Mplus VERSION 5.1
MUTHEN & MUTHEN
05/05/2008   8:26 PM

INPUT INSTRUCTIONS

  TITLE:
          cont12

          A 2-GROUP MIMIC model

          with specific across-group equality constraints
          applied to the factor residual variance
          and to the y residual variance

  DATA:
          FILE IS school.dat;

  VARIABLE:
          NAMES ARE x1 y1-y16 x2 school x3 x4;
          USEV ARE y6-y9 x1 x2 x3;

  !        relative to the input of wMimic1, x4 is moved
  !        from the USEV analysis variable list to the
  !        multiple-group definition below:

          GROUPING IS x4 (1 = groupA 2= groupB);

  ANALYSIS: TYPE = MEANSTRUCTURE;

  MODEL:

  !        with multiple-group analysis the statement MODEL: refers
  !        to the general model structure that holds for all groups
  !        which can then be modified by group-specific model
  !        statements. The default is measurement invariance for
  !        the y intercepts and the loadings.

          f BY y6-y9;

  !        the statement above refers to the measurement
  !        part of the model. The y6 loading is fixed to 1
  !        by default because y6 is the first variable in
  !        the BY statement list; the other loadings are free.
  !        The residuals are automatically included and are
  !        uncorrelated by default (a correlation betweeen
  !        the residuals of, say y6 and y9 is stated as
  !        y6 WITH y9).

          f ON x1-x3;

  !        the statement above refers to the structural part
  !        of the model. The residual is automatically included.
  !        The x variables are not modelled and their
  !        covariance matrix is held fixed at the sample values.

          f (1);

  !        the statement above constrains the residual factor variance
  !        to be equal across groups

          y6 (2); y7 (3); y8 (4); y9 (5);

  !        the statements above constrain the y residual variances
  !        to be equal across groups

  !        The intercept of y8 has been found not group-invariant
  !        in a previous analysis. In the current analysis
  !        the default invariance setting is therefore modified
  !        using the group 2 (typeB) model statement below

  MODEL groupB:

          [y8];

  !        the statement above lets the intercept of y8 differ
  !        across the 2 groups

  OUTPUT:  SAMPSTAT STANDARDIZED MODINDICES(0.0);




*** WARNING in ANALYSIS command
  Starting with Version 5, TYPE=MEANSTRUCTURE is the default for all
  analyses.  To remove means from the model, use
  MODEL=NOMEANSTRUCTURE in the ANALYSIS command.
   1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS




cont12

A 2-GROUP MIMIC model

with specific across-group equality constraints
applied to the factor residual variance
and to the y residual variance

SUMMARY OF ANALYSIS

Number of groups                                                 2
Number of observations
   Group GROUPA                                               4154
   Group GROUPB                                               1044

Number of dependent variables                                    4
Number of independent variables                                  3
Number of continuous latent variables                            1

Observed dependent variables

  Continuous
   Y6          Y7          Y8          Y9

Observed independent variables
   X1          X2          X3

Continuous latent variables
   F

Variables with special functions

  Grouping variable     X4

Estimator                                                       ML
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20

Input data file(s)
  school.dat

Input data format  FREE


SAMPLE STATISTICS


     SAMPLE STATISTICS FOR GROUPA


           Means
              Y6            Y7            Y8            Y9            X1
              ________      ________      ________      ________      ________
      1         2.405         2.528         2.146         2.832         2.231


           Means
              X2            X3
              ________      ________
      1         0.493         4.960


           Covariances
              Y6            Y7            Y8            Y9            X1
              ________      ________      ________      ________      ________
 Y6             1.376
 Y7             1.066         1.378
 Y8             0.687         0.689         1.825
 Y9             1.087         1.143         0.693         3.696
 X1             0.486         0.499         0.356         0.525         1.163
 X2             0.001         0.029         0.024         0.054         0.019
 X3            -0.586        -0.631        -0.419        -0.668        -0.716


           Covariances
              X2            X3
              ________      ________
 X2             0.250
 X3            -0.008         3.016


           Correlations
              Y6            Y7            Y8            Y9            X1
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.775         1.000
 Y8             0.434         0.435         1.000
 Y9             0.482         0.506         0.267         1.000
 X1             0.384         0.394         0.244         0.253         1.000
 X2             0.001         0.049         0.035         0.056         0.036
 X3            -0.288        -0.309        -0.178        -0.200        -0.382


           Correlations
              X2            X3
              ________      ________
 X2             1.000
 X3            -0.010         1.000


     SAMPLE STATISTICS FOR GROUPB


           Means
              Y6            Y7            Y8            Y9            X1
              ________      ________      ________      ________      ________
      1         2.787         2.929         2.215         3.319         2.898


           Means
              X2            X3
              ________      ________
      1         0.488         2.492


           Covariances
              Y6            Y7            Y8            Y9            X1
              ________      ________      ________      ________      ________
 Y6             1.172
 Y7             0.904         1.267
 Y8             0.585         0.690         1.793
 Y9             0.729         0.864         0.494         3.209
 X1             0.299         0.255         0.243         0.261         0.985
 X2             0.004         0.009         0.023         0.058         0.014
 X3            -0.560        -0.765        -0.451        -0.604        -0.198


           Covariances
              X2            X3
              ________      ________
 X2             0.250
 X3             0.014         5.760


           Correlations
              Y6            Y7            Y8            Y9            X1
              ________      ________      ________      ________      ________
 Y6             1.000
 Y7             0.742         1.000
 Y8             0.404         0.458         1.000
 Y9             0.376         0.429         0.206         1.000
 X1             0.278         0.229         0.183         0.147         1.000
 X2             0.007         0.016         0.034         0.065         0.028
 X3            -0.215        -0.283        -0.140        -0.141        -0.083


           Correlations
              X2            X3
              ________      ________
 X2             1.000
 X3             0.011         1.000


THE MODEL ESTIMATION TERMINATED NORMALLY



TESTS OF MODEL FIT

Chi-Square Test of Model Fit

          Value                             89.352
          Degrees of Freedom                    32
          P-Value                           0.0000

Chi-Square Contributions From Each Group

          GROUPA                            44.407
          GROUPB                            44.945

Chi-Square Test of Model Fit for the Baseline Model

          Value                           8638.602
          Degrees of Freedom                    36
          P-Value                           0.0000

CFI/TLI

          CFI                                0.993
          TLI                                0.992

Loglikelihood

          H0 Value                      -53339.849
          H1 Value                      -53295.173

Information Criteria

          Number of Free Parameters             20
          Akaike (AIC)                  106719.697
          Bayesian (BIC)                106850.818
          Sample-Size Adjusted BIC      106787.264
            (n* = (n + 2) / 24)

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.026
          90 Percent C.I.                    0.020  0.033

SRMR (Standardized Root Mean Square Residual)

          Value                              0.021



MODEL RESULTS

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

Group GROUPA

 F        BY
    Y6                 1.000      0.000    999.000    999.000
    Y7                 1.053      0.016     67.787      0.000
    Y8                 0.673      0.019     35.974      0.000
    Y9                 1.050      0.026     40.822      0.000

 F        ON
    X1                 0.342      0.015     22.646      0.000
    X2                 0.047      0.029      1.609      0.108
    X3                -0.117      0.009    -12.714      0.000

 Intercepts
    Y6                 2.197      0.069     31.998      0.000
    Y7                 2.309      0.072     32.040      0.000
    Y8                 2.008      0.049     40.631      0.000
    Y9                 2.632      0.075     35.021      0.000
    F                  0.000      0.000    999.000    999.000

 Residual Variances
    Y6                 0.354      0.013     27.128      0.000
    Y7                 0.268      0.013     20.265      0.000
    Y8                 1.374      0.028     48.815      0.000
    Y9                 2.528      0.053     48.143      0.000
    F                  0.765      0.022     35.210      0.000

Group GROUPB

 F        BY
    Y6                 1.000      0.000    999.000    999.000
    Y7                 1.053      0.016     67.787      0.000
    Y8                 0.673      0.019     35.974      0.000
    Y9                 1.050      0.026     40.822      0.000

 F        ON
    X1                 0.251      0.030      8.430      0.000
    X2                 0.034      0.059      0.578      0.563
    X3                -0.105      0.012     -8.571      0.000

 Intercepts
    Y6                 2.197      0.069     31.998      0.000
    Y7                 2.309      0.072     32.040      0.000
    Y8                 1.816      0.060     30.265      0.000
    Y9                 2.632      0.075     35.021      0.000
    F                  0.111      0.122      0.908      0.364

 Residual Variances
    Y6                 0.354      0.013     27.128      0.000
    Y7                 0.268      0.013     20.265      0.000
    Y8                 1.374      0.028     48.815      0.000
    Y9                 2.528      0.053     48.143      0.000
    F                  0.765      0.022     35.210      0.000


STANDARDIZED MODEL RESULTS


STDYX Standardization

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

Group GROUPA

 F        BY
    Y6                 0.860      0.006    143.028      0.000
    Y7                 0.897      0.006    159.378      0.000
    Y8                 0.498      0.012     43.237      0.000
    Y9                 0.551      0.011     51.808      0.000

 F        ON
    X1                 0.368      0.015     24.696      0.000
    X2                 0.024      0.015      1.609      0.108
    X3                -0.203      0.016    -12.997      0.000

 Intercepts
    Y6                 1.888      0.063     29.919      0.000
    Y7                 1.968      0.066     29.950      0.000
    Y8                 1.485      0.040     37.003      0.000
    Y9                 1.381      0.043     32.415      0.000
    F                  0.000      0.000    999.000    999.000

 Residual Variances
    Y6                 0.261      0.010     25.263      0.000
    Y7                 0.195      0.010     19.261      0.000
    Y8                 0.752      0.011     65.610      0.000
    Y9                 0.696      0.012     59.353      0.000
    F                  0.765      0.012     62.087      0.000

Group GROUPB

 F        BY
    Y6                 0.848      0.007    123.430      0.000
    Y7                 0.888      0.006    138.251      0.000
    Y8                 0.478      0.012     39.826      0.000
    Y9                 0.531      0.011     46.936      0.000

 F        ON
    X1                 0.262      0.030      8.875      0.000
    X2                 0.018      0.031      0.578      0.563
    X3                -0.266      0.030     -9.001      0.000

 Intercepts
    Y6                 1.961      0.066     29.600      0.000
    Y7                 2.051      0.070     29.488      0.000
    Y8                 1.360      0.048     28.285      0.000
    Y9                 1.402      0.043     32.554      0.000
    F                  0.117      0.129      0.904      0.366

 Residual Variances
    Y6                 0.282      0.012     24.194      0.000
    Y7                 0.212      0.011     18.542      0.000
    Y8                 0.771      0.011     67.067      0.000
    Y9                 0.718      0.012     59.674      0.000
    F                  0.849      0.021     39.781      0.000


STDY Standardization

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

Group GROUPA

 F        BY
    Y6                 0.860      0.006    143.028      0.000
    Y7                 0.897      0.006    159.378      0.000
    Y8                 0.498      0.012     43.237      0.000
    Y9                 0.551      0.011     51.808      0.000

 F        ON
    X1                 0.342      0.014     25.259      0.000
    X2                 0.047      0.029      1.609      0.108
    X3                -0.117      0.009    -13.099      0.000

 Intercepts
    Y6                 1.888      0.063     29.919      0.000
    Y7                 1.968      0.066     29.950      0.000
    Y8                 1.485      0.040     37.003      0.000
    Y9                 1.381      0.043     32.415      0.000
    F                  0.000      0.000    999.000    999.000

 Residual Variances
    Y6                 0.261      0.010     25.263      0.000
    Y7                 0.195      0.010     19.261      0.000
    Y8                 0.752      0.011     65.610      0.000
    Y9                 0.696      0.012     59.353      0.000
    F                  0.765      0.012     62.087      0.000

Group GROUPB

 F        BY
    Y6                 0.848      0.007    123.430      0.000
    Y7                 0.888      0.006    138.251      0.000
    Y8                 0.478      0.012     39.826      0.000
    Y9                 0.531      0.011     46.936      0.000

 F        ON
    X1                 0.264      0.029      9.018      0.000
    X2                 0.036      0.062      0.578      0.563
    X3                -0.111      0.012     -9.150      0.000

 Intercepts
    Y6                 1.961      0.066     29.600      0.000
    Y7                 2.051      0.070     29.488      0.000
    Y8                 1.360      0.048     28.285      0.000
    Y9                 1.402      0.043     32.554      0.000
    F                  0.117      0.129      0.904      0.366

 Residual Variances
    Y6                 0.282      0.012     24.194      0.000
    Y7                 0.212      0.011     18.542      0.000
    Y8                 0.771      0.011     67.067      0.000
    Y9                 0.718      0.012     59.674      0.000
    F                  0.849      0.021     39.781      0.000


STD Standardization

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

Group GROUPA

 F        BY
    Y6                 1.000      0.014     69.703      0.000
    Y7                 1.053      0.014     73.768      0.000
    Y8                 0.673      0.019     35.656      0.000
    Y9                 1.050      0.026     40.568      0.000

 F        ON
    X1                 0.342      0.014     25.259      0.000
    X2                 0.047      0.029      1.609      0.108
    X3                -0.117      0.009    -13.099      0.000

 Intercepts
    Y6                 2.197      0.069     31.998      0.000
    Y7                 2.309      0.072     32.040      0.000
    Y8                 2.008      0.049     40.631      0.000
    Y9                 2.632      0.075     35.021      0.000
    F                  0.000      0.000    999.000    999.000

 Residual Variances
    Y6                 0.354      0.013     27.128      0.000
    Y7                 0.268      0.013     20.265      0.000
    Y8                 1.374      0.028     48.815      0.000
    Y9                 2.528      0.053     48.143      0.000
    F                  0.765      0.012     62.087      0.000

Group GROUPB

 F        BY
    Y6                 0.950      0.017     55.932      0.000
    Y7                 1.000      0.017     57.556      0.000
    Y8                 0.639      0.019     33.305      0.000
    Y9                 0.997      0.027     37.246      0.000

 F        ON
    X1                 0.264      0.029      9.018      0.000
    X2                 0.036      0.062      0.578      0.563
    X3                -0.111      0.012     -9.150      0.000

 Intercepts
    Y6                 2.197      0.069     31.998      0.000
    Y7                 2.309      0.072     32.040      0.000
    Y8                 1.816      0.060     30.265      0.000
    Y9                 2.632      0.075     35.021      0.000
    F                  0.117      0.129      0.904      0.366

 Residual Variances
    Y6                 0.354      0.013     27.128      0.000
    Y7                 0.268      0.013     20.265      0.000
    Y8                 1.374      0.028     48.815      0.000
    Y9                 2.528      0.053     48.143      0.000
    F                  0.849      0.021     39.781      0.000


R-SQUARE

Group GROUPA

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

    Y6                 0.739      0.010     71.514      0.000
    Y7                 0.805      0.010     79.689      0.000
    Y8                 0.248      0.011     21.618      0.000
    Y9                 0.304      0.012     25.904      0.000

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

    F                  0.235      0.012     19.109      0.000

Group GROUPB

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

    Y6                 0.718      0.012     61.715      0.000
    Y7                 0.788      0.011     69.126      0.000
    Y8                 0.229      0.011     19.913      0.000
    Y9                 0.282      0.012     23.468      0.000

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

    F                  0.151      0.021      7.099      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.278E-03
       (ratio of smallest to largest eigenvalue)


MODEL MODIFICATION INDICES

Minimum M.I. value for printing the modification index     0.000

                            M.I.     E.P.C.  Std E.P.C.  StdYX E.P.C.
Group GROUPA


BY Statements

F        BY Y6              3.775     0.046      0.046        0.040
F        BY Y7              1.490    -0.007     -0.007       -0.006
F        BY Y8              1.357    -0.010     -0.010       -0.007
F        BY Y9              3.097     0.021      0.021        0.011

ON/BY Statements

F        ON F        /
F        BY F               1.524     0.035      0.035        0.035

WITH Statements

Y7       WITH Y6            0.489     0.009      0.009        0.031
Y8       WITH Y6            2.645     0.025      0.025        0.036
Y8       WITH Y7            6.041    -0.038     -0.038       -0.063
Y9       WITH Y6            0.059    -0.005     -0.005       -0.006
Y9       WITH Y7            1.060     0.023      0.023        0.028
Y9       WITH Y8            0.913    -0.029     -0.029       -0.016

Variances/Residual Variances

Y6                          0.002     0.000      0.000        0.000
Y7                          0.050    -0.001     -0.001       -0.001
Y8                          0.155     0.006      0.006        0.003
Y9                          0.103     0.008      0.008        0.002
F                           1.524     0.011      0.011        0.011

Means/Intercepts/Thresholds

[ Y6       ]                0.072     0.001      0.001        0.001
[ Y7       ]                0.223     0.001      0.001        0.001
[ Y9       ]                2.358    -0.015     -0.015       -0.008

Group GROUPB


BY Statements

F        BY Y6              3.780    -0.046     -0.044       -0.039
F        BY Y7              1.490     0.022      0.021        0.018
F        BY Y8              1.357     0.044      0.041        0.031
F        BY Y9              3.088    -0.075     -0.071       -0.038

ON/BY Statements

F        ON F        /
F        BY F               1.523    -0.035     -0.035       -0.035

WITH Statements

Y7       WITH Y6            0.019    -0.002     -0.002       -0.007
Y8       WITH Y6            0.944    -0.026     -0.026       -0.038
Y8       WITH Y7            4.501     0.057      0.057        0.093
Y9       WITH Y6            3.256    -0.067     -0.067       -0.071
Y9       WITH Y7            0.204     0.017      0.017        0.020
Y9       WITH Y8            1.978    -0.085     -0.085       -0.046

Variances/Residual Variances

Y6                          0.002    -0.001     -0.001       -0.001
Y7                          0.050     0.004      0.004        0.003
Y8                          0.155    -0.022     -0.022       -0.012
Y9                          0.103    -0.033     -0.033       -0.009
F                           1.523    -0.043     -0.048       -0.048

Means/Intercepts/Thresholds

[ Y6       ]                0.072    -0.006     -0.006       -0.006
[ Y7       ]                0.223    -0.012     -0.012       -0.011
[ Y9       ]                2.357     0.073      0.073        0.039



     Beginning Time:  20:26:27
        Ending Time:  20:26:28
       Elapsed Time:  00:00:01



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