Mplus VERSION 7.2
MUTHEN & MUTHEN
05/07/2014   3:07 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of two-level path
  	analysis with continuous dependent
  	variables and random slopes
  DATA:	FILE IS ex9.5.dat;
  VARIABLE:	NAMES ARE y1 y2 x1 x2 w clus;
  	WITHIN = x1 x2;
  	BETWEEN = w;
  	CLUSTER IS clus;
  ANALYSIS:	TYPE = TWOLEVEL RANDOM;
  	ALGORITHM = INTEGRATION;
  MODEL:
  	%WITHIN%
  	s2 | y2 ON y1;
  	y2 ON x2;
  	s1 | y1 ON x2;
  	y1 ON x1;
  	%BETWEEN%
  	y1 y2 s1 s2 ON w;
  OUTPUT:	TECH1 TECH8;



INPUT READING TERMINATED NORMALLY



this is an example of two-level path
analysis with continuous dependent
variables and random slopes

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

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

Observed dependent variables

  Continuous
   Y1          Y2

Observed independent variables
   X1          X2          W

Continuous latent variables
   S2          S1

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
Optimization algorithm                                         EMA
Integration Specifications
  Type                                                    STANDARD
  Number of integration points                                  15
  Dimensions of numerical integration                            0
  Adaptive quadrature                                           ON
Cholesky                                                       OFF

Input data file(s)
  ex9.5.dat
Input data format  FREE


SUMMARY OF DATA

     Number of clusters                         90




THE MODEL ESTIMATION TERMINATED NORMALLY



MODEL FIT INFORMATION

Number of Free Parameters                       17

Loglikelihood

          H0 Value                       -1663.599
          H0 Scaling Correction Factor      1.0333
            for MLR

Information Criteria

          Akaike (AIC)                    3361.198
          Bayesian (BIC)                  3432.847
          Sample-Size Adjusted BIC        3378.888
            (n* = (n + 2) / 24)



MODEL RESULTS

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

Within Level

 Y2         ON
    X2                 0.531      0.049     10.917      0.000

 Y1         ON
    X1                 0.300      0.062      4.848      0.000

 Residual Variances
    Y1                 1.080      0.064     16.954      0.000
    Y2                 0.957      0.076     12.606      0.000

Between Level

 S1         ON
    W                  0.277      0.106      2.603      0.009

 S2         ON
    W                  0.631      0.112      5.652      0.000

 Y1         ON
    W                  1.206      0.110     10.973      0.000

 Y2         ON
    W                  0.825      0.098      8.441      0.000

 Y2       WITH
    Y1                -0.048      0.090     -0.537      0.591

 Intercepts
    Y1                -0.011      0.102     -0.106      0.916
    Y2                -0.062      0.081     -0.767      0.443
    S2                 0.819      0.105      7.784      0.000
    S1                 0.428      0.097      4.420      0.000

 Residual Variances
    Y1                 0.600      0.110      5.433      0.000
    Y2                 0.214      0.084      2.553      0.011
    S2                 0.735      0.190      3.864      0.000
    S1                 0.498      0.106      4.698      0.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.446E-01
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION FOR WITHIN


           NU
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           LAMBDA
              X2            W
              ________      ________
 Y1                 0             0
 Y2                 0             0
 X1                 0             0
 X2                 0             0
 W                  0             0


           THETA
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


           ALPHA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           ALPHA
              X2            W
              ________      ________
 1                  0             0


           BETA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2                 0             0             0             0             0
 S1                 0             0             0             0             0
 Y1                 0             0             0             0             1
 Y2                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           BETA
              X2            W
              ________      ________
 S2                 0             0
 S1                 0             0
 Y1                 0             0
 Y2                 2             0
 X1                 0             0
 X2                 0             0
 W                  0             0


           PSI
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2                 0
 S1                 0             0
 Y1                 0             0             3
 Y2                 0             0             0             4
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              X2            W
              ________      ________
 X2                 0
 W                  0             0


     PARAMETER SPECIFICATION FOR BETWEEN


           NU
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           LAMBDA
              X2            W
              ________      ________
 Y1                 0             0
 Y2                 0             0
 X1                 0             0
 X2                 0             0
 W                  0             0


           THETA
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 Y1                 0
 Y2                 0             0
 X1                 0             0             0
 X2                 0             0             0             0
 W                  0             0             0             0             0


           ALPHA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 1                  5             6             7             8             0


           ALPHA
              X2            W
              ________      ________
 1                  0             0


           BETA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2                 0             0             0             0             0
 S1                 0             0             0             0             0
 Y1                 0             0             0             0             0
 Y2                 0             0             0             0             0
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           BETA
              X2            W
              ________      ________
 S2                 0             9
 S1                 0            10
 Y1                 0            11
 Y2                 0            12
 X1                 0             0
 X2                 0             0
 W                  0             0


           PSI
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2                13
 S1                 0            14
 Y1                 0             0            15
 Y2                 0             0            16            17
 X1                 0             0             0             0             0
 X2                 0             0             0             0             0
 W                  0             0             0             0             0


           PSI
              X2            W
              ________      ________
 X2                 0
 W                  0             0


     STARTING VALUES FOR WITHIN


           NU
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         1.000         0.000         0.000
 Y2             0.000         0.000         0.000         1.000         0.000
 X1             0.000         0.000         0.000         0.000         1.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X2            W
              ________      ________
 Y1             0.000         0.000
 Y2             0.000         0.000
 X1             0.000         0.000
 X2             1.000         0.000
 W              0.000         1.000


           THETA
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 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         0.000


           ALPHA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           ALPHA
              X2            W
              ________      ________
 1              0.000         0.000


           BETA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2             0.000         0.000         0.000         0.000         0.000
 S1             0.000         0.000         0.000         0.000         0.000
 Y1             0.000         0.000         0.000         0.000         0.000
 Y2             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


           BETA
              X2            W
              ________      ________
 S2             0.000         0.000
 S1             0.000         0.000
 Y1             0.000         0.000
 Y2             0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              0.000         0.000


           PSI
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2             0.000
 S1             0.000         0.000
 Y1             0.000         0.000         2.042
 Y2             0.000         0.000         0.000         5.189
 X1             0.000         0.000         0.000         0.000         0.507
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           PSI
              X2            W
              ________      ________
 X2             0.578
 W              0.000         0.000


     STARTING VALUES FOR BETWEEN


           NU
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 Y1             0.000         0.000         1.000         0.000         0.000
 Y2             0.000         0.000         0.000         1.000         0.000
 X1             0.000         0.000         0.000         0.000         1.000
 X2             0.000         0.000         0.000         0.000         0.000
 W              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              X2            W
              ________      ________
 Y1             0.000         0.000
 Y2             0.000         0.000
 X1             0.000         0.000
 X2             1.000         0.000
 W              0.000         1.000


           THETA
              Y1            Y2            X1            X2            W
              ________      ________      ________      ________      ________
 Y1             0.000
 Y2             0.000         0.000
 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         0.000


           ALPHA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 1              0.000         0.000        -0.132         0.632         0.000


           ALPHA
              X2            W
              ________      ________
 1              0.000         0.000


           BETA
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2             0.000         0.000         0.000         0.000         0.000
 S1             0.000         0.000         0.000         0.000         0.000
 Y1             0.000         0.000         0.000         0.000         0.000
 Y2             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


           BETA
              X2            W
              ________      ________
 S2             0.000         0.000
 S1             0.000         0.000
 Y1             0.000         0.000
 Y2             0.000         0.000
 X1             0.000         0.000
 X2             0.000         0.000
 W              0.000         0.000


           PSI
              S2            S1            Y1            Y2            X1
              ________      ________      ________      ________      ________
 S2             1.000
 S1             0.000         1.000
 Y1             0.000         0.000         2.042
 Y2             0.000         0.000         0.000         5.189
 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
              X2            W
              ________      ________
 X2             0.000
 W              0.000         0.402


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.20167591D+04    0.0000000    0.0000000  EM
              2 -0.17641962D+04  252.5629032    0.1252321  EM
              3 -0.16867969D+04   77.3992654    0.0438723  EM
              4 -0.16702420D+04   16.5549130    0.0098144  EM
              5 -0.16664568D+04    3.7851645    0.0022662  EM
              6 -0.16651602D+04    1.2966536    0.0007781  EM
              7 -0.16645521D+04    0.6080330    0.0003651  EM
              8 -0.16642159D+04    0.3362356    0.0002020  EM
              9 -0.16640128D+04    0.2031192    0.0001221  EM
             10 -0.16638833D+04    0.1294525    0.0000778  EM
             11 -0.16637978D+04    0.0855397    0.0000514  EM
             12 -0.16637398D+04    0.0580323    0.0000349  EM
             13 -0.16636996D+04    0.0401726    0.0000241  EM
             14 -0.16636713D+04    0.0282557    0.0000170  EM
             15 -0.16636512D+04    0.0201303    0.0000121  EM
             16 -0.16636367D+04    0.0144931    0.0000087  EM
             17 -0.16636262D+04    0.0105255    0.0000063  EM
             18 -0.16636185D+04    0.0077004    0.0000046  EM
             19 -0.16636128D+04    0.0056679    0.0000034  EM
             20 -0.16636086D+04    0.0041939    0.0000025  EM
             21 -0.16636055D+04    0.0031168    0.0000019  EM
             22 -0.16636032D+04    0.0023252    0.0000014  EM
             23 -0.16636014D+04    0.0017402    0.0000010  EM
             24 -0.16636001D+04    0.0013061    0.0000008  EM
             25 -0.16635991D+04    0.0009826    0.0000006  EM


     Beginning Time:  15:07:21
        Ending Time:  15:07:21
       Elapsed Time:  00:00:00



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