Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:09 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level CFA
  	with categorical factor indicators, a random
  	intercept factor, and covariates

  montecarlo:
  	names are u1-u4 x1 x2 w;
  	generate = u1-u4(1);
  	categorical = u1-u4;
  	nobservations = 1000;
  	ncsizes = 3;
  	csizes = 40 (5) 50 (10) 20 (15);
  	seed = 58459;
  	nreps = 1;
  	save = ex9.7.dat;
  	within = x1 x2;
  	between = w;

  ANALYSIS:	
  	TYPE IS TWOLEVEL;

  MODEL POPULATION:

  	%Within%
  	x1-x2@1;

  	fw BY u1@1
  	u2*1
  	u3*1
  	u4*1;
  	fw ON x1*1 x2*.5;
  	fw*1;

  	%Between%
  	[w@0]; w@.7;

  	fb BY u1@1
  	u2*1
  	u3*1
  	u4*1;
  	fb ON w*.5;
  	fb*.4;

  MODEL:
  	
  	
  	%Within%

  	fw BY u1@1
  	u2*1
  	u3*1
  	u4*1;
  	fw ON x1*1 x2*.5;
  	fw*1;

  	%Between%

  	fb BY u1@1
  	u2*1
  	u3*1
  	u4*1;
  	fb ON w*.5;
  	fb*.4;

  output:
  	tech8 tech9;



INPUT READING TERMINATED NORMALLY



this is an example of a two-level CFA
with categorical factor indicators, a random
intercept factor, and covariates

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of replications
    Requested                                                    1
    Completed                                                    1
Value of seed                                                58459

Number of dependent variables                                    4
Number of independent variables                                  3
Number of continuous latent variables                            2

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Observed independent variables
   X1          X2          W

Continuous latent variables
   FW          FB

Variables with special functions

  Within variables
   X1          X2

  Between variables
   W


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-02
    Relative loglikelihood change                        0.100D-05
    Derivative                                           0.100D-02
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-02
  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-02
  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
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            2
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON


SUMMARY OF DATA FOR THE FIRST REPLICATION

     Cluster information

       Size (s)    Number of clusters of Size s

          5            40
         10            50
         15            20


SAMPLE STATISTICS FOR THE FIRST REPLICATION


     SAMPLE STATISTICS


           Means
              X1            X2            W
              ________      ________      ________
 1              0.021        -0.007        -0.154


           Covariances
              X1            X2            W
              ________      ________      ________
 X1             0.952
 X2            -0.006         1.088
 W             -0.004         0.025         0.615


           Correlations
              X1            X2            W
              ________      ________      ________
 X1             1.000
 X2            -0.006         1.000
 W             -0.005         0.030         1.000




MODEL FIT INFORMATION

Number of Free Parameters                       15

Loglikelihood

    H0 Value

        Mean                             -2352.335
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000        -2352.335      -2352.335
           0.980       0.000        -2352.335      -2352.335
           0.950       0.000        -2352.335      -2352.335
           0.900       0.000        -2352.335      -2352.335
           0.800       0.000        -2352.335      -2352.335
           0.700       0.000        -2352.335      -2352.335
           0.500       0.000        -2352.335      -2352.335
           0.300       0.000        -2352.335      -2352.335
           0.200       0.000        -2352.335      -2352.335
           0.100       0.000        -2352.335      -2352.335
           0.050       0.000        -2352.335      -2352.335
           0.020       0.000        -2352.335      -2352.335
           0.010       0.000        -2352.335      -2352.335

Information Criteria

    Akaike (AIC)

        Mean                              4734.669
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4734.669       4734.669
           0.980       0.000         4734.669       4734.669
           0.950       0.000         4734.669       4734.669
           0.900       0.000         4734.669       4734.669
           0.800       0.000         4734.669       4734.669
           0.700       0.000         4734.669       4734.669
           0.500       0.000         4734.669       4734.669
           0.300       0.000         4734.669       4734.669
           0.200       0.000         4734.669       4734.669
           0.100       0.000         4734.669       4734.669
           0.050       0.000         4734.669       4734.669
           0.020       0.000         4734.669       4734.669
           0.010       0.000         4734.669       4734.669

    Bayesian (BIC)

        Mean                              4808.286
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4808.286       4808.286
           0.980       0.000         4808.286       4808.286
           0.950       0.000         4808.286       4808.286
           0.900       0.000         4808.286       4808.286
           0.800       0.000         4808.286       4808.286
           0.700       0.000         4808.286       4808.286
           0.500       0.000         4808.286       4808.286
           0.300       0.000         4808.286       4808.286
           0.200       0.000         4808.286       4808.286
           0.100       0.000         4808.286       4808.286
           0.050       0.000         4808.286       4808.286
           0.020       0.000         4808.286       4808.286
           0.010       0.000         4808.286       4808.286

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

        Mean                              4760.645
        Std Dev                              0.000
        Number of successful computations        1

             Proportions                   Percentiles
        Expected    Observed         Expected       Observed
           0.990       0.000         4760.645       4760.645
           0.980       0.000         4760.645       4760.645
           0.950       0.000         4760.645       4760.645
           0.900       0.000         4760.645       4760.645
           0.800       0.000         4760.645       4760.645
           0.700       0.000         4760.645       4760.645
           0.500       0.000         4760.645       4760.645
           0.300       0.000         4760.645       4760.645
           0.200       0.000         4760.645       4760.645
           0.100       0.000         4760.645       4760.645
           0.050       0.000         4760.645       4760.645
           0.020       0.000         4760.645       4760.645
           0.010       0.000         4760.645       4760.645



MODEL RESULTS

                              ESTIMATES              S. E.     M. S. E.  95%  % Sig
                 Population   Average   Std. Dev.   Average             Cover Coeff
Within Level

 FW       BY
  U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2                  1.000     1.2344     0.0000     0.1769     0.0549 1.000 1.000
  U3                  1.000     1.3080     0.0000     0.1705     0.0949 1.000 1.000
  U4                  1.000     1.2960     0.0000     0.1675     0.0876 1.000 1.000

 FW         ON
  X1                  1.000     0.8344     0.0000     0.0890     0.0274 1.000 1.000
  X2                  0.500     0.3870     0.0000     0.0471     0.0128 0.000 1.000

 Residual Variances
  FW                  1.000     0.6605     0.0000     0.1353     0.1152 0.000 1.000

Between Level

 FB       BY
  U1                  1.000     1.0000     0.0000     0.0000     0.0000 1.000 0.000
  U2                  1.000     1.5645     0.0000     0.5985     0.3187 1.000 1.000
  U3                  1.000     1.3676     0.0000     0.4245     0.1351 1.000 1.000
  U4                  1.000     1.7137     0.0000     0.5953     0.5094 1.000 1.000

 FB         ON
  W                   0.500     0.2428     0.0000     0.0828     0.0662 0.000 1.000

 Thresholds
  U1$1                0.000     0.0106     0.0000     0.0870     0.0001 1.000 0.000
  U2$1                0.000     0.1350     0.0000     0.0962     0.0182 1.000 0.000
  U3$1                0.000     0.0634     0.0000     0.0938     0.0040 1.000 0.000
  U4$1                0.000    -0.0165     0.0000     0.1113     0.0003 1.000 0.000

 Residual Variances
  FB                  0.400     0.1103     0.0000     0.0618     0.0839 0.000 0.000


QUALITY OF NUMERICAL RESULTS

     Average Condition Number for the Information Matrix      0.160E-02
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1                  0             0             0             0


           NU
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              X2            W
              ________      ________
 1                  0             0


           LAMBDA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 U1                 0             0             0             0             0
 U2                 1             0             0             0             0
 U3                 2             0             0             0             0
 U4                 3             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              X2            W
              ________      ________
 X2                 0
 W                  0             0


           ALPHA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           BETA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW                 0             0             4             5             0
 FB                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW                 6
 FB                 0             0
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1                 12            13            14            15


           NU
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              X2            W
              ________      ________
 1                  0             0


           LAMBDA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 U1                 0             0             0             0             0
 U2                 0             7             0             0             0
 U3                 0             8             0             0             0
 U4                 0             9             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           THETA
              X2            W
              ________      ________
 X2                 0
 W                  0             0


           ALPHA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           BETA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW                 0             0             0             0             0
 FB                 0             0             0             0            10
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW                 0
 FB                 0            11
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


     STARTING VALUES FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              X2            W
              ________      ________
 1              0.000         0.000


           LAMBDA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 U1             1.000         0.000         0.000         0.000         0.000
 U2             1.000         0.000         0.000         0.000         0.000
 U3             1.000         0.000         0.000         0.000         0.000
 U4             1.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           THETA
              X2            W
              ________      ________
 X2             0.000
 W              0.000         0.000


           ALPHA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             0.000         0.000         1.000         0.500         0.000
 FB             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
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             1.000
 FB             0.000         0.000
 X1             0.000         0.000         0.500
 X2             0.000         0.000         0.000         0.500
 W              0.000         0.000         0.000         0.000         0.000


     STARTING VALUES FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              X2            W
              ________      ________
 1              0.000         0.000


           LAMBDA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 U1             0.000         1.000         0.000         0.000         0.000
 U2             0.000         1.000         0.000         0.000         0.000
 U3             0.000         1.000         0.000         0.000         0.000
 U4             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 U1             0.000
 U2             0.000         0.000
 U3             0.000         0.000         0.000
 U4             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
 W              0.000         0.000         0.000         0.000         0.000


           THETA
              X2            W
              ________      ________
 X2             0.000
 W              0.000         0.000


           ALPHA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             0.000         0.000         0.000         0.000         0.000
 FB             0.000         0.000         0.000         0.000         0.500
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             0.000
 FB             0.000         0.400
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.500


     POPULATION VALUES FOR WITHIN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              X2            W
              ________      ________
 1              0.000         0.000


           LAMBDA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 U1             1.000         0.000         0.000         0.000         0.000
 U2             1.000         0.000         0.000         0.000         0.000
 U3             1.000         0.000         0.000         0.000         0.000
 U4             1.000         0.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 U1             0.000
 U2             0.000         0.000
 U3             0.000         0.000         0.000
 U4             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
 W              0.000         0.000         0.000         0.000         0.000


           THETA
              X2            W
              ________      ________
 X2             0.000
 W              0.000         0.000


           ALPHA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             0.000         0.000         1.000         0.500         0.000
 FB             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
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             1.000
 FB             0.000         0.000
 X1             0.000         0.000         1.000
 X2             0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000


     POPULATION VALUES FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000


           NU
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              X2            W
              ________      ________
 1              0.000         0.000


           LAMBDA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 U1             0.000         1.000         0.000         0.000         0.000
 U2             0.000         1.000         0.000         0.000         0.000
 U3             0.000         1.000         0.000         0.000         0.000
 U4             0.000         1.000         0.000         0.000         0.000
 X1             0.000         0.000         1.000         0.000         0.000
 X2             0.000         0.000         0.000         1.000         0.000
 W              0.000         0.000         0.000         0.000         1.000


           THETA
              U1            U2            U3            U4            X1
              ________      ________      ________      ________      ________
 U1             0.000
 U2             0.000         0.000
 U3             0.000         0.000         0.000
 U4             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
 W              0.000         0.000         0.000         0.000         0.000


           THETA
              X2            W
              ________      ________
 X2             0.000
 W              0.000         0.000


           ALPHA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           BETA
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             0.000         0.000         0.000         0.000         0.000
 FB             0.000         0.000         0.000         0.000         0.500
 X1             0.000         0.000         0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              FW            FB            X1            X2            W
              ________      ________      ________      ________      ________
 FW             0.000
 FB             0.000         0.400
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.700


TECHNICAL 8 OUTPUT


  TECHNICAL 8 OUTPUT FOR REPLICATION 1


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.23613274D+04    0.0000000    0.0000000  EM
              2 -0.23540324D+04    7.2949791    0.0030894  EM
              3 -0.23528562D+04    1.1762740    0.0004997  EM
              4 -0.23525291D+04    0.3271132    0.0001390  EM
              5 -0.23524202D+04    0.1088548    0.0000463  EM
              6 -0.23523760D+04    0.0441996    0.0000188  EM
              7 -0.23523554D+04    0.0206495    0.0000088  EM
              8 -0.23523450D+04    0.0103375    0.0000044  EM
              9 -0.23523397D+04    0.0053316    0.0000023  EM
             10 -0.23523369D+04    0.0027870    0.0000012  EM
             11 -0.23523354D+04    0.0014677    0.0000006  EM
             12 -0.23523347D+04    0.0007772    0.0000003  EM


TECHNICAL 9 OUTPUT

  Error messages for each replication (if any)



SAVEDATA INFORMATION

  Order of variables

    U1
    U2
    U3
    U4
    X1
    X2
    W
    CLUSTER

  Save file
    ex9.7.dat

  Save file format           Free
  Save file record length    10000


     Beginning Time:  14:09:04
        Ending Time:  14:09:06
       Elapsed Time:  00:00:02



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