Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   2:53 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-level
  	growth model for a categorical outcome
  	(three-level analysis)
  DATA:	FILE IS ex9.13.dat;
  VARIABLE:	NAMES ARE u1-u4 x w clus;
  	CATEGORICAL = u1-u4;
  	WITHIN = x;
  	BETWEEN = w;
  	CLUSTER = clus;
  ANALYSIS:	TYPE = TWOLEVEL;
  	INTEGRATION = 7;
  MODEL:
  	%WITHIN%
  	iw sw | u1@0 u2@1 u3@2 u4@3;
  	iw sw ON x;
  	%BETWEEN%
  	ib sb | u1@0 u2@1 u3@2 u4@3;
  	ib sb ON w;
  OUTPUT:	TECH1 TECH8;



INPUT READING TERMINATED NORMALLY



this is an example of a two-level
growth model for a categorical outcome
(three-level analysis)

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

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

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4

Observed independent variables
   X           W

Continuous latent variables
   IW          SW          IB          SB

Variables with special functions

  Cluster variable      CLUS

  Within variables
   X

  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                                   7
  Dimensions of numerical integration                            4
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON

Input data file(s)
  ex9.13.dat
Input data format  FREE


SUMMARY OF DATA

     Number of clusters                         90



UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.452      226.000
      Category 2    0.548      274.000
    U2
      Category 1    0.432      216.000
      Category 2    0.568      284.000
    U3
      Category 1    0.382      191.000
      Category 2    0.618      309.000
    U4
      Category 1    0.364      182.000
      Category 2    0.636      318.000



THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       12

Loglikelihood

          H0 Value                       -1053.709
          H0 Scaling Correction Factor      0.9258
            for MLR

Information Criteria

          Akaike (AIC)                    2131.419
          Bayesian (BIC)                  2181.994
          Sample-Size Adjusted BIC        2143.905
            (n* = (n + 2) / 24)



MODEL RESULTS

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

Within Level

 IW       |
    U1                 1.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 1.000      0.000    999.000    999.000
    U4                 1.000      0.000    999.000    999.000

 SW       |
    U1                 0.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 2.000      0.000    999.000    999.000
    U4                 3.000      0.000    999.000    999.000

 IW         ON
    X                  1.119      0.133      8.402      0.000

 SW         ON
    X                  0.103      0.082      1.258      0.208

 SW       WITH
    IW                 0.177      0.099      1.794      0.073

 Residual Variances
    IW                 0.539      0.287      1.878      0.060
    SW                 0.232      0.122      1.907      0.057

Between Level

 IB       |
    U1                 1.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 1.000      0.000    999.000    999.000
    U4                 1.000      0.000    999.000    999.000

 SB       |
    U1                 0.000      0.000    999.000    999.000
    U2                 1.000      0.000    999.000    999.000
    U3                 2.000      0.000    999.000    999.000
    U4                 3.000      0.000    999.000    999.000

 IB         ON
    W                  0.350      0.114      3.078      0.002

 SB         ON
    W                  0.319      0.093      3.432      0.001

 SB       WITH
    IB                -0.181      0.124     -1.456      0.145

 Intercepts
    IB                 0.000      0.000    999.000    999.000
    SB                 0.352      0.093      3.762      0.000

 Thresholds
    U1$1              -0.137      0.131     -1.047      0.295
    U2$1              -0.137      0.131     -1.047      0.295
    U3$1              -0.137      0.131     -1.047      0.295
    U4$1              -0.137      0.131     -1.047      0.295

 Residual Variances
    IB                 0.514      0.235      2.186      0.029
    SB                 0.308      0.118      2.607      0.009


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.347E-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            X
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              W
              ________
 1                  0


           LAMBDA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 U1                 0             0             0             0             0
 U2                 0             0             0             0             0
 U3                 0             0             0             0             0
 U4                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0


           LAMBDA
              W
              ________
 U1                 0
 U2                 0
 U3                 0
 U4                 0
 X                  0
 W                  0


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


           THETA
              W
              ________
 W                  0


           ALPHA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           ALPHA
              W
              ________
 1                  0


           BETA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW                 0             0             0             0             1
 SW                 0             0             0             0             2
 IB                 0             0             0             0             0
 SB                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0


           BETA
              W
              ________
 IW                 0
 SW                 0
 IB                 0
 SB                 0
 X                  0
 W                  0


           PSI
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW                 3
 SW                 4             5
 IB                 0             0             0
 SB                 0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              W
              ________
 W                  0


     PARAMETER SPECIFICATION FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1                 12            12            12            12


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


           NU
              W
              ________
 1                  0


           LAMBDA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 U1                 0             0             0             0             0
 U2                 0             0             0             0             0
 U3                 0             0             0             0             0
 U4                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0


           LAMBDA
              W
              ________
 U1                 0
 U2                 0
 U3                 0
 U4                 0
 X                  0
 W                  0


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


           THETA
              W
              ________
 W                  0


           ALPHA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 1                  0             0             0             6             0


           ALPHA
              W
              ________
 1                  0


           BETA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW                 0             0             0             0             0
 SW                 0             0             0             0             0
 IB                 0             0             0             0             0
 SB                 0             0             0             0             0
 X                  0             0             0             0             0
 W                  0             0             0             0             0


           BETA
              W
              ________
 IW                 0
 SW                 0
 IB                 7
 SB                 8
 X                  0
 W                  0


           PSI
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW                 0
 SW                 0             0
 IB                 0             0             9
 SB                 0             0            10            11
 X                  0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              W
              ________
 W                  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            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              W
              ________
 1              0.000


           LAMBDA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 U1             1.000         0.000         0.000         0.000         0.000
 U2             1.000         1.000         0.000         0.000         0.000
 U3             1.000         2.000         0.000         0.000         0.000
 U4             1.000         3.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000


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


           THETA
              U1            U2            U3            U4            X
              ________      ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           THETA
              W
              ________
 W              0.000


           ALPHA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              W
              ________
 1              0.000


           BETA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW             0.000         0.000         0.000         0.000         0.000
 SW             0.000         0.000         0.000         0.000         0.000
 IB             0.000         0.000         0.000         0.000         0.000
 SB             0.000         0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           BETA
              W
              ________
 IW             0.000
 SW             0.000
 IB             0.000
 SB             0.000
 X              0.000
 W              0.000


           PSI
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW             0.050
 SW             0.000         0.050
 IB             0.000         0.000         0.000
 SB             0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.524
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              W
              ________
 W              0.000


     STARTING VALUES FOR BETWEEN


           TAU
              U1$1          U2$1          U3$1          U4$1
              ________      ________      ________      ________
 1             -0.376        -0.376        -0.376        -0.376


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


           NU
              W
              ________
 1              0.000


           LAMBDA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 U1             0.000         0.000         1.000         0.000         0.000
 U2             0.000         0.000         1.000         1.000         0.000
 U3             0.000         0.000         1.000         2.000         0.000
 U4             0.000         0.000         1.000         3.000         0.000
 X              0.000         0.000         0.000         0.000         1.000
 W              0.000         0.000         0.000         0.000         0.000


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


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


           THETA
              W
              ________
 W              0.000


           ALPHA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              W
              ________
 1              0.000


           BETA
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW             0.000         0.000         0.000         0.000         0.000
 SW             0.000         0.000         0.000         0.000         0.000
 IB             0.000         0.000         0.000         0.000         0.000
 SB             0.000         0.000         0.000         0.000         0.000
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           BETA
              W
              ________
 IW             0.000
 SW             0.000
 IB             0.000
 SB             0.000
 X              0.000
 W              0.000


           PSI
              IW            SW            IB            SB            X
              ________      ________      ________      ________      ________
 IW             0.000
 SW             0.000         0.000
 IB             0.000         0.000         0.050
 SB             0.000         0.000         0.000         0.050
 X              0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              W
              ________
 W              0.610


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.12658086D+04    0.0000000    0.0000000  EM
              2 -0.12086660D+04   57.1426365    0.0451432  FS
              3 -0.11639679D+04   44.6980350    0.0369813  FS
              4 -0.11254112D+04   38.5567602    0.0331253  FS
              5 -0.10920824D+04   33.3287306    0.0296147  FS
              6 -0.10686368D+04   23.4456551    0.0214688  FS
              7 -0.10570201D+04   11.6166712    0.0108706  FS
              8 -0.10541172D+04    2.9029111    0.0027463  FS
              9 -0.10538863D+04    0.2308671    0.0002190  EM
             10 -0.10538302D+04    0.0561775    0.0000533  EM
             11 -0.10538072D+04    0.0229585    0.0000218  EM
             12 -0.10537954D+04    0.0117841    0.0000112  EM
             13 -0.10537881D+04    0.0073030    0.0000069  EM
             14 -0.10537829D+04    0.0052467    0.0000050  EM
             15 -0.10537787D+04    0.0041791    0.0000040  EM
             16 -0.10537751D+04    0.0035637    0.0000034  EM
             17 -0.10537719D+04    0.0031770    0.0000030  EM
             18 -0.10537690D+04    0.0029151    0.0000028  EM
             19 -0.10537663D+04    0.0027256    0.0000026  EM
             20 -0.10537637D+04    0.0025800    0.0000024  EM
             21 -0.10537613D+04    0.0024619    0.0000023  EM
             22 -0.10537589D+04    0.0023620    0.0000022  EM
             23 -0.10537566D+04    0.0022744    0.0000022  EM
             24 -0.10537544D+04    0.0021957    0.0000021  EM
             25 -0.10537523D+04    0.0021235    0.0000020  EM
             26 -0.10537502D+04    0.0020565    0.0000020  EM
             27 -0.10537483D+04    0.0019937    0.0000019  EM
             28 -0.10537463D+04    0.0019345    0.0000018  EM
             29 -0.10537444D+04    0.0018783    0.0000018  EM
             30 -0.10537426D+04    0.0018249    0.0000017  EM
             31 -0.10537408D+04    0.0017740    0.0000017  EM
             32 -0.10537391D+04    0.0017252    0.0000016  EM
             33 -0.10537374D+04    0.0016786    0.0000016  EM
             34 -0.10537358D+04    0.0016339    0.0000016  EM
             35 -0.10537342D+04    0.0015910    0.0000015  EM
             36 -0.10537327D+04    0.0015497    0.0000015  EM
             37 -0.10537312D+04    0.0015101    0.0000014  EM
             38 -0.10537297D+04    0.0014719    0.0000014  EM
             39 -0.10537282D+04    0.0014351    0.0000014  EM
             40 -0.10537268D+04    0.0013997    0.0000013  EM
             41 -0.10537255D+04    0.0013655    0.0000013  EM
             42 -0.10537241D+04    0.0013325    0.0000013  EM
             43 -0.10537228D+04    0.0013006    0.0000012  EM
             44 -0.10537216D+04    0.0012698    0.0000012  EM
             45 -0.10537203D+04    0.0012401    0.0000012  EM
             46 -0.10537191D+04    0.0012113    0.0000011  EM
             47 -0.10537179D+04    0.0011835    0.0000011  EM
             48 -0.10537168D+04    0.0011565    0.0000011  EM
             49 -0.10537157D+04    0.0011305    0.0000011  EM
             50 -0.10537145D+04    0.0011052    0.0000010  EM
             51 -0.10537135D+04    0.0010807    0.0000010  EM
             52 -0.10537124D+04    0.0010570    0.0000010  EM
             53 -0.10537114D+04    0.0010347    0.0000010  EM
             54 -0.10537104D+04    0.0010117    0.0000010  EM
             55 -0.10537094D+04    0.0009900    0.0000009  EM


     Beginning Time:  14:53:07
        Ending Time:  14:54:03
       Elapsed Time:  00:00:56



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