Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 10:25 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level SEM with
continuous factor indicators and a random
slope for a factor
montecarlo:
names are y1-y5 w;
nobservations = 500;
ncsizes = 3;
csizes = 10 (5) 50 (3) 30 (10);
seed = 58459;
nreps = 1;
save = ex9.10.dat;
between = w;
ANALYSIS:
TYPE = TWOLEVEL RANDOM;
algo = int;
integration = 10;
MODEL POPULATION:
%WITHIN%
fw BY y1@1 y2-y4*1;
y1-y4*1;
fw*1;
s | y5 on fw;
y5*.5;
%BETWEEN%
[w@0]; w*1;
fb BY y1@1 y2-y4*1;
y1-y4@0;
fb*.5;
y5 on fb*.5 w*.6;
y5*.3;
s on fb*.2 w*.3;
[s*1]; s*.5;
MODEL:
%WITHIN%
fw BY y1@1 y2-y4*1;
y1-y4*1;
fw*1;
s | y5 on fw;
y5*.5;
%BETWEEN%
fb BY y1@1 y2-y4*1;
y1-y4@0;
fb*.5;
y5 on fb*.5 w*.6;
y5*.3;
s on fb*.2 w*.3;
[s*1]; s*.5;
output:
tech8 tech9;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level SEM with
continuous factor indicators and a random
slope for a factor
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 5
Number of independent variables 1
Number of continuous latent variables 3
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5
Observed independent variables
W
Continuous latent variables
FW FB S
Variables with special functions
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 10
Dimensions of numerical integration 4
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 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.151 -0.101 -0.084 -0.116 -0.128
Means
W
________
-0.040
Covariances
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 2.247
Y2 1.362 2.570
Y3 1.428 1.626 2.586
Y4 1.362 1.686 1.630 2.637
Y5 1.180 1.388 1.291 1.357 2.783
W -0.008 -0.075 -0.128 -0.058 0.606
Covariances
W
________
W 1.048
Correlations
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.567 1.000
Y3 0.593 0.631 1.000
Y4 0.559 0.648 0.624 1.000
Y5 0.472 0.519 0.481 0.501 1.000
W -0.005 -0.046 -0.078 -0.035 0.355
Correlations
W
________
W 1.000
MODEL FIT INFORMATION
Number of Free Parameters 25
Loglikelihood
H0 Value
Mean -4009.729
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 -4009.729 -4009.729
0.980 0.000 -4009.729 -4009.729
0.950 0.000 -4009.729 -4009.729
0.900 0.000 -4009.729 -4009.729
0.800 0.000 -4009.729 -4009.729
0.700 0.000 -4009.729 -4009.729
0.500 0.000 -4009.729 -4009.729
0.300 0.000 -4009.729 -4009.729
0.200 0.000 -4009.729 -4009.729
0.100 0.000 -4009.729 -4009.729
0.050 0.000 -4009.729 -4009.729
0.020 0.000 -4009.729 -4009.729
0.010 0.000 -4009.729 -4009.729
Information Criteria
Akaike (AIC)
Mean 8069.458
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8069.458 8069.458
0.980 0.000 8069.458 8069.458
0.950 0.000 8069.458 8069.458
0.900 0.000 8069.458 8069.458
0.800 0.000 8069.458 8069.458
0.700 0.000 8069.458 8069.458
0.500 0.000 8069.458 8069.458
0.300 0.000 8069.458 8069.458
0.200 0.000 8069.458 8069.458
0.100 0.000 8069.458 8069.458
0.050 0.000 8069.458 8069.458
0.020 0.000 8069.458 8069.458
0.010 0.000 8069.458 8069.458
Bayesian (BIC)
Mean 8174.823
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8174.823 8174.823
0.980 0.000 8174.823 8174.823
0.950 0.000 8174.823 8174.823
0.900 0.000 8174.823 8174.823
0.800 0.000 8174.823 8174.823
0.700 0.000 8174.823 8174.823
0.500 0.000 8174.823 8174.823
0.300 0.000 8174.823 8174.823
0.200 0.000 8174.823 8174.823
0.100 0.000 8174.823 8174.823
0.050 0.000 8174.823 8174.823
0.020 0.000 8174.823 8174.823
0.010 0.000 8174.823 8174.823
Sample-Size Adjusted BIC (n* = (n + 2) / 24)
Mean 8095.472
Std Dev 0.000
Number of successful computations 1
Proportions Percentiles
Expected Observed Expected Observed
0.990 0.000 8095.472 8095.472
0.980 0.000 8095.472 8095.472
0.950 0.000 8095.472 8095.472
0.900 0.000 8095.472 8095.472
0.800 0.000 8095.472 8095.472
0.700 0.000 8095.472 8095.472
0.500 0.000 8095.472 8095.472
0.300 0.000 8095.472 8095.472
0.200 0.000 8095.472 8095.472
0.100 0.000 8095.472 8095.472
0.050 0.000 8095.472 8095.472
0.020 0.000 8095.472 8095.472
0.010 0.000 8095.472 8095.472
MODEL RESULTS
ESTIMATES S. E. M. S. E. 95% % Sig
Population Average Std. Dev. Average Cover Coeff
Within Level
FW BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 1.2680 0.0000 0.1156 0.0718 0.000 1.000
Y3 1.000 1.1836 0.0000 0.0947 0.0337 1.000 1.000
Y4 1.000 1.2450 0.0000 0.0926 0.0600 0.000 1.000
Variances
FW 1.000 0.7518 0.0000 0.1128 0.0616 0.000 1.000
Residual Variances
Y1 1.000 1.0385 0.0000 0.0831 0.0015 1.000 1.000
Y2 1.000 0.9123 0.0000 0.0596 0.0077 1.000 1.000
Y3 1.000 0.9829 0.0000 0.0809 0.0003 1.000 1.000
Y4 1.000 0.9962 0.0000 0.0692 0.0000 1.000 1.000
Y5 0.500 0.4750 0.0000 0.0456 0.0006 1.000 1.000
Between Level
FB BY
Y1 1.000 1.0000 0.0000 0.0000 0.0000 1.000 0.000
Y2 1.000 0.9832 0.0000 0.0954 0.0003 1.000 1.000
Y3 1.000 1.0902 0.0000 0.0946 0.0081 1.000 1.000
Y4 1.000 1.0127 0.0000 0.1263 0.0002 1.000 1.000
S ON
FB 0.200 -0.0283 0.0000 0.1913 0.0521 1.000 0.000
S ON
W 0.300 0.3622 0.0000 0.1077 0.0039 1.000 1.000
Y5 ON
FB 0.500 0.4522 0.0000 0.1421 0.0023 1.000 1.000
Y5 ON
W 0.600 0.6305 0.0000 0.0715 0.0009 1.000 1.000
Intercepts
Y1 0.000 -0.0689 0.0000 0.0964 0.0048 1.000 0.000
Y2 0.000 -0.0098 0.0000 0.0962 0.0001 1.000 0.000
Y3 0.000 0.0097 0.0000 0.1024 0.0001 1.000 0.000
Y4 0.000 -0.0241 0.0000 0.0990 0.0006 1.000 0.000
Y5 0.000 -0.0223 0.0000 0.0890 0.0005 1.000 0.000
S 1.000 1.2150 0.0000 0.1198 0.0462 1.000 1.000
Variances
FB 0.500 0.4503 0.0000 0.1108 0.0025 1.000 1.000
Residual Variances
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
Y3 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y4 0.000 0.0000 0.0000 0.0000 0.0000 1.000 0.000
Y5 0.300 0.2016 0.0000 0.0569 0.0097 1.000 1.000
S 0.500 0.5634 0.0000 0.1198 0.0040 1.000 1.000
QUALITY OF NUMERICAL RESULTS
Average Condition Number for the Information Matrix 0.172E-03
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
FW Y5
________ ________
Y1 0 0
Y2 1 0
Y3 2 0
Y4 3 0
Y5 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 4
Y2 0 5
Y3 0 0 6
Y4 0 0 0 7
Y5 0 0 0 0 0
ALPHA
FW Y5
________ ________
0 0
BETA
FW Y5
________ ________
FW 0 0
Y5 0 0
PSI
FW Y5
________ ________
FW 8
Y5 0 9
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
10 11 12 13 0
NU
W
________
0
LAMBDA
FB S Y5 W
________ ________ ________ ________
Y1 0 0 0 0
Y2 14 0 0 0
Y3 15 0 0 0
Y4 16 0 0 0
Y5 0 0 0 0
W 0 0 0 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
Y5 0 0 0 0 0
W 0 0 0 0 0
THETA
W
________
W 0
ALPHA
FB S Y5 W
________ ________ ________ ________
0 17 18 0
BETA
FB S Y5 W
________ ________ ________ ________
FB 0 0 0 0
S 19 0 0 20
Y5 21 0 0 22
W 0 0 0 0
PSI
FB S Y5 W
________ ________ ________ ________
FB 23
S 0 24
Y5 0 0 25
W 0 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FW Y5
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
Y5 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 0.000
ALPHA
FW Y5
________ ________
0.000 0.000
BETA
FW Y5
________ ________
FW 0.000 0.000
Y5 0.000 0.000
PSI
FW Y5
________ ________
FW 1.000
Y5 0.000 0.500
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
W
________
0.000
LAMBDA
FB S Y5 W
________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000
Y4 1.000 0.000 0.000 0.000
Y5 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
THETA
W
________
W 0.000
ALPHA
FB S Y5 W
________ ________ ________ ________
0.000 1.000 0.000 0.000
BETA
FB S Y5 W
________ ________ ________ ________
FB 0.000 0.000 0.000 0.000
S 0.200 0.000 0.000 0.300
Y5 0.500 0.000 0.000 0.600
W 0.000 0.000 0.000 0.000
PSI
FB S Y5 W
________ ________ ________ ________
FB 0.500
S 0.000 0.500
Y5 0.000 0.000 0.300
W 0.000 0.000 0.000 0.500
POPULATION VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
FW Y5
________ ________
Y1 1.000 0.000
Y2 1.000 0.000
Y3 1.000 0.000
Y4 1.000 0.000
Y5 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.000
Y2 0.000 1.000
Y3 0.000 0.000 1.000
Y4 0.000 0.000 0.000 1.000
Y5 0.000 0.000 0.000 0.000 0.000
ALPHA
FW Y5
________ ________
0.000 0.000
BETA
FW Y5
________ ________
FW 0.000 0.000
Y5 0.000 0.000
PSI
FW Y5
________ ________
FW 1.000
Y5 0.000 0.500
POPULATION VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
W
________
0.000
LAMBDA
FB S Y5 W
________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000
Y4 1.000 0.000 0.000 0.000
Y5 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
THETA
W
________
W 0.000
ALPHA
FB S Y5 W
________ ________ ________ ________
0.000 1.000 0.000 0.000
BETA
FB S Y5 W
________ ________ ________ ________
FB 0.000 0.000 0.000 0.000
S 0.200 0.000 0.000 0.300
Y5 0.500 0.000 0.000 0.600
W 0.000 0.000 0.000 0.000
PSI
FB S Y5 W
________ ________ ________ ________
FB 0.500
S 0.000 0.500
Y5 0.000 0.000 0.300
W 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 -0.40227731D+04 0.0000000 0.0000000 EM
2 -0.40158524D+04 6.9207393 0.0017204 EM
3 -0.40138569D+04 1.9954947 0.0004969 EM
4 -0.40128285D+04 1.0283836 0.0002562 EM
5 -0.40121650D+04 0.6635204 0.0001653 EM
6 -0.40116879D+04 0.4771311 0.0001189 EM
7 -0.40113262D+04 0.3617043 0.0000902 EM
8 -0.40110439D+04 0.2822842 0.0000704 EM
9 -0.40108195D+04 0.2244130 0.0000559 EM
10 -0.40106387D+04 0.1807750 0.0000451 EM
11 -0.40104916D+04 0.1471209 0.0000367 EM
12 -0.40103708D+04 0.1207370 0.0000301 EM
13 -0.40102711D+04 0.0997750 0.0000249 EM
14 -0.40101881D+04 0.0829431 0.0000207 EM
15 -0.40101188D+04 0.0693028 0.0000173 EM
16 -0.40100606D+04 0.0581626 0.0000145 EM
17 -0.40100116D+04 0.0490019 0.0000122 EM
18 -0.40099702D+04 0.0414245 0.0000103 EM
19 -0.40099351D+04 0.0351237 0.0000088 EM
20 -0.40099052D+04 0.0298600 0.0000074 EM
21 -0.40098798D+04 0.0254449 0.0000063 EM
22 -0.40098581D+04 0.0217277 0.0000054 EM
23 -0.40098395D+04 0.0185879 0.0000046 EM
24 -0.40098235D+04 0.0159290 0.0000040 EM
25 -0.40098099D+04 0.0136710 0.0000034 EM
26 -0.40097981D+04 0.0117486 0.0000029 EM
27 -0.40097880D+04 0.0101090 0.0000025 EM
28 -0.40097793D+04 0.0087082 0.0000022 EM
29 -0.40097718D+04 0.0075089 0.0000019 EM
30 -0.40097653D+04 0.0064808 0.0000016 EM
31 -0.40097597D+04 0.0055981 0.0000014 EM
32 -0.40097549D+04 0.0048396 0.0000012 EM
33 -0.40097507D+04 0.0041867 0.0000010 EM
34 -0.40097471D+04 0.0036246 0.0000009 EM
35 -0.40097439D+04 0.0031402 0.0000008 EM
36 -0.40097412D+04 0.0027214 0.0000007 EM
37 -0.40097389D+04 0.0023603 0.0000006 EM
38 -0.40097368D+04 0.0020481 0.0000005 EM
39 -0.40097350D+04 0.0017781 0.0000004 EM
40 -0.40097335D+04 0.0015445 0.0000004 EM
41 -0.40097321D+04 0.0013421 0.0000003 EM
42 -0.40097310D+04 0.0011669 0.0000003 EM
43 -0.40097300D+04 0.0010149 0.0000003 EM
44 -0.40097291D+04 0.0008832 0.0000002 EM
TECHNICAL 9 OUTPUT
Error messages for each replication (if any)
SAVEDATA INFORMATION
Order of variables
Y1
Y2
Y3
Y4
Y5
W
CLUSTER
Save file
ex9.10.dat
Save file format Free
Save file record length 10000
Beginning Time: 22:25:09
Ending Time: 22:25:43
Elapsed Time: 00:00:34
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