000 0.000
COVARIAT 0.000 0.000 0.000
ALPHA
OUTCOME TRTMENT COVARIAT
________ ________ ________
1 1.500 0.000 0.000
BETA
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 0.000 -0.500 0.000
TRTMENT 0.000 0.000 0.000
COVARIAT 0.000 0.000 0.000
PSI
OUTCOME TRTMENT COVARIAT
________ ________ ________
OUTCOME 1.000
TRTMENT 0.000 1.000
COVARIAT 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U1$1
________
1 15.000
TAU(U) FOR LATENT CLASS 2
U1$1
________
1 -15.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0.000 0.000
GAMMA(C)
TRTMENT COVARIAT
________ ________
C#1 0.000 0.000
C#2 0.000 0.000
Beginning Time: 22:58:28
Ending Time: 22:59:00
Elapsed Time: 00:00:32
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