Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:17 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level SEM with
continuous factor indicators and a random
slope for a factor
DATA: FILE IS ex9.10.dat;
VARIABLE: NAMES ARE y1-y5 w clus;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ALGORITHM = INTEGRATION;
INTEGRATION = 10;
MODEL:
%WITHIN%
fw BY y1-y4;
s | y5 ON fw;
%BETWEEN%
fb BY y1-y4;
y1-y4@0;
y5 s ON fb w;
OUTPUT: TECH1 TECH8;
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 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
Cluster variable CLUS
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
Input data file(s)
ex9.10.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 90
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 -0.151 -0.122 -5.275 0.20% -1.386 -0.546 -0.111
500.000 2.247 0.081 4.027 0.20% 0.257 1.122
Y2 -0.101 -0.005 -5.126 0.20% -1.451 -0.523 -0.068
500.000 2.570 -0.131 4.886 0.20% 0.307 1.252
Y3 -0.084 -0.119 -4.515 0.20% -1.430 -0.463 -0.054
500.000 2.586 -0.253 4.425 0.20% 0.334 1.309
Y4 -0.116 0.066 -5.125 0.20% -1.399 -0.632 -0.186
500.000 2.637 0.236 5.830 0.20% 0.244 1.277
Y5 -0.128 -0.109 -6.680 0.20% -1.440 -0.533 -0.181
500.000 2.783 0.490 5.026 0.20% 0.249 1.247
W -0.074 0.191 -2.980 1.11% -0.954 -0.419 -0.236
90.000 0.989 0.488 2.876 1.11% 0.122 0.789
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 25
Loglikelihood
H0 Value -4009.729
H0 Scaling Correction Factor 0.9481
for MLR
Information Criteria
Akaike (AIC) 8069.458
Bayesian (BIC) 8174.823
Sample-Size Adjusted BIC 8095.472
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
FW BY
Y1 1.000 0.000 999.000 999.000
Y2 1.286 0.119 10.813 0.000
Y3 1.199 0.098 12.282 0.000
Y4 1.262 0.096 13.201 0.000
Variances
FW 0.732 0.112 6.539 0.000
Residual Variances
Y1 1.041 0.083 12.502 0.000
Y2 0.911 0.060 15.276 0.000
Y3 0.983 0.081 12.151 0.000
Y4 0.995 0.069 14.392 0.000
Y5 0.475 0.046 10.400 0.000
Between Level
FB BY
Y1 1.000 0.000 999.000 999.000
Y2 0.978 0.094 10.403 0.000
Y3 1.085 0.093 11.628 0.000
Y4 1.007 0.125 8.045 0.000
S ON
FB -0.029 0.192 -0.151 0.880
S ON
W 0.366 0.109 3.350 0.001
Y5 ON
FB 0.450 0.142 3.181 0.001
Y5 ON
W 0.630 0.072 8.801 0.000
Intercepts
Y1 -0.074 0.096 -0.765 0.444
Y2 -0.015 0.096 -0.154 0.878
Y3 0.005 0.103 0.044 0.965
Y4 -0.029 0.099 -0.294 0.769
Y5 -0.026 0.089 -0.286 0.775
S 1.232 0.122 10.070 0.000
Variances
FB 0.455 0.111 4.110 0.000
Residual Variances
Y1 0.000 0.000 999.000 999.000
Y2 0.000 0.000 999.000 999.000
Y3 0.000 0.000 999.000 999.000
Y4 0.000 0.000 999.000 999.000
Y5 0.203 0.057 3.554 0.000
S 0.579 0.124 4.657 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.283E-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 1.124
Y2 0.000 1.285
Y3 0.000 0.000 1.293
Y4 0.000 0.000 0.000 1.319
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 0.050
Y5 0.000 1.392
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.151 -0.101 -0.084 -0.116 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 0.000 -0.128 0.000
BETA
FB S Y5 W
________ ________ ________ ________
FB 0.000 0.000 0.000 0.000
S 0.000 0.000 0.000 0.000
Y5 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000
PSI
FB S Y5 W
________ ________ ________ ________
FB 0.050
S 0.000 1.000
Y5 0.000 0.000 1.392
W 0.000 0.000 0.000 0.524
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.46483821D+04 0.0000000 0.0000000 EM
2 -0.42605354D+04 387.8466457 0.0834369 EM
3 -0.41474468D+04 113.0885830 0.0265433 EM
4 -0.40969572D+04 50.4896512 0.0121737 EM
5 -0.40725645D+04 24.3927043 0.0059539 EM
6 -0.40603322D+04 12.2322571 0.0030036 EM
7 -0.40538313D+04 6.5008972 0.0016011 EM
8 -0.40498863D+04 3.9450360 0.0009732 EM
9 -0.40471181D+04 2.7681540 0.0006835 EM
10 -0.40449462D+04 2.1719321 0.0005367 EM
11 -0.40431086D+04 1.8376241 0.0004543 EM
12 -0.40414759D+04 1.6326735 0.0004038 EM
13 -0.40399798D+04 1.4961390 0.0003702 EM
14 -0.40385820D+04 1.3977230 0.0003460 EM
15 -0.40372603D+04 1.3217232 0.0003273 EM
16 -0.40360005D+04 1.2598610 0.0003121 EM
17 -0.40347928D+04 1.2076156 0.0002992 EM
18 -0.40336304D+04 1.1624073 0.0002881 EM
19 -0.40325078D+04 1.1225991 0.0002783 EM
20 -0.40314208D+04 1.0870641 0.0002696 EM
21 -0.40303659D+04 1.0549082 0.0002617 EM
22 -0.40293405D+04 1.0254100 0.0002544 EM
23 -0.40283426D+04 0.9978547 0.0002476 EM
24 -0.40273709D+04 0.9716777 0.0002412 EM
25 -0.40264246D+04 0.9463542 0.0002350 EM
26 -0.40255031D+04 0.9214678 0.0002289 EM
27 -0.40246065D+04 0.8966325 0.0002227 EM
28 -0.40237349D+04 0.8715417 0.0002166 EM
29 -0.40228889D+04 0.8459864 0.0002102 EM
30 -0.40220692D+04 0.8197883 0.0002038 EM
31 -0.40212763D+04 0.7928333 0.0001971 EM
32 -0.40205112D+04 0.7650904 0.0001903 EM
33 -0.40197747D+04 0.7365399 0.0001832 EM
34 -0.40190675D+04 0.7072365 0.0001759 EM
35 -0.40183902D+04 0.6772434 0.0001685 EM
36 -0.40177435D+04 0.6466786 0.0001609 EM
37 -0.40171279D+04 0.6156741 0.0001532 EM
38 -0.40165435D+04 0.5843710 0.0001455 EM
39 -0.40159905D+04 0.5529417 0.0001377 EM
40 -0.40154690D+04 0.5215586 0.0001299 EM
41 -0.40149786D+04 0.4903920 0.0001221 EM
42 -0.40145190D+04 0.4596132 0.0001145 EM
43 -0.40140896D+04 0.4293887 0.0001070 EM
44 -0.40136897D+04 0.3998727 0.0000996 EM
45 -0.40133185D+04 0.3712000 0.0000925 EM
46 -0.40129750D+04 0.3435069 0.0000856 EM
47 -0.40126581D+04 0.3169056 0.0000790 EM
48 -0.40123666D+04 0.2914797 0.0000726 EM
49 -0.40120993D+04 0.2672962 0.0000666 EM
50 -0.40118549D+04 0.2444099 0.0000609 EM
51 -0.40116321D+04 0.2228521 0.0000555 EM
52 -0.40114294D+04 0.2026460 0.0000505 EM
53 -0.40112456D+04 0.1837840 0.0000458 EM
54 -0.40110794D+04 0.1662522 0.0000414 EM
55 -0.40109294D+04 0.1500250 0.0000374 EM
56 -0.40107943D+04 0.1350634 0.0000337 EM
57 -0.40106730D+04 0.1213204 0.0000302 EM
58 -0.40105642D+04 0.1087403 0.0000271 EM
59 -0.40104670D+04 0.0972679 0.0000243 EM
60 -0.40103801D+04 0.0868347 0.0000217 EM
61 -0.40103028D+04 0.0773789 0.0000193 EM
62 -0.40101193D+04 0.1834889 0.0000458 QN
63 -0.40099873D+04 0.1319623 0.0000329 EM
64 -0.40099453D+04 0.0420035 0.0000105 EM
65 -0.40099144D+04 0.0308559 0.0000077 EM
66 -0.40098891D+04 0.0253863 0.0000063 EM
67 -0.40098674D+04 0.0216270 0.0000054 EM
68 -0.40098488D+04 0.0186759 0.0000047 EM
69 -0.40098325D+04 0.0162205 0.0000040 EM
70 -0.40098184D+04 0.0141242 0.0000035 EM
71 -0.40098061D+04 0.0123131 0.0000031 EM
72 -0.40097954D+04 0.0107376 0.0000027 EM
73 -0.40097860D+04 0.0093640 0.0000023 EM
74 -0.40097778D+04 0.0081653 0.0000020 EM
75 -0.40097707D+04 0.0071182 0.0000018 EM
76 -0.40097507D+04 0.0199968 0.0000050 QN
77 -0.40097381D+04 0.0126418 0.0000032 EM
78 -0.40097355D+04 0.0025505 0.0000006 EM
79 -0.40097337D+04 0.0017893 0.0000004 EM
80 -0.40097323D+04 0.0014743 0.0000004 EM
81 -0.40097310D+04 0.0012543 0.0000003 EM
82 -0.40097299D+04 0.0010771 0.0000003 EM
83 -0.40097290D+04 0.0009286 0.0000002 EM
Beginning Time: 23:17:42
Ending Time: 23:18:45
Elapsed Time: 00:01:03
MUTHEN & MUTHEN
3463 Stoner Ave.
Los Angeles, CA 90066
Tel: (310) 391-9971
Fax: (310) 391-8971
Web: www.StatModel.com
Support: Support@StatModel.com
Copyright (c) 1998-2022 Muthen & Muthen
Back to examples