Mplus VERSION 7
MUTHEN & MUTHEN
09/22/2012  10:03 PM

INPUT INSTRUCTIONS

  title:
  	this is an example of CFA with a non-parametric
  	representation of a non-normal factor
  montecarlo:
  	names are y1-y5;
  	genclasses = c(3);
  	classes = c(3);
  	nobs = 500;
  	seed = 3454367;
  	nrep = 1;
  	save = ex7.26.dat;

  analysis:
  	type = mixture;

  model population:

  	%overall%

  	y1-y5*.25;
  	f by y1@1 y2-y5*.75;
  	[f@0];
  	f@0;

  	[c#1*-2.5 c#2*-1.5];
  	
  	%c#1%
  	[f*4];

  	%c#2%
  	[f*2];

  model:
  	
  	%overall%
  	%overall%

  	y1-y5*.25;
  	f by y1@1 y2-y5*.75;
  	[f@0];
  	f@0;

  	[c#1*-2.5 c#2*-1.5];
  	
  	%c#1%
  	[f*4];

  	%c#2%
  	[f*2];

  output:
  	tech8 tech9;	
  	



INPUT READING TERMINATED NORMALLY




this is an example of CFA with a non-parametric
representation of a non-normal factor

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                              3454367

Number of dependent variables                                    5
Number of independent variables                                  0
Number of continuous latent variables                            1
Number of categorical latent variables                           1

Observed dependent variables

  Continuous
   Y1          Y2          Y3          Y4          Y5

Continuous latent variables
   F

Categorical latent variables
   C


Estimator                                                      MLR
Information matrix                                        OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
  Maximum number of iterations                                 100
  Convergence criterion                                  0.100D-05
Optimization Specifications for the EM Algorithm
  Maximum number of iterations                                 500
  Convergence criteria
    Loglikelihood change                                 0.100D-06
    Relative loglikelihood change                        0.100D-06
    Derivative                                           0.100D-05
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-05
  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-05
  Basis for M step termination                           ITERATION
  Maximum value for logit thresholds                            15
  Minimum value for logit thresholds                           -15
  Minimum expected cell size for chi-square              0.100D-01
Optimization algorithm                                         EMA


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.566         0.418         0.463         0.406         0.443


           Covariances
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.549
 Y2             0.969         1.007
 Y3             1.014         0.741         1.035
 Y4             1.025         0.758         0.763         1.022
 Y5             0.962         0.719         0.720         0.761         0.980


           Correlations
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             1.000
 Y2             0.776         1.000
 Y3             0.800         0.726         1.000
 Y4             0.814         0.747         0.741         1.000
 Y5             0.781         0.724         0.714         0.761         1.000




MODEL FIT INFORMATION

Number of Free Parameters                       18

Loglikelihood

    H0 Value

        Mean                             -2183.081
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2183.081      -2183.081
           0.980       0.000        -2183.081      -2183.081
           0.950       0.000        -2183.081      -2183.081
           0.900       0.000        -2183.081      -2183.081
           0.800       0.000        -2183.081      -2183.081
           0.700       0.000        -2183.081      -2183.081
           0.500       0.000        -2183.081      -2183.081
           0.300       0.000        -2183.081      -2183.081
           0.200       0.000        -2183.081      -2183.081
           0.100       0.000        -2183.081      -2183.081
           0.050       0.000        -2183.081      -2183.081
           0.020       0.000        -2183.081      -2183.081
           0.010       0.000        -2183.081      -2183.081

Information Criteria

    Akaike (AIC)

        Mean                              4402.163
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4402.163       4402.163
           0.980       0.000         4402.163       4402.163
           0.950       0.000         4402.163       4402.163
           0.900       0.000         4402.163       4402.163
           0.800       0.000         4402.163       4402.163
           0.700       0.000         4402.163       4402.163
           0.500       0.000         4402.163       4402.163
           0.300       0.000         4402.163       4402.163
           0.200       0.000         4402.163       4402.163
           0.100       0.000         4402.163       4402.163
           0.050       0.000         4402.163       4402.163
           0.020       0.000         4402.163       4402.163
           0.010       0.000         4402.163       4402.163

    Bayesian (BIC)

        Mean                              4478.026
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4478.026       4478.026
           0.980       0.000         4478.026       4478.026
           0.950       0.000         4478.026       4478.026
           0.900       0.000         4478.026       4478.026
           0.800       0.000         4478.026       4478.026
           0.700       0.000         4478.026       4478.026
           0.500       0.000         4478.026       4478.026
           0.300       0.000         4478.026       4478.026
           0.200       0.000         4478.026       4478.026
           0.100       0.000         4478.026       4478.026
           0.050       0.000         4478.026       4478.026
           0.020       0.000         4478.026       4478.026
           0.010       0.000         4478.026       4478.026

    Sample-Size Adjusted BIC (n* = (n + 2) / 24)

        Mean                              4420.893
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4420.893       4420.893
           0.980       0.000         4420.893       4420.893
           0.950       0.000         4420.893       4420.893
           0.900       0.000         4420.893       4420.893
           0.800       0.000         4420.893       4420.893
           0.700       0.000         4420.893       4420.893
           0.500       0.000         4420.893       4420.893
           0.300       0.000         4420.893       4420.893
           0.200       0.000         4420.893       4420.893
           0.100       0.000         4420.893       4420.893
           0.050       0.000         4420.893       4420.893
           0.020       0.000         4420.893       4420.893
           0.010       0.000         4420.893       4420.893



FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL

    Latent
   Classes

       1         32.00001          0.06400
       2         85.06894          0.17014
       3        382.93105          0.76586


FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES

    Latent
   Classes

       1         32.00001          0.06400
       2         85.06896          0.17014
       3        382.93103          0.76586


CLASSIFICATION QUALITY

     Entropy                         0.999


CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP

Class Counts and Proportions

    Latent
   Classes

       1               32          0.06400
       2               85          0.17000
       3              383          0.76600


Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)

           1        2        3

    1   1.000    0.000    0.000
    2   0.000    1.000    0.000
    3   0.000    0.000    1.000


MODEL RESULTS

                           ESTIMATES              S. E.     M. S. E.  95%  % Sig
              Population   Average   Std. Dev.   Average             Cover Coeff
Latent Class 1

 F        BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               0.750     0.7485     0.0000     0.0273     0.0000 1.000 1.000
  Y3               0.750     0.7658     0.0000     0.0259     0.0002 1.000 1.000
  Y4               0.750     0.7757     0.0000     0.0241     0.0007 1.000 1.000
  Y5               0.750     0.7482     0.0000     0.0233     0.0000 1.000 1.000

 Means
  F                4.000     3.9278     0.0000     0.0788     0.0052 1.000 1.000

 Intercepts
  Y1               0.000    -0.0191     0.0000     0.0250     0.0004 1.000 0.000
  Y2               0.000    -0.0201     0.0000     0.0271     0.0004 1.000 0.000
  Y3               0.000     0.0147     0.0000     0.0258     0.0002 1.000 0.000
  Y4               0.000    -0.0480     0.0000     0.0245     0.0023 1.000 0.000
  Y5               0.000     0.0051     0.0000     0.0252     0.0000 1.000 0.000

 Variances
  F                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y1               0.250     0.2452     0.0000     0.0144     0.0000 1.000 1.000
  Y2               0.250     0.2766     0.0000     0.0179     0.0007 1.000 1.000
  Y3               0.250     0.2708     0.0000     0.0156     0.0004 1.000 1.000
  Y4               0.250     0.2380     0.0000     0.0136     0.0001 1.000 1.000
  Y5               0.250     0.2500     0.0000     0.0152     0.0000 1.000 1.000

Latent Class 2

 F        BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               0.750     0.7485     0.0000     0.0273     0.0000 1.000 1.000
  Y3               0.750     0.7658     0.0000     0.0259     0.0002 1.000 1.000
  Y4               0.750     0.7757     0.0000     0.0241     0.0007 1.000 1.000
  Y5               0.750     0.7482     0.0000     0.0233     0.0000 1.000 1.000

 Means
  F                2.000     1.9628     0.0000     0.0471     0.0014 1.000 1.000

 Intercepts
  Y1               0.000    -0.0191     0.0000     0.0250     0.0004 1.000 0.000
  Y2               0.000    -0.0201     0.0000     0.0271     0.0004 1.000 0.000
  Y3               0.000     0.0147     0.0000     0.0258     0.0002 1.000 0.000
  Y4               0.000    -0.0480     0.0000     0.0245     0.0023 1.000 0.000
  Y5               0.000     0.0051     0.0000     0.0252     0.0000 1.000 0.000

 Variances
  F                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y1               0.250     0.2452     0.0000     0.0144     0.0000 1.000 1.000
  Y2               0.250     0.2766     0.0000     0.0179     0.0007 1.000 1.000
  Y3               0.250     0.2708     0.0000     0.0156     0.0004 1.000 1.000
  Y4               0.250     0.2380     0.0000     0.0136     0.0001 1.000 1.000
  Y5               0.250     0.2500     0.0000     0.0152     0.0000 1.000 1.000

Latent Class 3

 F        BY
  Y1               1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  Y2               0.750     0.7485     0.0000     0.0273     0.0000 1.000 1.000
  Y3               0.750     0.7658     0.0000     0.0259     0.0002 1.000 1.000
  Y4               0.750     0.7757     0.0000     0.0241     0.0007 1.000 1.000
  Y5               0.750     0.7482     0.0000     0.0233     0.0000 1.000 1.000

 Means
  F                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Intercepts
  Y1               0.000    -0.0191     0.0000     0.0250     0.0004 1.000 0.000
  Y2               0.000    -0.0201     0.0000     0.0271     0.0004 1.000 0.000
  Y3               0.000     0.0147     0.0000     0.0258     0.0002 1.000 0.000
  Y4               0.000    -0.0480     0.0000     0.0245     0.0023 1.000 0.000
  Y5               0.000     0.0051     0.0000     0.0252     0.0000 1.000 0.000

 Variances
  F                0.000     0.0000     0.0000     0.0000     0.0000 1.000 0.000

 Residual Variances
  Y1               0.250     0.2452     0.0000     0.0144     0.0000 1.000 1.000
  Y2               0.250     0.2766     0.0000     0.0179     0.0007 1.000 1.000
  Y3               0.250     0.2708     0.0000     0.0156     0.0004 1.000 1.000
  Y4               0.250     0.2380     0.0000     0.0136     0.0001 1.000 1.000
  Y5               0.250     0.2500     0.0000     0.0152     0.0000 1.000 1.000

Categorical Latent Variables

 Means
  C#1             -2.500    -2.4821     0.0000     0.1840     0.0003 1.000 1.000
  C#2             -1.500    -1.5044     0.0000     0.1199     0.0000 1.000 1.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.761E-03
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR LATENT CLASS 1


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1                  1             2             3             4             5


           LAMBDA
              F
              ________
 Y1                 0
 Y2                 6
 Y3                 7
 Y4                 8
 Y5                 9


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                10
 Y2                 0            11
 Y3                 0             0            12
 Y4                 0             0             0            13
 Y5                 0             0             0             0            14


           ALPHA
              F
              ________
 1                 15


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS 2


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1                  1             2             3             4             5


           LAMBDA
              F
              ________
 Y1                 0
 Y2                 6
 Y3                 7
 Y4                 8
 Y5                 9


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                10
 Y2                 0            11
 Y3                 0             0            12
 Y4                 0             0             0            13
 Y5                 0             0             0             0            14


           ALPHA
              F
              ________
 1                 16


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS 3


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1                  1             2             3             4             5


           LAMBDA
              F
              ________
 Y1                 0
 Y2                 6
 Y3                 7
 Y4                 8
 Y5                 9


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1                10
 Y2                 0            11
 Y3                 0             0            12
 Y4                 0             0             0            13
 Y5                 0             0             0             0            14


           ALPHA
              F
              ________
 1                  0


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2           C#3
              ________      ________      ________
 1                 17            18             0


     STARTING VALUES FOR LATENT CLASS 1


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 Y1             1.000
 Y2             0.750
 Y3             0.750
 Y4             0.750
 Y5             0.750


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 Y5             0.000         0.000         0.000         0.000         0.250


           ALPHA
              F
              ________
 1              4.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              0.000


     STARTING VALUES FOR LATENT CLASS 2


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 Y1             1.000
 Y2             0.750
 Y3             0.750
 Y4             0.750
 Y5             0.750


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 Y5             0.000         0.000         0.000         0.000         0.250


           ALPHA
              F
              ________
 1              2.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              0.000


     STARTING VALUES FOR LATENT CLASS 3


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 Y1             1.000
 Y2             0.750
 Y3             0.750
 Y4             0.750
 Y5             0.750


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 Y5             0.000         0.000         0.000         0.000         0.250


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              0.000


     STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2           C#3
              ________      ________      ________
 1             -2.500        -1.500         0.000


     POPULATION VALUES FOR LATENT CLASS 1


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 Y1             1.000
 Y2             0.750
 Y3             0.750
 Y4             0.750
 Y5             0.750


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 Y5             0.000         0.000         0.000         0.000         0.250


           ALPHA
              F
              ________
 1              4.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              0.000


     POPULATION VALUES FOR LATENT CLASS 2


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 Y1             1.000
 Y2             0.750
 Y3             0.750
 Y4             0.750
 Y5             0.750


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 Y5             0.000         0.000         0.000         0.000         0.250


           ALPHA
              F
              ________
 1              2.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              0.000


     POPULATION VALUES FOR LATENT CLASS 3


           NU
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 Y1             1.000
 Y2             0.750
 Y3             0.750
 Y4             0.750
 Y5             0.750


           THETA
              Y1            Y2            Y3            Y4            Y5
              ________      ________      ________      ________      ________
 Y1             0.250
 Y2             0.000         0.250
 Y3             0.000         0.000         0.250
 Y4             0.000         0.000         0.000         0.250
 Y5             0.000         0.000         0.000         0.000         0.250


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              0.000


     POPULATION VALUES FOR LATENT CLASS REGRESSION MODEL PART


           ALPHA(C)
              C#1           C#2           C#3
              ________      ________      ________
 1             -2.500        -1.500         0.000


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE      CLASS COUNTS    ALGORITHM
     1 -0.21905381D+04    0.0000000    0.0000000     32.000    85.037    EM
                                                    382.963
     2 -0.21830815D+04    7.4565552    0.0034040     32.000    85.068    EM
                                                    382.932
     3 -0.21830813D+04    0.0001745    0.0000001     32.000    85.069    EM
                                                    382.931
     4 -0.21830813D+04    0.0000001    0.0000000     32.000    85.069    EM
                                                    382.931


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    Y1
    Y2
    Y3
    Y4
    Y5
    C

  Save file
    ex7.26.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  22:03:07
        Ending Time:  22:03:07
       Elapsed Time:  00:00:00



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