Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:19 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level growth
model for a continuous outcome (three-
level analysis) with variation on both the
within and between levels for a random
slope of a time-varying covariate
DATA: FILE IS ex9.14.dat;
VARIABLE: NAMES ARE y1-y4 x a1-a4 w clus;
WITHIN = x a1-a4;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
ALGORITHM = INTEGRATION;
INTEGRATION = 10;
MODEL:
%WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@3;
y1-y4 (1);
iw sw ON x;
s* | y1 ON a1;
s* | y2 ON a2;
s* | y3 ON a3;
s* | y4 ON a4;
%BETWEEN%
ib sb | y1@0 y2@1 y3@2 y4@3;
y1-y4@0;
ib sb s ON w;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level growth
model for a continuous outcome (three-
level analysis) with variation on both the
within and between levels for a random
slope of a time-varying covariate
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 4
Number of independent variables 6
Number of continuous latent variables 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X A1 A2 A3 A4 W
Continuous latent variables
IW SW S IB SB
Variables with special functions
Cluster variable CLUS
Within variables
X A1 A2 A3 A4
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)
ex9.14.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 1.019 -0.173 -6.659 0.20% -0.804 0.508 0.996
500.000 5.276 0.607 8.514 0.20% 1.671 2.898
Y2 1.653 0.272 -8.895 0.20% -0.740 0.790 1.636
500.000 8.072 1.079 14.780 0.20% 2.349 3.870
Y3 2.015 0.103 -7.211 0.20% -0.864 1.124 1.858
500.000 10.410 -0.297 11.121 0.20% 2.802 4.853
Y4 2.701 0.024 -8.351 0.20% -0.880 1.593 2.498
500.000 16.330 -0.311 12.714 0.20% 3.841 6.329
X 0.033 0.061 -2.556 0.20% -0.728 -0.211 0.010
500.000 0.922 0.097 3.085 0.20% 0.227 0.820
A1 -0.078 0.018 -2.864 0.20% -0.939 -0.337 -0.090
500.000 0.985 -0.175 2.782 0.20% 0.191 0.733
A2 -0.061 -0.008 -3.420 0.20% -0.951 -0.312 -0.075
500.000 1.073 -0.107 3.217 0.20% 0.207 0.789
A3 -0.002 0.046 -2.961 0.20% -0.910 -0.272 0.010
500.000 1.022 -0.125 3.212 0.20% 0.212 0.848
A4 0.039 -0.052 -2.922 0.20% -0.919 -0.240 0.046
500.000 1.080 -0.313 3.272 0.20% 0.368 0.995
W -0.163 0.098 -2.529 1.11% -0.983 -0.402 -0.162
90.000 0.918 -0.101 1.965 1.11% 0.066 0.525
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 17
Loglikelihood
H0 Value -3616.302
H0 Scaling Correction Factor 0.9831
for MLR
Information Criteria
Akaike (AIC) 7266.605
Bayesian (BIC) 7338.253
Sample-Size Adjusted BIC 7284.294
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
IW |
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 1.000 0.000 999.000 999.000
Y4 1.000 0.000 999.000 999.000
SW |
Y1 0.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 2.000 0.000 999.000 999.000
Y4 3.000 0.000 999.000 999.000
IW ON
X 1.006 0.063 15.840 0.000
SW ON
X 0.262 0.045 5.831 0.000
SW WITH
IW 0.045 0.051 0.882 0.378
Variances
S 0.614 0.048 12.852 0.000
Residual Variances
Y1 0.509 0.031 16.191 0.000
Y2 0.509 0.031 16.191 0.000
Y3 0.509 0.031 16.191 0.000
Y4 0.509 0.031 16.191 0.000
IW 0.836 0.083 10.115 0.000
SW 0.560 0.050 11.165 0.000
Between Level
IB |
Y1 1.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 1.000 0.000 999.000 999.000
Y4 1.000 0.000 999.000 999.000
SB |
Y1 0.000 0.000 999.000 999.000
Y2 1.000 0.000 999.000 999.000
Y3 2.000 0.000 999.000 999.000
Y4 3.000 0.000 999.000 999.000
IB ON
W 0.527 0.100 5.289 0.000
SB ON
W 0.319 0.059 5.425 0.000
S ON
W 0.617 0.068 9.018 0.000
SB WITH
IB -0.066 0.061 -1.077 0.281
Intercepts
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
IB 1.088 0.088 12.337 0.000
SB 0.567 0.063 8.998 0.000
S 1.058 0.072 14.630 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
IB 0.411 0.093 4.414 0.000
SB 0.199 0.056 3.548 0.000
S 0.275 0.064 4.281 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.218E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0 0 0 0 0
NU
A1 A2 A3 A4
________ ________ ________ ________
0 0 0 0
LAMBDA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
LAMBDA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
LAMBDA
A3 A4
________ ________
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
X 0 0
A1 0 0
A2 0 0
A3 0 0
A4 0 0
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
THETA
A1 A2 A3 A4
________ ________ ________ ________
A1 0
A2 0 0
A3 0 0 0
A4 0 0 0 0
ALPHA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
0 0 0 0 0
ALPHA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
0 0 0 0 0
ALPHA
A3 A4
________ ________
0 0
BETA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 0 0 0 0 0
SW 0 0 0 0 0
S%W 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
BETA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
IW 0 0 1 0 0
SW 0 0 2 0 0
S%W 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
BETA
A3 A4
________ ________
IW 0 0
SW 0 0
S%W 0 0
Y1 0 0
Y2 0 0
Y3 0 0
Y4 0 0
X 0 0
A1 0 0
A2 0 0
A3 0 0
A4 0 0
PSI
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 3
SW 4 5
S%W 0 0 6
Y1 0 0 0 7
Y2 0 0 0 0 7
Y3 0 0 0 0 0
Y4 0 0 0 0 0
X 0 0 0 0 0
A1 0 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
PSI
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y3 7
Y4 0 7
X 0 0 0
A1 0 0 0 0
A2 0 0 0 0 0
A3 0 0 0 0 0
A4 0 0 0 0 0
PSI
A3 A4
________ ________
A3 0
A4 0 0
PARAMETER SPECIFICATION FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
LAMBDA
Y3 Y4 W
________ ________ ________
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
W 0 0 0
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0
Y2 0 0
Y3 0 0 0
Y4 0 0 0 0
W 0 0 0 0 0
ALPHA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
8 9 10 0 0
ALPHA
Y3 Y4 W
________ ________ ________
0 0 0
BETA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0 0 0 0 0
SB 0 0 0 0 0
S%B 0 0 0 0 0
Y1 0 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
BETA
Y3 Y4 W
________ ________ ________
IB 0 0 11
SB 0 0 12
S%B 0 0 13
Y1 0 0 0
Y2 0 0 0
Y3 0 0 0
Y4 0 0 0
W 0 0 0
PSI
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 14
SB 15 16
S%B 0 0 17
Y1 0 0 0 0
Y2 0 0 0 0 0
Y3 0 0 0 0 0
Y4 0 0 0 0 0
W 0 0 0 0 0
PSI
Y3 Y4 W
________ ________ ________
Y3 0
Y4 0 0
W 0 0 0
STARTING VALUES FOR WITHIN
NU
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
NU
A1 A2 A3 A4
________ ________ ________ ________
0.000 0.000 0.000 0.000
LAMBDA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
X 0.000 0.000 1.000 0.000 0.000
A1 0.000 0.000 0.000 1.000 0.000
A2 0.000 0.000 0.000 0.000 1.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
LAMBDA
A3 A4
________ ________
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
X 0.000 0.000
A1 0.000 0.000
A2 0.000 0.000
A3 1.000 0.000
A4 0.000 1.000
THETA
Y1 Y2 Y3 Y4 X
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
THETA
A1 A2 A3 A4
________ ________ ________ ________
A1 0.000
A2 0.000 0.000
A3 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000
ALPHA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
A3 A4
________ ________
0.000 0.000
BETA
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 0.000 0.000 0.000 0.000 0.000
SW 0.000 0.000 0.000 0.000 0.000
S%W 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
IW 0.000 0.000 0.000 0.000 0.000
SW 0.000 0.000 0.000 0.000 0.000
S%W 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
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
BETA
A3 A4
________ ________
IW 0.000 0.000
SW 0.000 0.000
S%W 0.000 0.000
Y1 0.000 0.000
Y2 0.000 0.000
Y3 0.000 0.000
Y4 0.000 0.000
X 0.000 0.000
A1 0.000 0.000
A2 0.000 0.000
A3 0.000 0.000
A4 0.000 0.000
PSI
IW SW S%W Y1 Y2
________ ________ ________ ________ ________
IW 0.050
SW 0.000 0.050
S%W 0.000 0.000 1.000
Y1 0.000 0.000 0.000 2.638
Y2 0.000 0.000 0.000 0.000 4.036
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
X 0.000 0.000 0.000 0.000 0.000
A1 0.000 0.000 0.000 0.000 0.000
A2 0.000 0.000 0.000 0.000 0.000
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 X A1 A2
________ ________ ________ ________ ________
Y3 5.205
Y4 0.000 8.165
X 0.000 0.000 0.461
A1 0.000 0.000 0.000 0.493
A2 0.000 0.000 0.000 0.000 0.536
A3 0.000 0.000 0.000 0.000 0.000
A4 0.000 0.000 0.000 0.000 0.000
PSI
A3 A4
________ ________
A3 0.511
A4 0.000 0.540
STARTING VALUES FOR BETWEEN
NU
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
Y1 0.000 0.000 0.000 1.000 0.000
Y2 0.000 0.000 0.000 0.000 1.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
LAMBDA
Y3 Y4 W
________ ________ ________
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 1.000 0.000 0.000
Y4 0.000 1.000 0.000
W 0.000 0.000 1.000
THETA
Y1 Y2 Y3 Y4 W
________ ________ ________ ________ ________
Y1 0.000
Y2 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
ALPHA
Y3 Y4 W
________ ________ ________
0.000 0.000 0.000
BETA
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0.000 0.000 0.000 0.000 0.000
SB 0.000 0.000 0.000 0.000 0.000
S%B 0.000 0.000 0.000 0.000 0.000
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 1.000 0.000 0.000 0.000
Y3 1.000 2.000 0.000 0.000 0.000
Y4 1.000 3.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
BETA
Y3 Y4 W
________ ________ ________
IB 0.000 0.000 0.000
SB 0.000 0.000 0.000
S%B 0.000 0.000 0.000
Y1 0.000 0.000 0.000
Y2 0.000 0.000 0.000
Y3 0.000 0.000 0.000
Y4 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
IB SB S%B Y1 Y2
________ ________ ________ ________ ________
IB 0.050
SB 0.000 0.050
S%B 0.000 0.000 1.000
Y1 0.000 0.000 0.000 0.000
Y2 0.000 0.000 0.000 0.000 0.000
Y3 0.000 0.000 0.000 0.000 0.000
Y4 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
Y3 Y4 W
________ ________ ________
Y3 0.000
Y4 0.000 0.000
W 0.000 0.000 0.478
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.50157733D+04 0.0000000 0.0000000 EM
2 -0.39023182D+04 1113.4551631 0.2219907 EM
3 -0.37225826D+04 179.7355836 0.0460587 EM
4 -0.36731856D+04 49.3969876 0.0132695 EM
5 -0.36536065D+04 19.5790913 0.0053303 EM
6 -0.36425589D+04 11.0475897 0.0030237 EM
7 -0.36351657D+04 7.3932688 0.0020297 EM
8 -0.36299240D+04 5.2416756 0.0014419 EM
9 -0.36261639D+04 3.7600446 0.0010358 EM
10 -0.36234520D+04 2.7119919 0.0007479 EM
11 -0.36214628D+04 1.9891611 0.0005490 EM
12 -0.36199692D+04 1.4936004 0.0004124 EM
13 -0.36188344D+04 1.1348133 0.0003135 EM
14 -0.36179838D+04 0.8505718 0.0002350 EM
15 -0.36173703D+04 0.6135457 0.0001696 EM
16 -0.36169507D+04 0.4195892 0.0001160 EM
17 -0.36166798D+04 0.2708686 0.0000749 EM
18 -0.36165142D+04 0.1655898 0.0000458 EM
19 -0.36164177D+04 0.0965534 0.0000267 EM
20 -0.36163635D+04 0.0541520 0.0000150 EM
21 -0.36163341D+04 0.0294546 0.0000081 EM
22 -0.36163184D+04 0.0156495 0.0000043 EM
23 -0.36163102D+04 0.0081660 0.0000023 EM
24 -0.36163060D+04 0.0042026 0.0000012 EM
25 -0.36163039D+04 0.0021387 0.0000006 EM
26 -0.36163028D+04 0.0010776 0.0000003 EM
27 -0.36163023D+04 0.0005380 0.0000001 EM
Beginning Time: 23:19:24
Ending Time: 23:20:13
Elapsed Time: 00:00:49
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