Mplus VERSION 6
MUTHEN & MUTHEN
04/25/2010 11:28 PM
INPUT INSTRUCTIONS
title: jasac.inp
montecarlo:
names are y1 y2 x;
nobs = 2000;
nreps = 500;
seed = 578243;
classes = c(2);
genclasses = c(2);
cutpoints = x(0);
analysis:
type = mixture;
model montecarlo:
%overall%
[x@0]; x@1;
i by y1-y2@1;
s by y1@0 y2@1;
[y1-y2@0 i*0 s*1];
i*6.25; ! SD = 2.5
s*1;
!total s variance is 1.25 (1/5 of i variance), SD = 1.12
i with s*.699; !this gives correlation 0.25
y1*2.083 y2*0.417; !this gives y1 and y2 r-square 0.75
! y1 variance = 8.333, SD = 2.89
! y2 variance = 9.135, SD = 3.052
! within-group y2 variance = 9.135 - 0.25 = 9.065, SD = 3.01
s on x*1;
!this gives ES = 0.33 in y2 within-group SD terms (for low class)
!r-squared for s is 20%
[c#1*0];
%c#1% ! high class
[i*2.5 s*2.25];
!high class grows at 3/4 SD per grade
s on x*.25;
! high class has 1/4 effect of low class, ES = 0.08
%c#2% !low class
[i*0.0 s*.75];
!low class grows at 1/4 SD per grade
!low class is lower by 1 SD for intercept,
!about 1.5 SD lower for slope
model:
%overall%
i by y1-y2@1;
s by y1@0 y2@1;
[y1-y2@0 i*0 s*1];
i*6.25; ! SD = 2.5
s@0; !misspecified
!total s variance is 1.25 (1/5 of i variance), SD = 1.12
i with s@0; !misspecified
y1*2.083 y2*0.417; !this gives y1 and y2 r-square 0.75
! y1 variance = 8.333, SD = 2.89
! y2 variance = 9.135, SD = 3.052
! within-group y2 variance = 9.135 - 0.25 = 9.065, SD = 3.01
s on x*1;
!this gives ES = 0.33 in y2 within-group SD terms (for low class)
!r-squared for s is 20%
[c#1*0];
%c#1% ! high class
[i*2.5 s*2.25];
!high class grows at 3/4 SD per grade
s on x*.25;
! high class has 1/4 effect of low class, ES = 0.08
%c#2% !low class
[i*0.0 s*.75];
!low class grows at 1/4 SD per grade
!low class is lower by 1 SD for intercept,
!about 1.5 SD lower for slope
output:
tech9;
INPUT READING TERMINATED NORMALLY
jasac.inp
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 2000
Number of replications
Requested 500
Completed 500
Value of seed 578243
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 2
Number of categorical latent variables 1
Observed dependent variables
Continuous
Y1 Y2
Observed independent variables
X
Continuous latent variables
I S
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
Optimization algorithm EMA
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 X
________ ________ ________
1 1.189 3.033 0.497
Covariances
Y1 Y2 X
________ ________ ________
Y1 10.112
Y2 9.460 12.845
X -0.032 0.111 0.250
Correlations
Y1 Y2 X
________ ________ ________
Y1 1.000
Y2 0.830 1.000
X -0.020 0.062 1.000
TESTS OF MODEL FIT
Number of Free Parameters 10
Loglikelihood
H0 Value
Mean -9296.290
Std Dev 43.757
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.996 -9398.083 -9395.713
0.980 0.974 -9386.155 -9390.063
0.950 0.944 -9368.267 -9372.902
0.900 0.900 -9352.370 -9353.321
0.800 0.794 -9333.117 -9334.188
0.700 0.694 -9319.237 -9320.084
0.500 0.510 -9296.290 -9295.160
0.300 0.300 -9273.344 -9273.498
0.200 0.214 -9259.464 -9258.510
0.100 0.096 -9240.211 -9240.559
0.050 0.052 -9224.314 -9224.168
0.020 0.016 -9206.426 -9209.654
0.010 0.010 -9194.497 -9198.116
Information Criteria
Akaike (AIC)
Mean 18612.581
Std Dev 87.515
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 18408.995 18397.719
0.980 0.984 18432.851 18437.372
0.950 0.948 18468.627 18465.954
0.900 0.904 18500.422 18500.769
0.800 0.786 18538.928 18533.514
0.700 0.700 18566.688 18566.375
0.500 0.490 18612.581 18609.790
0.300 0.306 18658.473 18658.822
0.200 0.206 18686.233 18687.212
0.100 0.100 18724.740 18723.781
0.050 0.056 18756.534 18764.992
0.020 0.026 18792.310 18795.835
0.010 0.004 18816.166 18809.595
Bayesian (BIC)
Mean 18668.590
Std Dev 87.515
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 18465.004 18453.728
0.980 0.984 18488.860 18493.381
0.950 0.948 18524.636 18521.963
0.900 0.904 18556.431 18556.778
0.800 0.786 18594.937 18589.523
0.700 0.700 18622.697 18622.384
0.500 0.490 18668.590 18665.799
0.300 0.306 18714.482 18714.831
0.200 0.206 18742.242 18743.221
0.100 0.100 18780.749 18779.790
0.050 0.056 18812.543 18821.001
0.020 0.026 18848.319 18851.844
0.010 0.004 18872.176 18865.604
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 18636.819
Std Dev 87.515
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 18433.233 18421.958
0.980 0.984 18457.090 18461.611
0.950 0.948 18492.866 18490.193
0.900 0.904 18524.660 18525.008
0.800 0.786 18563.167 18557.752
0.700 0.700 18590.926 18590.614
0.500 0.490 18636.819 18634.028
0.300 0.306 18682.712 18683.060
0.200 0.206 18710.472 18711.451
0.100 0.100 18748.978 18748.019
0.050 0.056 18780.772 18789.230
0.020 0.026 18816.548 18820.073
0.010 0.004 18840.405 18833.834
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 996.02167 0.49801
2 1003.97833 0.50199
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 996.02166 0.49801
2 1003.97834 0.50199
CLASSIFICATION QUALITY
Entropy 0.287
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 990 0.49511
2 1010 0.50489
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 0.745 0.255
2 0.255 0.745
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Latent Class 1
I BY
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
S BY
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
S ON
X 0.250 0.1598 0.4394 0.2816 0.2008 0.914 0.312
I WITH
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 2.500 2.4208 0.5286 0.4725 0.2852 0.824 0.942
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
S 2.250 2.3008 0.3900 0.3123 0.1544 0.878 0.984
Variances
I 6.250 7.1659 1.0393 0.9698 1.9170 0.788 0.988
Residual Variances
Y1 2.083 1.2453 0.3479 0.3401 0.8226 0.256 0.874
Y2 0.417 2.1656 0.4721 0.4891 3.2799 0.094 0.952
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Latent Class 2
I BY
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
S BY
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
S ON
X 1.000 1.0897 0.4316 0.2961 0.1940 0.928 0.950
I WITH
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Means
I 0.000 0.1082 0.5541 0.4819 0.3182 0.830 0.170
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
S 0.750 0.7024 0.3462 0.3197 0.1219 0.892 0.696
Variances
I 6.250 7.1659 1.0393 0.9698 1.9170 0.788 0.988
Residual Variances
Y1 2.083 1.2453 0.3479 0.3401 0.8226 0.256 0.874
Y2 0.417 2.1656 0.4721 0.4891 3.2799 0.094 0.952
S 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Categorical Latent Variables
Means
C#1 0.000 -0.0079 0.6143 0.4992 0.3767 0.946 0.054
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.483E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
Y1 Y2 X
________ ________ ________
1 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
X 0 0 0
THETA
Y1 Y2 X
________ ________ ________
Y1 1
Y2 0 2
X 0 0 0
ALPHA
I S X
________ ________ ________
1 3 4 0
BETA
I S X
________ ________ ________
I 0 0 0
S 0 0 5
X 0 0 0
PSI
I S X
________ ________ ________
I 6
S 0 0
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
Y1 Y2 X
________ ________ ________
1 0 0 0
LAMBDA
I S X
________ ________ ________
Y1 0 0 0
Y2 0 0 0
X 0 0 0
THETA
Y1 Y2 X
________ ________ ________
Y1 1
Y2 0 2
X 0 0 0
ALPHA
I S X
________ ________ ________
1 7 8 0
BETA
I S X
________ ________ ________
I 0 0 0
S 0 0 9
X 0 0 0
PSI
I S X
________ ________ ________
I 6
S 0 0
X 0 0 0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 10 0
GAMMA(C)
X
________
C#1 0
C#2 0
STARTING VALUES FOR LATENT CLASS 1
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 2.500 2.250 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.000 0.000
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS 2
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 0.000 0.750 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 1.000
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.000 0.000
X 0.000 0.000 0.500
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0.000 0.000
GAMMA(C)
X
________
C#1 0.000
C#2 0.000
POPULATION VALUES FOR LATENT CLASS 1
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 2.500 2.250 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 0.250
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.699 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS 2
NU
Y1 Y2 X
________ ________ ________
1 0.000 0.000 0.000
LAMBDA
I S X
________ ________ ________
Y1 1.000 0.000 0.000
Y2 1.000 1.000 0.000
X 0.000 0.000 1.000
THETA
Y1 Y2 X
________ ________ ________
Y1 2.083
Y2 0.000 0.417
X 0.000 0.000 0.000
ALPHA
I S X
________ ________ ________
1 0.000 0.750 0.000
BETA
I S X
________ ________ ________
I 0.000 0.000 0.000
S 0.000 0.000 1.000
X 0.000 0.000 0.000
PSI
I S X
________ ________ ________
I 6.250
S 0.699 1.000
X 0.000 0.000 1.000
POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0.000 0.000
GAMMA(C)
X
________
C#1 0.000
C#2 0.000
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
REPLICATION 154:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 1 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 154:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 2 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 350:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 1 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 350:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 2 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 490:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 1 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
REPLICATION 490:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN CLASS 2 IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE Y1.
Beginning Time: 23:28:16
Ending Time: 23:29:34
Elapsed Time: 00:01:18
MUTHEN & MUTHEN
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Los Angeles, CA 90066
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Fax: (310) 391-8971
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