Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:56 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level SEM with categorical
factor indicators on the within level and cluster-level
continuous observed and random intercept factor indicators
on the between level
DATA: FILE IS ex9.9.dat;
VARIABLE: NAMES ARE u1-u6 y1-y4 x1 x2 w clus;
CATEGORICAL = u1-u6;
WITHIN = x1 x2;
BETWEEN = w y1-y4;
CLUSTER IS clus;
ANALYSIS: TYPE IS TWOLEVEL;
ESTIMATOR = WLSMV;
MODEL:
%WITHIN%
fw1 BY u1-u3;
fw2 BY u4-u6;
fw1 fw2 ON x1 x2;
%BETWEEN%
fb BY u1-u6;
f BY y1-y4;
fb ON w f;
f ON w;
SAVEDATA: SWMATRIX = ex9.9sw.dat;
*** WARNING
One or more individual-level variables have no variation within a
cluster for the following clusters.
Variable Cluster IDs with no within-cluster variation
U1 2 5 7 8 11 16 19 24 25 26 29 31 33 34 35 36 42 48 50 73 82 97
U2 5 7 8 16 18 19 20 33 34 36 42 50 67 71 93 97
U3 5 7 8 14 18 24 26 32 34 36 40 47 48 50 51 71 76 82 93 97
U4 5 7 8 13 18 25 26 34 36 39 41 49 51 73 82 108
U5 5 7 8 17 18 24 27 28 32 34 36 39 42 50 51 77 82 93 97 108
U6 1 6 7 8 13 17 19 25 27 28 29 31 32 34 50 64 82 88 93 108
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a two-level SEM with categorical
factor indicators on the within level and cluster-level
continuous observed and random intercept factor indicators
on the between level
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 10
Number of independent variables 3
Number of continuous latent variables 4
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4
Binary and ordered categorical (ordinal)
U1 U2 U3 U4 U5 U6
Observed independent variables
X1 X2 W
Continuous latent variables
FW1 FW2 FB F
Variables with special functions
Cluster variable CLUS
Within variables
X1 X2
Between variables
Y1 Y2 Y3 Y4 W
Estimator WLSMV
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 1000
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 10
Minimum value for logit thresholds -10
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA/FS
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 0
Adaptive quadrature ON
Link PROBIT
Cholesky ON
Input data file(s)
ex9.9.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
U1 0.417 U2 0.380 U3 0.432
U4 0.394 U5 0.440 U6 0.390
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.476 476.000
Category 2 0.524 524.000
U2
Category 1 0.447 447.000
Category 2 0.553 553.000
U3
Category 1 0.473 473.000
Category 2 0.527 527.000
U4
Category 1 0.479 479.000
Category 2 0.521 521.000
U5
Category 1 0.490 490.000
Category 2 0.510 510.000
U6
Category 1 0.513 513.000
Category 2 0.487 487.000
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 0.081 0.033 -2.262 0.91% -0.812 -0.265 0.000
110.000 0.843 -0.369 2.325 0.91% 0.313 0.988
Y2 -0.040 0.120 -2.676 0.91% -0.853 -0.369 -0.111
110.000 1.009 -0.391 2.426 0.91% 0.236 0.837
Y3 -0.024 -0.239 -2.973 0.91% -0.933 -0.223 0.030
110.000 0.997 0.034 2.374 0.91% 0.191 0.789
Y4 0.009 0.545 -2.488 0.91% -0.839 -0.382 -0.132
110.000 1.143 0.489 3.467 0.91% 0.264 0.774
X1 0.065 0.089 -2.794 0.10% -0.760 -0.211 0.057
1000.000 1.037 -0.042 3.123 0.10% 0.336 0.899
X2 0.053 -0.018 -3.420 0.10% -0.823 -0.229 0.013
1000.000 1.084 -0.051 3.624 0.10% 0.318 0.971
W 0.061 0.318 -2.063 0.91% -0.659 -0.177 0.042
110.000 0.780 0.754 3.088 0.91% 0.161 0.745
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 44
Chi-Square Test of Model Fit
Value 69.697*
Degrees of Freedom 58
P-Value 0.1397
* 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 0.014
CFI/TLI
CFI 0.990
TLI 0.986
Chi-Square Test of Model Fit for the Baseline Model
Value 1225.492
Degrees of Freedom 82
P-Value 0.0000
SRMR (Standardized Root Mean Square Residual)
Value for Within 0.038
Value for Between 0.086
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
FW1 BY
U1 1.000 0.000 999.000 999.000
U2 0.827 0.146 5.653 0.000
U3 1.029 0.200 5.139 0.000
FW2 BY
U4 1.000 0.000 999.000 999.000
U5 1.113 0.198 5.609 0.000
U6 0.952 0.136 6.983 0.000
FW1 ON
X1 0.525 0.073 7.152 0.000
X2 0.694 0.098 7.091 0.000
FW2 ON
X1 0.692 0.091 7.640 0.000
X2 0.559 0.077 7.226 0.000
FW2 WITH
FW1 -0.034 0.079 -0.430 0.667
Residual Variances
FW1 1.157 0.303 3.822 0.000
FW2 1.240 0.266 4.664 0.000
Between Level
FB BY
U1 1.000 0.000 999.000 999.000
U2 0.798 0.135 5.928 0.000
U3 1.007 0.172 5.836 0.000
U4 1.062 0.182 5.836 0.000
U5 1.050 0.205 5.120 0.000
U6 0.845 0.163 5.181 0.000
F BY
Y1 1.000 0.000 999.000 999.000
Y2 1.225 0.246 4.972 0.000
Y3 0.901 0.200 4.507 0.000
Y4 1.412 0.268 5.260 0.000
FB ON
F 0.873 0.243 3.588 0.000
FB ON
W 1.003 0.160 6.283 0.000
F ON
W 0.259 0.078 3.307 0.001
Intercepts
Y1 0.063 0.084 0.741 0.459
Y2 -0.056 0.095 -0.590 0.555
Y3 -0.048 0.091 -0.528 0.598
Y4 -0.010 0.107 -0.093 0.926
Thresholds
U1$1 -0.118 0.137 -0.863 0.388
U2$1 -0.232 0.106 -2.190 0.029
U3$1 -0.168 0.130 -1.289 0.197
U4$1 -0.128 0.124 -1.032 0.302
U5$1 -0.107 0.137 -0.780 0.435
U6$1 0.103 0.118 0.880 0.379
Residual Variances
U1 0.612 0.235 2.601 0.009
U2 0.189 0.124 1.516 0.130
U3 0.302 0.162 1.861 0.063
U4 0.224 0.131 1.719 0.086
U5 0.416 0.210 1.985 0.047
U6 0.344 0.143 2.397 0.017
Y1 0.447 0.077 5.823 0.000
Y2 0.464 0.095 4.891 0.000
Y3 0.606 0.104 5.823 0.000
Y4 0.415 0.099 4.201 0.000
FB 0.439 0.143 3.065 0.002
F 0.328 0.097 3.371 0.001
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.124E-02
(ratio of smallest to largest eigenvalue)
SAVEDATA INFORMATION
Within and between sample statistics with Weight matrix
Save file
ex9.9sw.dat
Save format Free
Beginning Time: 23:56:40
Ending Time: 23:56:45
Elapsed Time: 00:00:05
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