Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:56 PM
INPUT INSTRUCTIONS
TITLE: this is an example of two-level path
analysis with continuous dependent
variables and random slopes
DATA: FILE IS ex9.5.dat;
VARIABLE: NAMES ARE y1 y2 x1 x2 w clus;
WITHIN = x1 x2;
BETWEEN = w;
CLUSTER IS clus;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ALGORITHM = INTEGRATION;
MODEL:
%WITHIN%
s2 | y2 ON y1;
y2 ON x2;
s1 | y1 ON x2;
y1 ON x1;
%BETWEEN%
y1 y2 s1 s2 ON w;
OUTPUT: TECH1 TECH8;
*** 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
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of two-level path
analysis with continuous dependent
variables and random slopes
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
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
Cluster variable CLUS
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
Input data file(s)
ex9.5.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 -0.132 0.110 -6.706 0.20% -1.782 -0.639 -0.150
500.000 4.085 0.282 6.017 0.20% 0.254 1.381
Y2 0.632 1.107 -6.558 0.20% -1.702 -0.568 0.092
500.000 10.377 1.751 14.772 0.20% 0.557 2.584
X1 -0.040 -0.008 -2.926 0.20% -0.875 -0.305 -0.039
500.000 1.013 0.012 2.846 0.20% 0.161 0.790
X2 0.015 -0.088 -3.060 0.20% -0.884 -0.236 0.048
500.000 1.155 -0.306 3.217 0.20% 0.283 0.905
W -0.130 -0.367 -2.154 1.11% -0.935 -0.218 0.002
90.000 0.810 -0.601 1.513 1.11% 0.241 0.670
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value -1663.599
H0 Scaling Correction Factor 1.0333
for MLR
Information Criteria
Akaike (AIC) 3361.198
Bayesian (BIC) 3432.847
Sample-Size Adjusted BIC 3378.888
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Y2 ON
X2 0.531 0.049 10.917 0.000
Y1 ON
X1 0.300 0.062 4.848 0.000
Residual Variances
Y1 1.080 0.064 16.954 0.000
Y2 0.957 0.076 12.606 0.000
Between Level
S1 ON
W 0.277 0.106 2.603 0.009
S2 ON
W 0.631 0.112 5.652 0.000
Y1 ON
W 1.206 0.110 10.973 0.000
Y2 ON
W 0.825 0.098 8.441 0.000
Y2 WITH
Y1 -0.048 0.090 -0.537 0.591
Intercepts
Y1 -0.011 0.102 -0.106 0.916
Y2 -0.062 0.081 -0.767 0.443
S2 0.819 0.105 7.784 0.000
S1 0.428 0.097 4.420 0.000
Residual Variances
Y1 0.600 0.110 5.433 0.000
Y2 0.214 0.084 2.553 0.011
S2 0.735 0.190 3.864 0.000
S1 0.498 0.106 4.698 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.446E-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 0.000 0.000
Y2 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
PSI
Y1 Y2 X1 X2
________ ________ ________ ________
Y1 2.042
Y2 0.000 5.189
X1 0.000 0.000 0.507
X2 0.000 0.000 0.000 0.578
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
________ ________ ________ ________ ________
0.000 0.000 -0.132 0.632 0.000
BETA
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 0.000 0.000 0.000 0.000 0.000
S1 0.000 0.000 0.000 0.000 0.000
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
S2 S1 Y1 Y2 W
________ ________ ________ ________ ________
S2 1.000
S1 0.000 1.000
Y1 0.000 0.000 2.042
Y2 0.000 0.000 0.000 5.189
W 0.000 0.000 0.000 0.000 0.402
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.20167591D+04 0.0000000 0.0000000 EM
2 -0.17641962D+04 252.5629032 0.1252321 EM
3 -0.16867969D+04 77.3992654 0.0438723 EM
4 -0.16702420D+04 16.5549130 0.0098144 EM
5 -0.16664568D+04 3.7851645 0.0022662 EM
6 -0.16651602D+04 1.2966536 0.0007781 EM
7 -0.16645521D+04 0.6080330 0.0003651 EM
8 -0.16642159D+04 0.3362356 0.0002020 EM
9 -0.16640128D+04 0.2031192 0.0001221 EM
10 -0.16638833D+04 0.1294525 0.0000778 EM
11 -0.16637978D+04 0.0855397 0.0000514 EM
12 -0.16637398D+04 0.0580323 0.0000349 EM
13 -0.16636996D+04 0.0401726 0.0000241 EM
14 -0.16636713D+04 0.0282557 0.0000170 EM
15 -0.16636512D+04 0.0201303 0.0000121 EM
16 -0.16636367D+04 0.0144931 0.0000087 EM
17 -0.16636262D+04 0.0105255 0.0000063 EM
18 -0.16636185D+04 0.0077004 0.0000046 EM
19 -0.16636128D+04 0.0056679 0.0000034 EM
20 -0.16636086D+04 0.0041939 0.0000025 EM
21 -0.16636055D+04 0.0031168 0.0000019 EM
22 -0.16636032D+04 0.0023252 0.0000014 EM
23 -0.16636014D+04 0.0017402 0.0000010 EM
24 -0.16636001D+04 0.0013061 0.0000008 EM
25 -0.16635991D+04 0.0009826 0.0000006 EM
Beginning Time: 23:56:34
Ending Time: 23:56:35
Elapsed Time: 00:00:01
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