Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:26 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level
regression analysis for a continuous
dependent variable with a random slope and a latent covariate
DATA: FILE = ex9.2c.dat;
VARIABLE: NAMES = y x w clus;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL RANDOM;
MODEL:
%WITHIN%
s | y ON x;
%BETWEEN%
y s ON w x;
y WITH s;
*** 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):
S | Y ON X
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a two-level
regression analysis for a continuous
dependent variable with a random slope and a latent covariate
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 1
Number of independent variables 2
Number of continuous latent variables 1
Observed dependent variables
Continuous
Y
Observed independent variables
X W
Continuous latent variables
S
Variables with special functions
Cluster variable CLUS
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)
ex9.2c.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
Variable Correlation Variable Correlation
Y 0.626
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
Y 2.045 1.000 -4.224 0.10% -0.163 1.203 1.828
1000.000 7.046 2.558 17.676 0.10% 2.467 3.887
X -0.095 -0.056 -3.654 0.10% -1.113 -0.368 -0.092
1000.000 1.401 -0.311 3.140 0.10% 0.212 0.923
W -0.106 -0.067 -2.364 0.91% -0.879 -0.365 -0.079
110.000 0.808 0.110 2.177 0.91% 0.124 0.513
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 10
Loglikelihood
H0 Value -3088.493
H0 Scaling Correction Factor 0.9978
for MLR
Information Criteria
Akaike (AIC) 6196.986
Bayesian (BIC) 6246.063
Sample-Size Adjusted BIC 6214.303
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
Residual Variances
Y 1.026 0.052 19.706 0.000
Between Level
S ON
W 0.569 0.094 6.087 0.000
X 0.315 0.180 1.752 0.080
Y ON
W 1.186 0.113 10.453 0.000
X 1.024 0.217 4.719 0.000
Y WITH
S 0.268 0.061 4.392 0.000
Intercepts
Y 2.087 0.083 25.173 0.000
S 1.017 0.071 14.415 0.000
Residual Variances
Y 0.483 0.098 4.950 0.000
S 0.368 0.056 6.547 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.112E-01
(ratio of smallest to largest eigenvalue)
Beginning Time: 23:26:30
Ending Time: 23:26:30
Elapsed Time: 00:00:00
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