Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:05 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level CFA with
  	categorical factor indicators, a random intercept
      factor, and covariates
  DATA:	FILE IS ex9.7.dat;
  VARIABLE:	NAMES ARE u1-u4 x1 x2 w clus;
  	CATEGORICAL = u1-u4;
  	WITHIN = x1 x2;
  	BETWEEN = w;
  	CLUSTER = clus;
  	MISSING = ALL (999);
  ANALYSIS:	TYPE = TWOLEVEL;
  MODEL:
  	%WITHIN%
  	fw BY u1-u4;	
  	fw ON x1 x2;
  	%BETWEEN%
  	fb BY u1-u4; 	
  	fb ON w;
  OUTPUT:	TECH1 TECH8;



*** WARNING
  One or more individual-level variables have no variation within a
  cluster for the following clusters.

     Variable   Cluster IDs with no within-cluster variation

      U1          15 18
      U2          64
      U3          10 12
      U4          14 31 33 82

   1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS



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 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

  Cluster variable      CLUS

  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
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            2
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON

Input data file(s)
  ex9.7.dat
Input data format  FREE


SUMMARY OF DATA

     Number of missing data patterns             1
     Number of y missing data patterns           0
     Number of u missing data patterns           1
     Number of clusters                        110



COVARIANCE COVERAGE OF DATA

Minimum covariance coverage value   0.100


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.508          508.000
      Category 2    0.492          492.000
    U2
      Category 1    0.532          532.000
      Category 2    0.468          468.000
    U3
      Category 1    0.518          518.000
      Category 2    0.482          482.000
    U4
      Category 1    0.507          507.000
      Category 2    0.493          493.000



UNIVARIATE SAMPLE STATISTICS


     UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS

         Variable/         Mean/     Skewness/   Minimum/ % with                Percentiles
        Sample Size      Variance    Kurtosis    Maximum  Min/Max      20%/60%    40%/80%    Median

     X1                    0.021      -0.009      -2.794    0.10%      -0.852     -0.244      0.010
            1000.000       0.952      -0.331       2.962    0.10%       0.284      0.901
     X2                   -0.007      -0.036      -2.866    0.10%      -0.892     -0.266      0.006
            1000.000       1.088      -0.203       2.939    0.10%       0.279      0.846
     W                    -0.152      -0.048      -2.105    0.91%      -0.908     -0.351     -0.168
             110.000       0.594      -0.357       1.892    0.91%       0.112      0.525


THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       15

Loglikelihood

          H0 Value                       -2352.334
          H0 Scaling Correction Factor      1.0521
            for MLR

Information Criteria

          Akaike (AIC)                    4734.669
          Bayesian (BIC)                  4808.285
          Sample-Size Adjusted BIC        4760.644
            (n* = (n + 2) / 24)



MODEL RESULTS

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

Within Level

 FW       BY
    U1                 1.000      0.000    999.000    999.000
    U2                 1.234      0.177      6.980      0.000
    U3                 1.308      0.170      7.676      0.000
    U4                 1.296      0.167      7.741      0.000

 FW         ON
    X1                 0.834      0.089      9.379      0.000
    X2                 0.387      0.047      8.220      0.000

 Residual Variances
    FW                 0.660      0.135      4.886      0.000

Between Level

 FB       BY
    U1                 1.000      0.000    999.000    999.000
    U2                 1.563      0.596      2.621      0.009
    U3                 1.368      0.422      3.242      0.001
    U4                 1.714      0.592      2.894      0.004

 FB         ON
    W                  0.242      0.082      2.944      0.003

 Thresholds
    U1$1               0.011      0.087      0.132      0.895
    U2$1               0.136      0.096      1.418      0.156
    U3$1               0.065      0.094      0.689      0.491
    U4$1              -0.015      0.111     -0.137      0.891

 Residual Variances
    FB                 0.110      0.061      1.796      0.073


QUALITY OF NUMERICAL RESULTS

     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
              ________      ________      ________      ________
                    0             0             0             0


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


           NU
              X2
              ________
                    0


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


           THETA
              X2
              ________
 X2                 0


           ALPHA
              FW            X1            X2
              ________      ________      ________
                    0             0             0


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


           PSI
              FW            X1            X2
              ________      ________      ________
 FW                 6
 X1                 0             0
 X2                 0             0             0


     PARAMETER SPECIFICATION FOR BETWEEN


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


           NU
              U1            U2            U3            U4            W
              ________      ________      ________      ________      ________
                    0             0             0             0             0


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


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


           ALPHA
              FB            W
              ________      ________
                    0             0


           BETA
              FB            W
              ________      ________
 FB                 0            10
 W                  0             0


           PSI
              FB            W
              ________      ________
 FB                11
 W                  0             0


     STARTING VALUES FOR WITHIN


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


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


           NU
              X2
              ________
                0.000


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


           THETA
              X2
              ________
 X2             0.000


           ALPHA
              FW            X1            X2
              ________      ________      ________
                0.000         0.000         0.000


           BETA
              FW            X1            X2
              ________      ________      ________
 FW             0.000         0.000         0.000
 X1             0.000         0.000         0.000
 X2             0.000         0.000         0.000


           PSI
              FW            X1            X2
              ________      ________      ________
 FW             0.050
 X1             0.000         0.476
 X2             0.000         0.000         0.544


     STARTING VALUES FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
                0.032         0.128         0.072         0.028


           NU
              U1            U2            U3            U4            W
              ________      ________      ________      ________      ________
                0.000         0.000         0.000         0.000         0.000


           LAMBDA
              FB            W
              ________      ________
 U1             1.000         0.000
 U2             1.000         0.000
 U3             1.000         0.000
 U4             1.000         0.000
 W              0.000         1.000


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


           ALPHA
              FB            W
              ________      ________
                0.000         0.000


           BETA
              FB            W
              ________      ________
 FB             0.000         0.000
 W              0.000         0.000


           PSI
              FB            W
              ________      ________
 FB             0.050
 W              0.000         0.308


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.27181127D+04    0.0000000    0.0000000  EM
              2 -0.26423047D+04   75.8080890    0.0278900  EM
              3 -0.23792705D+04  263.0341739    0.0995473  EM
              4 -0.23598525D+04   19.4179878    0.0081613  EM
              5 -0.23556237D+04    4.2287706    0.0017920  EM
              6 -0.23538034D+04    1.8203093    0.0007728  EM
              7 -0.23529855D+04    0.8179035    0.0003475  EM
              8 -0.23526243D+04    0.3612025    0.0001535  EM
              9 -0.23524659D+04    0.1583870    0.0000673  EM
             10 -0.23523957D+04    0.0702196    0.0000298  EM
             11 -0.23523638D+04    0.0319116    0.0000136  EM
             12 -0.23523488D+04    0.0149795    0.0000064  EM
             13 -0.23523415D+04    0.0072796    0.0000031  EM
             14 -0.23523379D+04    0.0036567    0.0000016  EM
             15 -0.23523360D+04    0.0018911    0.0000008  EM
             16 -0.23523350D+04    0.0010017    0.0000004  EM
             17 -0.23523344D+04    0.0005407    0.0000002  EM


     Beginning Time:  17:05:32
        Ending Time:  17:05:36
       Elapsed Time:  00:00:04



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