Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:27 PM
INPUT INSTRUCTIONS
TITLE: Monte Carlo for a two-level path
analysis model with a continuous and a
categorical dependent variable
montecarlo:
names are y1 u2 x1 x2 w;
generate = u2(1);
categorical = u2;
nobservations = 1000;
ncsizes = 3;
csizes = 40 (5) 50 (10) 20 (15);
seed = 58459;
nreps = 1;
within = x1 x2;
between = w;
save = ex9.3.dat;
ANALYSIS:
TYPE = TWOLEVEL;
algo = int;
model population:
%WITHIN%
x1-x2@1;
u2 ON y1*.75 x2*.5;
y1 ON x1*.25 x2*.5;
y1*1;
%BETWEEN%
w@1;
u2 ON w*1;
y1 ON w*.5;
y1*.5; u2*.4;
model:
%WITHIN%
u2 ON y1*.75 x2*.5;
y1 ON x1*.25 x2*.5;
y1*1;
%BETWEEN%
u2 ON w*1;
y1 ON w*.5;
y1*.5; u2*.4;
output:
tech8 tech9;
*** WARNING in MODEL command
In the MODEL command, the predictor variable on the WITHIN level refers to the whole observed
variable. To use the latent within-level part, use ESTIMATOR=BAYES in the ANALYSIS command.
This applies to the following statement(s):
U2 ON Y1
*** WARNING in MODEL POPULATION command
In the MODEL POPULATION command, the predictor variable on the WITHIN level refers to the whole observed
variable. To use the latent within-level part, use ESTIMATOR=BAYES in the ANALYSIS command.
This applies to the following statement(s):
U2 ON Y1
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
Monte Carlo for a two-level path
analysis model with a continuous and a
categorical dependent variable
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of replications
Requested 1
Completed 1
Value of seed 58459
Number of dependent variables 2
Number of independent variables 3
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1
Binary and ordered categorical (ordinal)
U2
Observed independent variables
X1 X2 W
Variables with special functions
Within variables
X1 X2
Between variables
W
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
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
Cluster information
Size (s) Number of clusters of Size s
5 40
10 50
15 20
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 X1 X2 W
________ ________ ________ ________
0.155 -0.001 0.047 0.084
Covariances
Y1 X1 X2 W
________ ________ ________ ________
Y1 2.019
X1 0.223 1.039
X2 0.409 -0.023 0.984
W 0.589 -0.026 -0.003 1.067
Correlations
Y1 X1 X2 W
________ ________ ________ ________
Y1 1.000
X1 0.154 1.000
X2 0.290 -0.023 1.000
W 0.401 -0.025 -0.003 1.000
MODEL FIT INFORMATION
Number of Free Parameters 11
Loglikelihood
H0 Value
Mean -1965.263
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1965.263 -1965.263
0.980 0.000 -1965.263 -1965.263
0.950 0.000 -1965.263 -1965.263
0.900 0.000 -1965.263 -1965.263
0.800 0.000 -1965.263 -1965.263
0.700 0.000 -1965.263 -1965.263
0.500 0.000 -1965.263 -1965.263
0.300 0.000 -1965.263 -1965.263
0.200 0.000 -1965.263 -1965.263
0.100 0.000 -1965.263 -1965.263
0.050 0.000 -1965.263 -1965.263
0.020 0.000 -1965.263 -1965.263
0.010 0.000 -1965.263 -1965.263
Information Criteria
Akaike (AIC)
Mean 3952.526
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3952.526 3952.526
0.980 0.000 3952.526 3952.526
0.950 0.000 3952.526 3952.526
0.900 0.000 3952.526 3952.526
0.800 0.000 3952.526 3952.526
0.700 0.000 3952.526 3952.526
0.500 0.000 3952.526 3952.526
0.300 0.000 3952.526 3952.526
0.200 0.000 3952.526 3952.526
0.100 0.000 3952.526 3952.526
0.050 0.000 3952.526 3952.526
0.020 0.000 3952.526 3952.526
0.010 0.000 3952.526 3952.526
Bayesian (BIC)
Mean 4006.512
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 4006.512 4006.512
0.980 0.000 4006.512 4006.512
0.950 0.000 4006.512 4006.512
0.900 0.000 4006.512 4006.512
0.800 0.000 4006.512 4006.512
0.700 0.000 4006.512 4006.512
0.500 0.000 4006.512 4006.512
0.300 0.000 4006.512 4006.512
0.200 0.000 4006.512 4006.512
0.100 0.000 4006.512 4006.512
0.050 0.000 4006.512 4006.512
0.020 0.000 4006.512 4006.512
0.010 0.000 4006.512 4006.512
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 3971.575
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3971.575 3971.575
0.980 0.000 3971.575 3971.575
0.950 0.000 3971.575 3971.575
0.900 0.000 3971.575 3971.575
0.800 0.000 3971.575 3971.575
0.700 0.000 3971.575 3971.575
0.500 0.000 3971.575 3971.575
0.300 0.000 3971.575 3971.575
0.200 0.000 3971.575 3971.575
0.100 0.000 3971.575 3971.575
0.050 0.000 3971.575 3971.575
0.020 0.000 3971.575 3971.575
0.010 0.000 3971.575 3971.575
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
U2 ON
Y1 0.750 0.7453 0.0000 0.0850 0.0000 1.000 1.000
X2 0.500 0.5329 0.0000 0.1065 0.0011 1.000 1.000
Y1 ON
X1 0.250 0.2287 0.0000 0.0344 0.0005 1.000 1.000
X2 0.500 0.4536 0.0000 0.0331 0.0021 1.000 1.000
Residual Variances
Y1 1.000 1.0043 0.0000 0.0489 0.0000 1.000 1.000
Between Level
U2 ON
W 1.000 1.2667 0.0000 0.1322 0.0711 0.000 1.000
Y1 ON
W 0.500 0.5772 0.0000 0.0632 0.0060 1.000 1.000
Intercepts
Y1 0.000 0.0963 0.0000 0.0733 0.0093 1.000 0.000
Thresholds
U2$1 0.000 0.0743 0.0000 0.1009 0.0055 1.000 0.000
Residual Variances
U2 0.400 0.2672 0.0000 0.1400 0.0176 1.000 0.000
Y1 0.500 0.4552 0.0000 0.0690 0.0020 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.333E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U2$1
________
0
NU
U2 Y1 X1 X2
________ ________ ________ ________
0 0 0 0
LAMBDA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0 0 0 0
Y1 0 0 0 0
X1 0 0 0 0
X2 0 0 0 0
THETA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0
Y1 0 0
X1 0 0 0
X2 0 0 0 0
ALPHA
U2 Y1 X1 X2
________ ________ ________ ________
0 0 0 0
BETA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0 1 0 2
Y1 0 0 3 4
X1 0 0 0 0
X2 0 0 0 0
PSI
U2 Y1 X1 X2
________ ________ ________ ________
U2 0
Y1 0 5
X1 0 0 0
X2 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U2$1
________
11
NU
U2 Y1 W
________ ________ ________
0 0 0
LAMBDA
U2 Y1 W
________ ________ ________
U2 0 0 0
Y1 0 0 0
W 0 0 0
THETA
U2 Y1 W
________ ________ ________
U2 0
Y1 0 0
W 0 0 0
ALPHA
U2 Y1 W
________ ________ ________
0 6 0
BETA
U2 Y1 W
________ ________ ________
U2 0 0 7
Y1 0 0 8
W 0 0 0
PSI
U2 Y1 W
________ ________ ________
U2 9
Y1 0 10
W 0 0 0
STARTING VALUES FOR WITHIN
TAU
U2$1
________
0.000
NU
U2 Y1 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U2 Y1 X1 X2
________ ________ ________ ________
U2 1.000 0.000 0.000 0.000
Y1 0.000 1.000 0.000 0.000
X1 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 1.000
THETA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0.000
Y1 0.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
ALPHA
U2 Y1 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0.000 0.750 0.000 0.500
Y1 0.000 0.000 0.250 0.500
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
U2 Y1 X1 X2
________ ________ ________ ________
U2 1.000
Y1 0.000 1.000
X1 0.000 0.000 0.500
X2 0.000 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
TAU
U2$1
________
0.000
NU
U2 Y1 W
________ ________ ________
0.000 0.000 0.000
LAMBDA
U2 Y1 W
________ ________ ________
U2 1.000 0.000 0.000
Y1 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
U2 Y1 W
________ ________ ________
U2 0.000
Y1 0.000 0.000
W 0.000 0.000 0.000
ALPHA
U2 Y1 W
________ ________ ________
0.000 0.000 0.000
BETA
U2 Y1 W
________ ________ ________
U2 0.000 0.000 1.000
Y1 0.000 0.000 0.500
W 0.000 0.000 0.000
PSI
U2 Y1 W
________ ________ ________
U2 0.400
Y1 0.000 0.500
W 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
TAU
U2$1
________
0.000
NU
U2 Y1 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
U2 Y1 X1 X2
________ ________ ________ ________
U2 1.000 0.000 0.000 0.000
Y1 0.000 1.000 0.000 0.000
X1 0.000 0.000 1.000 0.000
X2 0.000 0.000 0.000 1.000
THETA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0.000
Y1 0.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
ALPHA
U2 Y1 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
U2 Y1 X1 X2
________ ________ ________ ________
U2 0.000 0.750 0.000 0.500
Y1 0.000 0.000 0.250 0.500
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
U2 Y1 X1 X2
________ ________ ________ ________
U2 0.000
Y1 0.000 1.000
X1 0.000 0.000 1.000
X2 0.000 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
TAU
U2$1
________
0.000
NU
U2 Y1 W
________ ________ ________
0.000 0.000 0.000
LAMBDA
U2 Y1 W
________ ________ ________
U2 1.000 0.000 0.000
Y1 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
U2 Y1 W
________ ________ ________
U2 0.000
Y1 0.000 0.000
W 0.000 0.000 0.000
ALPHA
U2 Y1 W
________ ________ ________
0.000 0.000 0.000
BETA
U2 Y1 W
________ ________ ________
U2 0.000 0.000 1.000
Y1 0.000 0.000 0.500
W 0.000 0.000 0.000
PSI
U2 Y1 W
________ ________ ________
U2 0.400
Y1 0.000 0.500
W 0.000 0.000 1.000
TECHNICAL 8 OUTPUT
TECHNICAL 8 OUTPUT FOR REPLICATION 1
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.19710748D+04 0.0000000 0.0000000 EM
2 -0.19671720D+04 3.9027486 0.0019800 EM
3 -0.19664382D+04 0.7338421 0.0003730 EM
4 -0.19660494D+04 0.3888077 0.0001977 EM
5 -0.19658046D+04 0.2448273 0.0001245 EM
6 -0.19656435D+04 0.1610463 0.0000819 EM
7 -0.19655350D+04 0.1085165 0.0000552 EM
8 -0.19654605D+04 0.0745013 0.0000379 EM
9 -0.19654085D+04 0.0520189 0.0000265 EM
10 -0.19653716D+04 0.0368916 0.0000188 EM
11 -0.19653450D+04 0.0265550 0.0000135 EM
12 -0.19653256D+04 0.0193917 0.0000099 EM
13 -0.19653113D+04 0.0143615 0.0000073 EM
14 -0.19653005D+04 0.0107844 0.0000055 EM
15 -0.19652923D+04 0.0082088 0.0000042 EM
16 -0.19652860D+04 0.0063319 0.0000032 EM
17 -0.19652810D+04 0.0049476 0.0000025 EM
18 -0.19652771D+04 0.0039142 0.0000020 EM
19 -0.19652740D+04 0.0031334 0.0000016 EM
20 -0.19652714D+04 0.0025363 0.0000013 EM
21 -0.19652694D+04 0.0020742 0.0000011 EM
22 -0.19652676D+04 0.0017125 0.0000009 EM
23 -0.19652662D+04 0.0014260 0.0000007 EM
24 -0.19652650D+04 0.0011966 0.0000006 EM
25 -0.19652640D+04 0.0010111 0.0000005 EM
26 -0.19652631D+04 0.0008595 0.0000004 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
U2
Y1
X1
X2
W
CLUSTER
Save file
ex9.3.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:27:58
Ending Time: 22:27:59
Elapsed Time: 00:00:01
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