Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:18 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level growth
model for a continuous outcome (three-
level analysis)
DATA: FILE IS ex9.12.dat;
VARIABLE: NAMES ARE y1-y4 x w clus;
WITHIN = x;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@3;
y1-y4 (1);
iw sw ON x;
%BETWEEN%
ib sb | y1@0 y2@1 y3@2 y4@3;
y1-y4@0;
ib sb ON w;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level growth
model for a continuous outcome (three-
level analysis)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 4
Number of independent variables 2
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Observed independent variables
X W
Continuous latent variables
IW SW IB SB
Variables with special functions
Cluster variable CLUS
Within variables
X
Between variables
W
Estimator MLR
Information matrix OBSERVED
Maximum number of iterations 100
Convergence criterion 0.100D-05
Maximum number of EM iterations 500
Convergence criteria for the EM algorithm
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-03
Minimum variance 0.100D-03
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
Input data file(s)
ex9.12.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 110
Average cluster size 9.091
Estimated Intraclass Correlations for the Y Variables
Intraclass Intraclass Intraclass
Variable Correlation Variable Correlation Variable Correlation
Y1 0.242 Y2 0.298 Y3 0.337
Y4 0.339
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 0.966 0.039 -5.130 0.10% -0.572 0.445 0.920
1000.000 3.305 -0.108 6.809 0.10% 1.472 2.506
Y2 1.408 0.087 -5.305 0.10% -0.402 0.799 1.358
1000.000 4.669 -0.036 8.695 0.10% 1.919 3.289
Y3 1.831 0.076 -6.408 0.10% -0.509 0.984 1.754
1000.000 7.658 -0.133 10.780 0.10% 2.496 4.171
Y4 2.299 0.045 -7.258 0.10% -0.617 1.403 2.241
1000.000 12.143 -0.217 12.444 0.10% 3.137 5.393
X -0.021 0.019 -3.780 0.10% -0.854 -0.283 -0.044
1000.000 0.960 0.034 3.217 0.10% 0.240 0.798
W -0.046 0.168 -2.855 0.91% -0.869 -0.315 -0.101
110.000 1.095 0.224 2.902 0.91% 0.033 0.823
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 13
Loglikelihood
H0 Value -6531.551
H0 Scaling Correction Factor 0.9572
for MLR
H1 Value -6522.817
H1 Scaling Correction Factor 0.8645
for MLR
Information Criteria
Akaike (AIC) 13089.103
Bayesian (BIC) 13152.904
Sample-Size Adjusted BIC 13111.615
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit
Value 21.808*
Degrees of Freedom 19
P-Value 0.2939
Scaling Correction Factor 0.8010
for MLR
* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used
for chi-square difference testing in the regular way. MLM, MLR and WLSM
chi-square difference testing is described on the Mplus website. MLMV, WLSMV,
and ULSMV difference testing is done using the DIFFTEST option.
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.012
CFI/TLI
CFI 1.000
TLI 1.000
Chi-Square Test of Model Fit for the Baseline Model
Value 6014.786
Degrees of Freedom 20
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.010
Value for Between 0.009
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 0.038 26.576 0.000
SW ON
X 0.167 0.027 6.299 0.000
SW WITH
IW 0.022 0.032 0.680 0.497
Residual Variances
Y1 0.511 0.015 33.838 0.000
Y2 0.511 0.015 33.838 0.000
Y3 0.511 0.015 33.838 0.000
Y4 0.511 0.015 33.838 0.000
IW 1.024 0.070 14.672 0.000
SW 0.473 0.025 19.088 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 0.574 0.080 7.129 0.000
SB ON
W 0.227 0.042 5.466 0.000
SB WITH
IB 0.023 0.042 0.543 0.587
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 1.059 0.076 13.841 0.000
SB 0.461 0.051 9.041 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 0.459 0.080 5.702 0.000
SB 0.214 0.035 6.066 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.335E-01
(ratio of smallest to largest eigenvalue)
Beginning Time: 23:18:46
Ending Time: 23:18:46
Elapsed Time: 00:00:00
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