Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:48 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of an EFA with covariates (MIMIC)
      with continuous factor indicators and direct effects
  DATA:	FILE IS ex5.24.dat;
  VARIABLE:	NAMES ARE y1-y8 x1 x2;
  MODEL:	f1-f2 BY y1-y8(*1);
      	f1-f2 ON x1-x2;
      	y1 ON x1;
      	y8 ON x2;
  OUTPUT:	TECH1;



INPUT READING TERMINATED NORMALLY



this is an example of an EFA with covariates (MIMIC)
with continuous factor indicators and direct effects

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of dependent variables                                    8
Number of independent variables                                  2
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5          Y6
   Y7          Y8

Observed independent variables
   X1          X2

Continuous latent variables

  EFA factors
  *1:   F1          F2


Estimator                                                       ML
Rotation                                                    GEOMIN
Row standardization                                    CORRELATION
Type of rotation                                           OBLIQUE
Epsilon value                                               Varies
Information matrix                                        OBSERVED
Maximum number of iterations                                  1000
Convergence criterion                                    0.500D-04
Maximum number of steepest descent iterations                   20
Optimization Specifications for the Exploratory Factor Analysis
Rotation Algorithm
  Number of random starts                                       30
  Maximum number of iterations                               10000
  Derivative convergence criterion                       0.100D-04

Input data file(s)
  ex5.24.dat

Input data format  FREE



THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       37

Loglikelihood

          H0 Value                       -4630.127
          H1 Value                       -4614.993

Information Criteria

          Akaike (AIC)                    9334.254
          Bayesian (BIC)                  9490.194
          Sample-Size Adjusted BIC        9372.754
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                             30.268
          Degrees of Freedom                    23
          P-Value                           0.1419

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.025
          90 Percent C.I.                    0.000  0.047
          Probability RMSEA <= .05           0.970

CFI/TLI

          CFI                                0.998
          TLI                                0.997

Chi-Square Test of Model Fit for the Baseline Model

          Value                           4254.549
          Degrees of Freedom                    44
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value                              0.010



MODEL RESULTS

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

 F1       BY
    Y1                 0.754      0.040     18.906      0.000
    Y2                 0.861      0.049     17.435      0.000
    Y3                 0.820      0.043     19.182      0.000
    Y4                 0.855      0.049     17.572      0.000
    Y5                 0.773      0.049     15.653      0.000
    Y6                -0.010      0.041     -0.247      0.805
    Y7                 0.003      0.022      0.125      0.900
    Y8                 0.009      0.040      0.226      0.821

 F2       BY
    Y1                 0.000      0.021      0.003      0.997
    Y2                -0.054      0.039     -1.375      0.169
    Y3                -0.004      0.025     -0.162      0.871
    Y4                 0.118      0.039      3.031      0.002
    Y5                 0.177      0.040      4.423      0.000
    Y6                 0.861      0.045     19.061      0.000
    Y7                 0.840      0.038     21.823      0.000
    Y8                 0.786      0.044     17.951      0.000

 F1       ON
    X1                 0.537      0.055      9.768      0.000
    X2                 0.271      0.050      5.390      0.000

 F2       ON
    X1                 0.946      0.061     15.571      0.000
    X2                 0.556      0.056      9.914      0.000

 Y1       ON
    X1                 0.387      0.039      9.855      0.000

 Y8       ON
    X2                 0.577      0.039     14.800      0.000

 F2       WITH
    F1                 0.593      0.039     15.216      0.000

 Intercepts
    Y1                 0.024      0.043      0.564      0.573
    Y2                -0.029      0.046     -0.641      0.521
    Y3                 0.023      0.045      0.516      0.606
    Y4                -0.020      0.049     -0.399      0.690
    Y5                 0.024      0.049      0.485      0.628
    Y6                 0.075      0.049      1.553      0.121
    Y7                 0.021      0.046      0.464      0.643
    Y8                 0.035      0.046      0.760      0.447

 Residual Variances
    Y1                 0.339      0.026     12.942      0.000
    Y2                 0.345      0.029     12.037      0.000
    Y3                 0.342      0.028     12.421      0.000
    Y4                 0.328      0.027     11.926      0.000
    Y5                 0.393      0.030     13.086      0.000
    Y6                 0.425      0.039     10.851      0.000
    Y7                 0.335      0.034      9.956      0.000
    Y8                 0.415      0.036     11.577      0.000
    F1                 1.000      0.000    999.000    999.000
    F2                 1.000      0.000    999.000    999.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.255E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     TECHNICAL 1 OUTPUT FOR THE UNROTATED SOLUTION


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1           0             1             2             3             4


           NU
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
      1           5             6             0             0             0


           LAMBDA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 7             8             0             0             0
 Y3                 9            10             0             0             0
 Y4                11            12             0             0             0
 Y5                13            14             0             0             0
 Y6                15            16             0             0             0
 Y7                17            18             0             0             0
 Y8                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           LAMBDA
              X2
              ________
 Y1                 0
 Y2                 0
 Y3                 0
 Y4                 0
 Y5                 0
 Y6                 0
 Y7                 0
 Y8                 0
 X1                 0
 X2                 0


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0            19
 Y3                 0             0            20
 Y4                 0             0             0            21
 Y5                 0             0             0             0            22
 Y6                 0             0             0             0             0
 Y7                 0             0             0             0             0
 Y8                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           THETA
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
 Y6                23
 Y7                 0            24
 Y8                 0             0             0
 X1                 0             0             0             0
 X2                 0             0             0             0             0


           ALPHA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
      1           0             0            25            26             0


           ALPHA
              X2
              ________
      1           0


           BETA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1                 0             0             0             0            27
 F2                 0             0             0             0            29
 Y1                31             0             0             0            32
 Y8                33            34             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           BETA
              X2
              ________
 F1                28
 F2                30
 Y1                 0
 Y8                35
 X1                 0
 X2                 0


           PSI
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1                 0
 F2                 0             0
 Y1                 0             0            36
 Y8                 0             0             0            37
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           PSI
              X2
              ________
 X2                 0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.000        -0.034         0.019        -0.024         0.020


           NU
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
      1         0.077         0.023         0.000         0.000         0.000


           LAMBDA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         1.000         0.000         0.000
 Y2             0.932         0.195         0.000         0.000         0.000
 Y3             0.943         0.133         0.000         0.000         0.000
 Y4             1.138         0.053         0.000         0.000         0.000
 Y5             1.118        -0.006         0.000         0.000         0.000
 Y6             1.049        -0.720         0.000         0.000         0.000
 Y7             1.038        -0.745         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         1.000         0.000
 X1             0.000         0.000         0.000         0.000         1.000
 X2             0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X2
              ________
 Y1             0.000
 Y2             0.000
 Y3             0.000
 Y4             0.000
 Y5             0.000
 Y6             0.000
 Y7             0.000
 Y8             0.000
 X1             0.000
 X2             1.000


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.348
 Y3             0.000         0.000         0.351
 Y4             0.000         0.000         0.000         0.326
 Y5             0.000         0.000         0.000         0.000         0.385
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
 Y6             0.452
 Y7             0.000         0.296
 Y8             0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000


           ALPHA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
      1         0.000         0.000        -0.008         0.109        -0.073


           ALPHA
              X2
              ________
      1         0.127


           BETA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1             0.000         0.000         0.000         0.000         0.000
 F2             0.000         0.000         0.000         0.000         0.000
 Y1             1.079         0.000         0.000         0.000         0.000
 Y8             1.142        -0.825         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000


           BETA
              X2
              ________
 F1             0.000
 F2             0.000
 Y1             0.000
 Y8             0.000
 X1             0.000
 X2             0.000


           PSI
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1             1.000
 F2             0.000         1.000
 Y1             0.000         0.000         0.427
 Y8             0.000         0.000         0.000         0.691
 X1             0.000         0.000         0.000         0.000         0.990
 X2             0.000         0.000         0.000         0.000         0.070


           PSI
              X2
              ________
 X2             0.945


     TECHNICAL 1 OUTPUT FOR THE ROTATED SOLUTION


     PARAMETER SPECIFICATION


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1           0             1             2             3             4


           NU
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
      1           5             6             0             0             0


           LAMBDA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 7             8             0             0             0
 Y3                 9            10             0             0             0
 Y4                11            12             0             0             0
 Y5                13            14             0             0             0
 Y6                15            16             0             0             0
 Y7                17            18             0             0             0
 Y8                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           LAMBDA
              X2
              ________
 Y1                 0
 Y2                 0
 Y3                 0
 Y4                 0
 Y5                 0
 Y6                 0
 Y7                 0
 Y8                 0
 X1                 0
 X2                 0


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0            19
 Y3                 0             0            20
 Y4                 0             0             0            21
 Y5                 0             0             0             0            22
 Y6                 0             0             0             0             0
 Y7                 0             0             0             0             0
 Y8                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           THETA
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
 Y6                23
 Y7                 0            24
 Y8                 0             0             0
 X1                 0             0             0             0
 X2                 0             0             0             0             0


           ALPHA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
      1           0             0            25            26             0


           ALPHA
              X2
              ________
      1           0


           BETA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1                 0             0             0             0            27
 F2                 0             0             0             0            29
 Y1                31            32             0             0            33
 Y8                34            35             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           BETA
              X2
              ________
 F1                28
 F2                30
 Y1                 0
 Y8                36
 X1                 0
 X2                 0


           PSI
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1                 0
 F2                37             0
 Y1                 0             0            38
 Y8                 0             0             0            39
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0


           PSI
              X2
              ________
 X2                 0


     STARTING VALUES


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
      1         0.000        -0.034         0.019        -0.024         0.020


           NU
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
      1         0.077         0.023         0.000         0.000         0.000


           LAMBDA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         1.000         0.000         0.000
 Y2             0.000         0.000         0.000         0.000         0.000
 Y3             0.000         0.000         0.000         0.000         0.000
 Y4             0.000         0.000         0.000         0.000         0.000
 Y5             0.000         0.000         0.000         0.000         0.000
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         1.000         0.000
 X1             0.000         0.000         0.000         0.000         1.000
 X2             0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X2
              ________
 Y1             0.000
 Y2             0.000
 Y3             0.000
 Y4             0.000
 Y5             0.000
 Y6             0.000
 Y7             0.000
 Y8             0.000
 X1             0.000
 X2             1.000


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.627
 Y3             0.000         0.000         0.629
 Y4             0.000         0.000         0.000         0.812
 Y5             0.000         0.000         0.000         0.000         0.817
 Y6             0.000         0.000         0.000         0.000         0.000
 Y7             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000


           THETA
              Y6            Y7            Y8            X1            X2
              ________      ________      ________      ________      ________
 Y6             1.036
 Y7             0.000         0.964
 Y8             0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000


           ALPHA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
      1         0.000         0.000        -0.008         0.109        -0.073


           ALPHA
              X2
              ________
      1         0.127


           BETA
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1             0.000         0.000         0.000         0.000         0.000
 F2             0.000         0.000         0.000         0.000         0.000
 Y1             0.000         0.000         0.000         0.000         0.000
 Y8             0.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000


           BETA
              X2
              ________
 F1             0.000
 F2             0.000
 Y1             0.000
 Y8             0.000
 X1             0.000
 X2             0.000


           PSI
              F1            F2            Y1            Y8            X1
              ________      ________      ________      ________      ________
 F1             1.000
 F2             0.000         1.000
 Y1             0.000         0.000         0.796
 Y8             0.000         0.000         0.000         1.338
 X1             0.000         0.000         0.000         0.000         0.990
 X2             0.000         0.000         0.000         0.000         0.070


           PSI
              X2
              ________
 X2             0.945


     Beginning Time:  17:48:37
        Ending Time:  17:48:37
       Elapsed Time:  00:00:00



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