Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022  11:56 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of two-level CFA with
  	continuous factor indicators, covariates,
  	and random slopes
  DATA:	FILE IS ex9.8.dat;
  VARIABLE:	NAMES ARE y1-y4 x1 x2 w clus;
  	CLUSTER = clus;
  	WITHIN = x1 x2;
  	BETWEEN = w;
  ANALYSIS:	TYPE = TWOLEVEL RANDOM;
  MODEL:
  	%WITHIN%
  	fw BY y1-y4;
  	s1 | fw ON x1;
  	s2 | fw ON x2;
  	%BETWEEN%
  	fb BY y1-y4;
  	y1-y4@0;
  	fb s1 s2 ON w;



INPUT READING TERMINATED NORMALLY



this is an example of two-level CFA with
continuous factor indicators, covariates,
and random slopes

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of dependent variables                                    4
Number of independent variables                                  3
Number of continuous latent variables                            4

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4

Observed independent variables
   X1          X2          W

Continuous latent variables
   FW          S1          S2          FB

Variables with special functions

  Cluster variable      CLUS

  Within variables
   X1          X2

  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)
  ex9.8.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           0.311      Y2           0.308      Y3           0.309
     Y4           0.327




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                   -0.049      -0.002      -8.015    0.10%      -2.063     -0.637     -0.042
            1000.000       6.006       0.096       7.694    0.10%       0.574      2.000
     Y2                   -0.066       0.093      -7.121    0.10%      -1.973     -0.696     -0.031
            1000.000       5.346       0.111       7.076    0.10%       0.492      1.787
     Y3                   -0.125       0.119      -7.005    0.10%      -2.164     -0.676     -0.118
            1000.000       5.722       0.111       7.888    0.10%       0.452      1.822
     Y4                   -0.049       0.136      -7.629    0.10%      -1.956     -0.690     -0.155
            1000.000       5.605       0.147       8.394    0.10%       0.437      1.965
     X1                   -0.038       0.007      -3.245    0.10%      -0.875     -0.312     -0.039
            1000.000       1.009      -0.006       3.794    0.10%       0.218      0.780
     X2                    0.033      -0.056      -3.263    0.10%      -0.769     -0.228     -0.001
            1000.000       0.959      -0.109       2.962    0.10%       0.303      0.863
     W                    -0.070      -0.100      -2.347    0.91%      -1.052     -0.306     -0.081
             110.000       1.138      -0.513       2.355    0.91%       0.249      0.840


THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       23

Loglikelihood

          H0 Value                       -6752.349
          H0 Scaling Correction Factor      0.9897
            for MLR

Information Criteria

          Akaike (AIC)                   13550.698
          Bayesian (BIC)                 13663.577
          Sample-Size Adjusted BIC       13590.528
            (n* = (n + 2) / 24)



MODEL RESULTS

                                                    Two-Tailed
                    Estimate       S.E.  Est./S.E.    P-Value

Within Level

 FW       BY
    Y1                 1.000      0.000    999.000    999.000
    Y2                 0.966      0.028     34.660      0.000
    Y3                 0.996      0.031     32.169      0.000
    Y4                 0.968      0.026     37.750      0.000

 Residual Variances
    Y1                 1.134      0.064     17.605      0.000
    Y2                 0.909      0.049     18.374      0.000
    Y3                 0.980      0.049     19.941      0.000
    Y4                 0.969      0.056     17.410      0.000
    FW                 1.200      0.081     14.743      0.000

Between Level

 FB       BY
    Y1                 1.000      0.000    999.000    999.000
    Y2                 0.934      0.036     25.863      0.000
    Y3                 0.970      0.033     29.172      0.000
    Y4                 0.987      0.042     23.278      0.000

 FB         ON
    W                  1.042      0.080     12.971      0.000

 S1         ON
    W                  0.510      0.086      5.964      0.000

 S2         ON
    W                  0.101      0.078      1.285      0.199

 Intercepts
    Y1                 0.058      0.090      0.641      0.522
    Y2                 0.033      0.084      0.399      0.690
    Y3                -0.022      0.091     -0.238      0.812
    Y4                 0.056      0.087      0.652      0.514
    S1                 0.560      0.087      6.421      0.000
    S2                 0.471      0.091      5.174      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
    S1                 0.524      0.097      5.409      0.000
    S2                 0.583      0.129      4.516      0.000
    FB                 0.568      0.127      4.460      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.694E-02
       (ratio of smallest to largest eigenvalue)


     Beginning Time:  23:56:39
        Ending Time:  23:56:40
       Elapsed Time:  00:00:01



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