Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:46 PM
INPUT INSTRUCTIONS
TITLE: Monte Carlo for a two-level path
analysis model with continuous dependent variables
and random slopes
montecarlo:
names are y1 y2 x1 x2 w;
nobservations = 500;
ncsizes = 3;
csizes = 10 (5) 50 (3) 30 (10);
seed = 58459;
nreps = 1;
within = x1 x2;
between = w;
save = ex9.5.dat;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
algorithm = integration;
model population:
%WITHIN%
x1-x2@1;
s2 | y2 on y1;
y2 on x2*.5;
s1 | y1 on x2;
y1 on x1*.25;
y1-y2*1;
%BETWEEN%
w@1;
y1 on w*1;
y2 on w*1;
y1-y2*.5;
s1 on w*.3;
s2 on w*.6;
s1*.5; s2*.75;
[s2*.75 s1*.5];
model:
%WITHIN%
s2 | y2 on y1;
y2 on x2*.5;
s1 | y1 on x2;
y1 on x1*.25;
y1-y2*1;
%BETWEEN%
y1 on w*1;
y2 on w*1;
y1-y2*.5;
s1 on w*.3;
s2 on w*.6;
s1*.5; s2*.75;
[s2*.75 s1*.5];
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):
S2 | Y2 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):
S2 | Y2 ON Y1
2 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
Monte Carlo for a two-level path
analysis model with continuous dependent variables
and random slopes
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
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 2
Observed dependent variables
Continuous
Y1 Y2
Observed independent variables
X1 X2 W
Continuous latent variables
S2 S1
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 0
Adaptive quadrature ON
Cholesky OFF
SUMMARY OF DATA FOR THE FIRST REPLICATION
Cluster information
Size (s) Number of clusters of Size s
3 50
5 10
10 30
SAMPLE STATISTICS FOR THE FIRST REPLICATION
SAMPLE STATISTICS
Means
Y1 Y2 X1 X2 W
________ ________ ________ ________ ________
-0.132 0.632 -0.040 0.015 -0.098
Covariances
Y1 Y2 X1 X2 W
________ ________ ________ ________ ________
Y1 4.085
Y2 4.373 10.377
X1 0.339 0.101 1.013
X2 0.411 1.292 -0.043 1.155
W 1.027 1.429 -0.008 -0.005 0.804
Correlations
Y1 Y2 X1 X2 W
________ ________ ________ ________ ________
Y1 1.000
Y2 0.672 1.000
X1 0.166 0.031 1.000
X2 0.189 0.373 -0.040 1.000
W 0.567 0.495 -0.008 -0.005 1.000
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value
Mean -1663.599
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -1663.599 -1663.599
0.980 0.000 -1663.599 -1663.599
0.950 0.000 -1663.599 -1663.599
0.900 0.000 -1663.599 -1663.599
0.800 0.000 -1663.599 -1663.599
0.700 0.000 -1663.599 -1663.599
0.500 0.000 -1663.599 -1663.599
0.300 0.000 -1663.599 -1663.599
0.200 0.000 -1663.599 -1663.599
0.100 0.000 -1663.599 -1663.599
0.050 0.000 -1663.599 -1663.599
0.020 0.000 -1663.599 -1663.599
0.010 0.000 -1663.599 -1663.599
Information Criteria
Akaike (AIC)
Mean 3361.197
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3361.197 3361.197
0.980 0.000 3361.197 3361.197
0.950 0.000 3361.197 3361.197
0.900 0.000 3361.197 3361.197
0.800 0.000 3361.197 3361.197
0.700 0.000 3361.197 3361.197
0.500 0.000 3361.197 3361.197
0.300 0.000 3361.197 3361.197
0.200 0.000 3361.197 3361.197
0.100 0.000 3361.197 3361.197
0.050 0.000 3361.197 3361.197
0.020 0.000 3361.197 3361.197
0.010 0.000 3361.197 3361.197
Bayesian (BIC)
Mean 3432.846
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3432.846 3432.846
0.980 0.000 3432.846 3432.846
0.950 0.000 3432.846 3432.846
0.900 0.000 3432.846 3432.846
0.800 0.000 3432.846 3432.846
0.700 0.000 3432.846 3432.846
0.500 0.000 3432.846 3432.846
0.300 0.000 3432.846 3432.846
0.200 0.000 3432.846 3432.846
0.100 0.000 3432.846 3432.846
0.050 0.000 3432.846 3432.846
0.020 0.000 3432.846 3432.846
0.010 0.000 3432.846 3432.846
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 3378.887
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 3378.887 3378.887
0.980 0.000 3378.887 3378.887
0.950 0.000 3378.887 3378.887
0.900 0.000 3378.887 3378.887
0.800 0.000 3378.887 3378.887
0.700 0.000 3378.887 3378.887
0.500 0.000 3378.887 3378.887
0.300 0.000 3378.887 3378.887
0.200 0.000 3378.887 3378.887
0.100 0.000 3378.887 3378.887
0.050 0.000 3378.887 3378.887
0.020 0.000 3378.887 3378.887
0.010 0.000 3378.887 3378.887
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
Y2 ON
X2 0.500 0.5314 0.0000 0.0487 0.0010 1.000 1.000
Y1 ON
X1 0.250 0.3001 0.0000 0.0619 0.0025 1.000 1.000
Residual Variances
Y1 1.000 1.0795 0.0000 0.0637 0.0063 1.000 1.000
Y2 1.000 0.9575 0.0000 0.0760 0.0018 1.000 1.000
Between Level
S1 ON
W 0.300 0.2772 0.0000 0.1065 0.0005 1.000 1.000
S2 ON
W 0.600 0.6304 0.0000 0.1116 0.0009 1.000 1.000
Y1 ON
W 1.000 1.2065 0.0000 0.1099 0.0426 1.000 1.000
Y2 ON
W 1.000 0.8252 0.0000 0.0977 0.0306 1.000 1.000
Y2 WITH
Y1 0.000 -0.0480 0.0000 0.0898 0.0023 1.000 0.000
Intercepts
Y1 0.000 -0.0108 0.0000 0.1022 0.0001 1.000 0.000
Y2 0.000 -0.0623 0.0000 0.0813 0.0039 1.000 0.000
S2 0.750 0.8191 0.0000 0.1052 0.0048 1.000 1.000
S1 0.500 0.4284 0.0000 0.0969 0.0051 1.000 1.000
Residual Variances
Y1 0.500 0.6003 0.0000 0.1105 0.0101 1.000 1.000
Y2 0.500 0.2134 0.0000 0.0836 0.0821 0.000 1.000
S2 0.750 0.7351 0.0000 0.1903 0.0002 1.000 1.000
S1 0.500 0.4983 0.0000 0.1061 0.0000 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.447E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 X1 X2
________ ________ ________ ________
0 0 0 0
LAMBDA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0 0 0 0
Y2 0 0 0 0
X1 0 0 0 0
X2 0 0 0 0
THETA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0
Y2 0 0
X1 0 0 0
X2 0 0 0 0
ALPHA
Y1 Y2 X1 X2
________ ________ ________ ________
0 0 0 0
BETA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0 0 1 0
Y2 0 0 0 2
X1 0 0 0 0
X2 0 0 0 0
PSI
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 3
Y2 0 4
X1 0 0 0
X2 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 W
________ ________ ________
0 0 0
LAMBDA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
W 0 0 0 0 0
THETA
Y1 Y2 W
________ ________ ________
Y1 0
Y2 0 0
W 0 0 0
ALPHA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
5 6 7 8 0
BETA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 0 0 0 0 9
S1 0 0 0 0 10
Y1 0 0 0 0 11
Y2 0 0 0 0 12
W 0 0 0 0 0
PSI
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 13
S1 0 14
Y1 0 0 15
Y2 0 0 16 17
W 0 0 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000
Y2 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
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
ALPHA
Y1 Y2 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0.000 0.000 0.250 0.000
Y2 0.000 0.000 0.000 0.500
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
X1 0.000 0.000 0.500
X2 0.000 0.000 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 W
________ ________ ________
0.000 0.000 0.000
LAMBDA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
Y1 Y2 W
________ ________ ________
Y1 0.000
Y2 0.000 0.000
W 0.000 0.000 0.000
ALPHA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
0.750 0.500 0.000 0.000 0.000
BETA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 0.000 0.000 0.000 0.000 0.600
S1 0.000 0.000 0.000 0.000 0.300
Y1 0.000 0.000 0.000 0.000 1.000
Y2 0.000 0.000 0.000 0.000 1.000
W 0.000 0.000 0.000 0.000 0.000
PSI
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 0.750
S1 0.000 0.500
Y1 0.000 0.000 0.500
Y2 0.000 0.000 0.000 0.500
W 0.000 0.000 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000
Y2 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
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
ALPHA
Y1 Y2 X1 X2
________ ________ ________ ________
0.000 0.000 0.000 0.000
BETA
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 0.000 0.000 0.250 0.000
Y2 0.000 0.000 0.000 0.500
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
X1 0.000 0.000 1.000
X2 0.000 0.000 0.000 1.000
POPULATION VALUES FOR BETWEEN
NU
Y1 Y2 W
________ ________ ________
0.000 0.000 0.000
LAMBDA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
Y1 0.000 0.000 1.000 0.000 0.000
Y2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
Y1 Y2 W
________ ________ ________
Y1 0.000
Y2 0.000 0.000
W 0.000 0.000 0.000
ALPHA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
0.750 0.500 0.000 0.000 0.000
BETA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 0.000 0.000 0.000 0.000 0.600
S1 0.000 0.000 0.000 0.000 0.300
Y1 0.000 0.000 0.000 0.000 1.000
Y2 0.000 0.000 0.000 0.000 1.000
W 0.000 0.000 0.000 0.000 0.000
PSI
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 0.750
S1 0.000 0.500
Y1 0.000 0.000 0.500
Y2 0.000 0.000 0.000 0.500
W 0.000 0.000 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 -0.16729298D+04 0.0000000 0.0000000 EM
2 -0.16662590D+04 6.6707345 0.0039875 EM
3 -0.16649011D+04 1.3579695 0.0008150 EM
4 -0.16643778D+04 0.5232411 0.0003143 EM
5 -0.16641022D+04 0.2756552 0.0001656 EM
6 -0.16639370D+04 0.1651424 0.0000992 EM
7 -0.16638317D+04 0.1053198 0.0000633 EM
8 -0.16637619D+04 0.0697774 0.0000419 EM
9 -0.16637145D+04 0.0474756 0.0000285 EM
10 -0.16636815D+04 0.0329517 0.0000198 EM
11 -0.16636583D+04 0.0232286 0.0000140 EM
12 -0.16636417D+04 0.0165822 0.0000100 EM
13 -0.16636297D+04 0.0119578 0.0000072 EM
14 -0.16636210D+04 0.0086966 0.0000052 EM
15 -0.16636147D+04 0.0063693 0.0000038 EM
16 -0.16636100D+04 0.0046927 0.0000028 EM
17 -0.16636065D+04 0.0034750 0.0000021 EM
18 -0.16636039D+04 0.0025843 0.0000016 EM
19 -0.16636020D+04 0.0019291 0.0000012 EM
20 -0.16636005D+04 0.0014444 0.0000009 EM
21 -0.16635995D+04 0.0010845 0.0000007 EM
22 -0.16635986D+04 0.0008162 0.0000005 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
X1
X2
W
CLUSTER
Save file
ex9.5.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:46:41
Ending Time: 22:46:42
Elapsed Time: 00:00:01
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