Mplus DEVELOPMENT (Mpdev 6/1/2016)
MUTHEN & MUTHEN
06/01/2016 4:12 PM
INPUT INSTRUCTIONS
title:
Simulating binary X, cont latent M, binary Y
Step 1
montecarlo:
names = y m1-m3 x;
generate = y(1 p);
categorical = y;
nobs = 200;
nreps = 500;
repsave = all;
save = n200Perc20rep*.dat;
cutpoints = x(0);
model population:
x@1;
fm by m1-m3*1;
fm*1;
m1-m3*.67; !reliability 0.6
y on x*-1
fm*-2.5;
[y$1*.75];
fm on x*.7; !R-square 0.11
analysis:
estimator = ml;
link = probit;
model:
fm by m1-m3*1;
fm@1;
m1-m3*.67; !reliability 0.6
y on x*-1
fm*-2.5;
[y$1*.75];
fm on x*.7; !R-square 0.11
model indirect:
y IND fm x;
INPUT READING TERMINATED NORMALLY
Simulating binary X, cont latent M, binary Y
Step 1
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 200
Number of replications
Requested 500
Completed 500
Value of seed 0
Number of dependent variables 4
Number of independent variables 1
Number of continuous latent variables 1
Observed dependent variables
Continuous
M1 M2 M3
Binary and ordered categorical (ordinal)
Y
Observed independent variables
X
Continuous latent variables
FM
Estimator ML
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 10
Minimum value for logit thresholds -10
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 1
Adaptive quadrature ON
Link PROBIT
Cholesky ON
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
M1 M2 M3 X
________ ________ ________ ________
1 0.401 0.375 0.471 0.500
Covariances
M1 M2 M3 X
________ ________ ________ ________
M1 1.975
M2 1.228 1.916
M3 1.148 1.196 1.743
X 0.193 0.169 0.183 0.250
Correlations
M1 M2 M3 X
________ ________ ________ ________
M1 1.000
M2 0.631 1.000
M3 0.619 0.655 1.000
X 0.275 0.245 0.278 1.000
MODEL FIT INFORMATION
Number of Free Parameters 13
Loglikelihood
H0 Value
Mean -949.904
Std Dev 19.458
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.994 -995.169 -990.186
0.980 0.990 -989.865 -986.366
0.950 0.950 -981.910 -982.416
0.900 0.896 -974.841 -976.084
0.800 0.814 -966.280 -965.808
0.700 0.682 -960.108 -960.752
0.500 0.498 -949.904 -950.001
0.300 0.290 -939.700 -940.270
0.200 0.198 -933.528 -934.088
0.100 0.110 -924.966 -924.549
0.050 0.062 -917.897 -917.134
0.020 0.018 -909.943 -910.557
0.010 0.010 -904.639 -905.606
Information Criteria
Akaike (AIC)
Mean 1925.808
Std Dev 38.916
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1835.277 1832.034
0.980 0.982 1845.886 1845.906
0.950 0.938 1861.795 1860.013
0.900 0.890 1875.933 1873.775
0.800 0.802 1893.056 1893.000
0.700 0.710 1905.400 1906.377
0.500 0.502 1925.808 1925.853
0.300 0.318 1946.215 1947.420
0.200 0.186 1958.559 1957.277
0.100 0.104 1975.682 1977.559
0.050 0.050 1989.821 1989.562
0.020 0.010 2005.730 1998.394
0.010 0.006 2016.338 2004.906
Bayesian (BIC)
Mean 1968.686
Std Dev 38.916
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1878.155 1874.912
0.980 0.982 1888.764 1888.784
0.950 0.938 1904.673 1902.891
0.900 0.890 1918.811 1916.654
0.800 0.802 1935.934 1935.878
0.700 0.710 1948.278 1949.255
0.500 0.502 1968.686 1968.731
0.300 0.318 1989.093 1990.298
0.200 0.186 2001.438 2000.155
0.100 0.104 2018.561 2020.437
0.050 0.050 2032.699 2032.440
0.020 0.010 2048.608 2041.272
0.010 0.006 2059.216 2047.784
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 1927.500
Std Dev 38.916
Number of successful computations 500
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.990 1836.970 1833.727
0.980 0.982 1847.579 1847.599
0.950 0.938 1863.487 1861.706
0.900 0.890 1877.626 1875.468
0.800 0.802 1894.749 1894.693
0.700 0.710 1907.093 1908.069
0.500 0.502 1927.500 1927.546
0.300 0.318 1947.908 1949.113
0.200 0.186 1960.252 1958.969
0.100 0.104 1977.375 1979.252
0.050 0.050 1991.513 1991.255
0.020 0.010 2007.422 2000.087
0.010 0.006 2018.031 2006.599
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
FM BY
M1 1.000 0.9991 0.0848 0.0803 0.0072 0.938 1.000
M2 1.000 0.9931 0.0854 0.0803 0.0073 0.938 1.000
M3 1.000 0.9956 0.0787 0.0803 0.0062 0.946 1.000
FM ON
X 0.700 0.7103 0.1632 0.1661 0.0267 0.952 0.994
Y ON
FM -2.500 -3.5070 2.6334 2.4513 7.9347 0.942 0.756
Y ON
X -1.000 -1.3116 1.0997 1.0176 1.3040 0.976 0.430
Intercepts
M1 0.000 -0.0046 0.1215 0.1248 0.0148 0.944 0.056
M2 0.000 -0.0074 0.1224 0.1245 0.0150 0.952 0.048
M3 0.000 0.0025 0.1210 0.1250 0.0146 0.954 0.046
Thresholds
Y$1 0.750 1.0262 0.9218 0.9716 0.9244 0.958 0.344
Residual Variances
M1 0.670 0.6568 0.1008 0.0929 0.0103 0.904 1.000
M2 0.670 0.6654 0.0965 0.0931 0.0093 0.944 1.000
M3 0.670 0.6645 0.0942 0.0933 0.0089 0.938 1.000
FM 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.226E-02
(ratio of smallest to largest eigenvalue)
TOTAL, TOTAL INDIRECT, SPECIFIC INDIRECT, AND DIRECT EFFECTS FOR LATENT RESPONSE VARIABLES
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Effects from X to Y
Indirect -1.750 -2.4986 1.9935 1.8272 4.5265 0.938 0.686
Direct effect -1.000 -1.3116 1.0997 1.0176 1.3040 0.976 0.430
TOTAL, INDIRECT, AND DIRECT EFFECTS BASED ON COUNTERFACTUALS (CAUSALLY-DEFINED EFFECTS)
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Effects from X to Y
Tot natural IE -0.161 -0.1629 0.0467 0.0473 0.0022 0.938 0.992
Pure natural DE -0.132 -0.1313 0.0583 0.0567 0.0034 0.934 0.636
Total effect -0.293 -0.2943 0.0549 0.0555 0.0030 0.932 0.996
Odds ratios for binary Y
Tot natural IE 0.309 0.3128 0.0893 0.0889 0.0080 0.930 0.998
Pure natural DE 0.543 0.5604 0.1620 0.1560 0.0265 0.936 0.996
Total effect 0.167 0.1739 0.0675 0.0646 0.0046 0.928 0.978
Other effects
Pure natural IE -0.214 -0.2150 0.0483 0.0498 0.0023 0.950 0.994
Tot natural DE -0.080 -0.0793 0.0370 0.0364 0.0014 0.934 0.592
Total effect -0.293 -0.2943 0.0549 0.0555 0.0030 0.932 0.996
Odds ratios for other effects for binary Y
Pure natural IE 0.335 0.3391 0.0908 0.0911 0.0082 0.930 0.998
Tot natural DE 0.500 0.5213 0.1719 0.1645 0.0300 0.938 0.992
Total effect 0.167 0.1739 0.0675 0.0646 0.0046 0.928 0.978
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
TAU
Y$1
________
1 13
NU
Y M1 M2 M3 X
________ ________ ________ ________ ________
1 0 1 2 3 0
LAMBDA
FM Y X
________ ________ ________
Y 0 0 0
M1 4 0 0
M2 5 0 0
M3 6 0 0
X 0 0 0
THETA
Y M1 M2 M3 X
________ ________ ________ ________ ________
Y 0
M1 0 7
M2 0 0 8
M3 0 0 0 9
X 0 0 0 0 0
ALPHA
FM Y X
________ ________ ________
1 0 0 0
BETA
FM Y X
________ ________ ________
FM 0 0 10
Y 11 0 12
X 0 0 0
PSI
FM Y X
________ ________ ________
FM 0
Y 0 0
X 0 0 0
STARTING VALUES
TAU
Y$1
________
1 0.750
NU
Y M1 M2 M3 X
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
LAMBDA
FM Y X
________ ________ ________
Y 0.000 1.000 0.000
M1 1.000 0.000 0.000
M2 1.000 0.000 0.000
M3 1.000 0.000 0.000
X 0.000 0.000 1.000
THETA
Y M1 M2 M3 X
________ ________ ________ ________ ________
Y 0.000
M1 0.000 0.670
M2 0.000 0.000 0.670
M3 0.000 0.000 0.000 0.670
X 0.000 0.000 0.000 0.000 0.000
ALPHA
FM Y X
________ ________ ________
1 0.000 0.000 0.000
BETA
FM Y X
________ ________ ________
FM 0.000 0.000 0.700
Y -2.500 0.000 -1.000
X 0.000 0.000 0.000
PSI
FM Y X
________ ________ ________
FM 1.000
Y 0.000 1.000
X 0.000 0.000 0.500
POPULATION VALUES
TAU
Y$1
________
1 0.750
NU
Y M1 M2 M3 X
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
LAMBDA
FM Y X
________ ________ ________
Y 0.000 1.000 0.000
M1 1.000 0.000 0.000
M2 1.000 0.000 0.000
M3 1.000 0.000 0.000
X 0.000 0.000 1.000
THETA
Y M1 M2 M3 X
________ ________ ________ ________ ________
Y 0.000
M1 0.000 0.670
M2 0.000 0.000 0.670
M3 0.000 0.000 0.000 0.670
X 0.000 0.000 0.000 0.000 0.000
ALPHA
FM Y X
________ ________ ________
1 0.000 0.000 0.000
BETA
FM Y X
________ ________ ________
FM 0.000 0.000 0.700
Y -2.500 0.000 -1.000
X 0.000 0.000 0.000
PSI
FM Y X
________ ________ ________
FM 1.000
Y 0.000 0.000
X 0.000 0.000 1.000
SAVEDATA INFORMATION
Order of variables
Y
M1
M2
M3
X
Save file
n200Perc20rep*.dat
Save file format Free
Save file record length 10000
Beginning Time: 16:12:54
Ending Time: 16:13:35
Elapsed Time: 00:00:41
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