Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:55 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a CFA with parameter
  	constraints
  DATA:	FILE = ex5.20.dat;
  VARIABLE: 	NAMES = y1-y6;
  MODEL:	f1 BY y1
  	y2-y3(lam2-lam3);
  	f2 BY y4
  	y5-y6(lam5-lam6);
  	f1 (vf1);
  	f2 (vf2);
  	y1-y3 (ve1-ve3);
  	y4-y6 (ve4-ve6);
  MODEL CONSTRAINT:
  	NEW(rel2 rel5 stan3 stan6);
  	rel2 = lam2**2*vf1/(lam2**2*vf1 + ve2);
  	rel5 = lam5**2*vf2/(lam5**2*vf2 + ve5);
  	rel5 = rel2;
  	stan3 = lam3*SQRT(vf1)/SQRT(lam3**2*vf1 + ve3);
  	stan6 = lam6*SQRT(vf2)/SQRT(lam6**2*vf2 + ve6);
  	0 = stan6 - stan3;
  	ve2 > ve5;
  	ve4 > 0;
  OUTPUT:	STANDARDIZED;



INPUT READING TERMINATED NORMALLY



this is an example of a CFA with parameter
constraints

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of dependent variables                                    6
Number of independent variables                                  0
Number of continuous latent variables                            2

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5          Y6

Continuous latent variables
   F1          F2


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)
  ex5.20.dat

Input data format  FREE



THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

          H0 Value                       -3898.949
          H1 Value                       -3896.904

Information Criteria

          Akaike (AIC)                    7831.898
          Bayesian (BIC)                  7903.547
          Sample-Size Adjusted BIC        7849.588
            (n* = (n + 2) / 24)

Chi-Square Test of Model Fit

          Value                              4.090
          Degrees of Freedom                    10
          P-Value                           0.9432

RMSEA (Root Mean Square Error Of Approximation)

          Estimate                           0.000
          90 Percent C.I.                    0.000  0.009
          Probability RMSEA <= .05           0.999

CFI/TLI

          CFI                                1.000
          TLI                                1.006

Chi-Square Test of Model Fit for the Baseline Model

          Value                           1418.024
          Degrees of Freedom                    15
          P-Value                           0.0000

SRMR (Standardized Root Mean Square Residual)

          Value                              0.012



MODEL RESULTS

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

 F1       BY
    Y1                 1.000      0.000    999.000    999.000
    Y2                 1.060      0.052     20.334      0.000
    Y3                 0.998      0.051     19.670      0.000

 F2       BY
    Y4                 1.000      0.000    999.000    999.000
    Y5                 0.876      0.041     21.322      0.000
    Y6                 0.813      0.040     20.574      0.000

 F2       WITH
    F1                -0.024      0.049     -0.495      0.621

 Intercepts
    Y1                -0.019      0.054     -0.355      0.723
    Y2                 0.015      0.054      0.268      0.789
    Y3                 0.022      0.054      0.416      0.677
    Y4                -0.018      0.052     -0.349      0.727
    Y5                -0.015      0.045     -0.340      0.734
    Y6                 0.022      0.044      0.497      0.619

 Variances
    F1                 0.942      0.092     10.230      0.000
    F2                 0.937      0.087     10.755      0.000

 Residual Variances
    Y1                 0.529      0.048     10.957      0.000
    Y2                 0.408      0.037     11.088      0.000
    Y3                 0.509      0.039     13.069      0.000
    Y4                 0.424      0.042     10.138      0.000
    Y5                 0.277      0.025     11.170      0.000
    Y6                 0.336      0.026     13.172      0.000

 New/Additional Parameters
    REL2               0.722      0.024     30.091      0.000
    REL5               0.722      0.024     30.091      0.000
    STAN3              0.805      0.015     52.744      0.000
    STAN6              0.805      0.015     52.744      0.000


STANDARDIZED MODEL RESULTS


STDYX Standardization

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

 F1       BY
    Y1                 0.800      0.022     36.300      0.000
    Y2                 0.850      0.014     60.183      0.000
    Y3                 0.805      0.015     52.744      0.000

 F2       BY
    Y4                 0.830      0.020     40.981      0.000
    Y5                 0.850      0.014     60.183      0.000
    Y6                 0.805      0.015     52.744      0.000

 F2       WITH
    F1                -0.026      0.052     -0.495      0.620

 Intercepts
    Y1                -0.016      0.045     -0.355      0.723
    Y2                 0.012      0.045      0.268      0.789
    Y3                 0.019      0.045      0.416      0.677
    Y4                -0.016      0.045     -0.349      0.727
    Y5                -0.015      0.045     -0.340      0.734
    Y6                 0.022      0.045      0.497      0.619

 Variances
    F1                 1.000      0.000    999.000    999.000
    F2                 1.000      0.000    999.000    999.000

 Residual Variances
    Y1                 0.359      0.035     10.186      0.000
    Y2                 0.278      0.024     11.589      0.000
    Y3                 0.352      0.025     14.305      0.000
    Y4                 0.311      0.034      9.265      0.000
    Y5                 0.278      0.024     11.589      0.000
    Y6                 0.352      0.025     14.305      0.000


STDY Standardization

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

 F1       BY
    Y1                 0.800      0.022     36.300      0.000
    Y2                 0.850      0.014     60.183      0.000
    Y3                 0.805      0.015     52.744      0.000

 F2       BY
    Y4                 0.830      0.020     40.981      0.000
    Y5                 0.850      0.014     60.183      0.000
    Y6                 0.805      0.015     52.744      0.000

 F2       WITH
    F1                -0.026      0.052     -0.495      0.620

 Intercepts
    Y1                -0.016      0.045     -0.355      0.723
    Y2                 0.012      0.045      0.268      0.789
    Y3                 0.019      0.045      0.416      0.677
    Y4                -0.016      0.045     -0.349      0.727
    Y5                -0.015      0.045     -0.340      0.734
    Y6                 0.022      0.045      0.497      0.619

 Variances
    F1                 1.000      0.000    999.000    999.000
    F2                 1.000      0.000    999.000    999.000

 Residual Variances
    Y1                 0.359      0.035     10.186      0.000
    Y2                 0.278      0.024     11.589      0.000
    Y3                 0.352      0.025     14.305      0.000
    Y4                 0.311      0.034      9.265      0.000
    Y5                 0.278      0.024     11.589      0.000
    Y6                 0.352      0.025     14.305      0.000


STD Standardization

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

 F1       BY
    Y1                 0.971      0.047     20.460      0.000
    Y2                 1.029      0.039     26.530      0.000
    Y3                 0.969      0.038     25.182      0.000

 F2       BY
    Y4                 0.968      0.045     21.511      0.000
    Y5                 0.848      0.032     26.290      0.000
    Y6                 0.787      0.032     24.963      0.000

 F2       WITH
    F1                -0.026      0.052     -0.495      0.620

 Intercepts
    Y1                -0.019      0.054     -0.355      0.723
    Y2                 0.015      0.054      0.268      0.789
    Y3                 0.022      0.054      0.416      0.677
    Y4                -0.018      0.052     -0.349      0.727
    Y5                -0.015      0.045     -0.340      0.734
    Y6                 0.022      0.044      0.497      0.619

 Variances
    F1                 1.000      0.000    999.000    999.000
    F2                 1.000      0.000    999.000    999.000

 Residual Variances
    Y1                 0.529      0.048     10.957      0.000
    Y2                 0.408      0.037     11.088      0.000
    Y3                 0.509      0.039     13.069      0.000
    Y4                 0.424      0.042     10.138      0.000
    Y5                 0.277      0.025     11.170      0.000
    Y6                 0.336      0.026     13.172      0.000


R-SQUARE

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

    Y1                 0.641      0.035     18.150      0.000
    Y2                 0.722      0.024     30.091      0.000
    Y3                 0.648      0.025     26.372      0.000
    Y4                 0.689      0.034     20.491      0.000
    Y5                 0.722      0.024     30.091      0.000
    Y6                 0.648      0.025     26.372      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.602E-04
       (ratio of smallest to largest eigenvalue)


     Beginning Time:  22:55:30
        Ending Time:  22:55:30
       Elapsed Time:  00:00:00



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