Mplus VERSION 7.3
MUTHEN & MUTHEN
09/22/2014   5:48 PM

INPUT INSTRUCTIONS

  TITLE:	this is an example of a two-parameter
            logistic item response theory (IRT) model
  DATA:	FILE IS ex5.5.dat;
  VARIABLE:	NAMES ARE u1-u20;
  	CATEGORICAL ARE u1-u20;
  ANALYSIS:	ESTIMATOR = MLR;
  MODEL:	f BY u1-u20*;
  	f@1;
  OUTPUT:	TECH1 TECH8;
  PLOT:	TYPE = PLOT3;




INPUT READING TERMINATED NORMALLY



this is an example of a two-parameter
logistic item response theory (IRT) model

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                         500

Number of dependent variables                                   20
Number of independent variables                                  0
Number of continuous latent variables                            1

Observed dependent variables

  Binary and ordered categorical (ordinal)
   U1          U2          U3          U4          U5          U6
   U7          U8          U9          U10         U11         U12
   U13         U14         U15         U16         U17         U18
   U19         U20

Continuous latent variables
   F


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                            1
  Adaptive quadrature                                           ON
Link                                                         LOGIT
Cholesky                                                        ON

Input data file(s)
  ex5.5.dat
Input data format  FREE


UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

    U1
      Category 1    0.426      213.000
      Category 2    0.574      287.000
    U2
      Category 1    0.412      206.000
      Category 2    0.588      294.000
    U3
      Category 1    0.432      216.000
      Category 2    0.568      284.000
    U4
      Category 1    0.436      218.000
      Category 2    0.564      282.000
    U5
      Category 1    0.410      205.000
      Category 2    0.590      295.000
    U6
      Category 1    0.400      200.000
      Category 2    0.600      300.000
    U7
      Category 1    0.412      206.000
      Category 2    0.588      294.000
    U8
      Category 1    0.416      208.000
      Category 2    0.584      292.000
    U9
      Category 1    0.412      206.000
      Category 2    0.588      294.000
    U10
      Category 1    0.408      204.000
      Category 2    0.592      296.000
    U11
      Category 1    0.614      307.000
      Category 2    0.386      193.000
    U12
      Category 1    0.614      307.000
      Category 2    0.386      193.000
    U13
      Category 1    0.596      298.000
      Category 2    0.404      202.000
    U14
      Category 1    0.562      281.000
      Category 2    0.438      219.000
    U15
      Category 1    0.562      281.000
      Category 2    0.438      219.000
    U16
      Category 1    0.584      292.000
      Category 2    0.416      208.000
    U17
      Category 1    0.618      309.000
      Category 2    0.382      191.000
    U18
      Category 1    0.592      296.000
      Category 2    0.408      204.000
    U19
      Category 1    0.642      321.000
      Category 2    0.358      179.000
    U20
      Category 1    0.596      298.000
      Category 2    0.404      202.000



THE MODEL ESTIMATION TERMINATED NORMALLY

     THE CHI-SQUARE TEST IS NOT COMPUTED BECAUSE THE FREQUENCY TABLE FOR THE
     LATENT CLASS INDICATOR MODEL PART IS TOO LARGE.




MODEL FIT INFORMATION

Number of Free Parameters                       40

Loglikelihood

          H0 Value                       -6265.315
          H0 Scaling Correction Factor      1.0029
            for MLR

Information Criteria

          Akaike (AIC)                   12610.630
          Bayesian (BIC)                 12779.214
          Sample-Size Adjusted BIC       12652.252
            (n* = (n + 2) / 24)



MODEL RESULTS

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

 F        BY
    U1                 1.026      0.152      6.755      0.000
    U2                 1.062      0.157      6.780      0.000
    U3                 0.916      0.141      6.482      0.000
    U4                 1.155      0.161      7.190      0.000
    U5                 0.980      0.151      6.471      0.000
    U6                 0.519      0.121      4.298      0.000
    U7                 1.128      0.159      7.085      0.000
    U8                 1.043      0.148      7.050      0.000
    U9                 1.021      0.150      6.827      0.000
    U10                0.969      0.141      6.852      0.000
    U11                1.235      0.165      7.484      0.000
    U12                0.982      0.148      6.651      0.000
    U13                1.007      0.146      6.900      0.000
    U14                0.760      0.127      5.990      0.000
    U15                0.791      0.128      6.203      0.000
    U16                0.950      0.141      6.739      0.000
    U17                1.144      0.161      7.119      0.000
    U18                1.125      0.154      7.323      0.000
    U19                0.781      0.131      5.942      0.000
    U20                1.094      0.151      7.223      0.000

 Thresholds
    U1$1              -0.368      0.111     -3.321      0.001
    U2$1              -0.443      0.114     -3.901      0.000
    U3$1              -0.327      0.107     -3.051      0.002
    U4$1              -0.333      0.115     -2.885      0.004
    U5$1              -0.441      0.111     -3.976      0.000
    U6$1              -0.432      0.098     -4.426      0.000
    U7$1              -0.453      0.115     -3.922      0.000
    U8$1              -0.420      0.112     -3.767      0.000
    U9$1              -0.437      0.112     -3.909      0.000
    U10$1             -0.450      0.110     -4.082      0.000
    U11$1              0.593      0.122      4.868      0.000
    U12$1              0.552      0.112      4.923      0.000
    U13$1              0.465      0.111      4.173      0.000
    U14$1              0.278      0.102      2.728      0.006
    U15$1              0.280      0.103      2.726      0.006
    U16$1              0.399      0.109      3.668      0.000
    U17$1              0.599      0.119      5.051      0.000
    U18$1              0.460      0.116      3.969      0.000
    U19$1              0.658      0.108      6.120      0.000
    U20$1              0.476      0.115      4.150      0.000

 Variances
    F                  1.000      0.000    999.000    999.000


IRT PARAMETERIZATION IN TWO-PARAMETER LOGISTIC METRIC
WHERE THE LOGIT IS DISCRIMINATION*(THETA - DIFFICULTY)

 Item Discriminations

 F        BY
    U1                 1.026      0.152      6.755      0.000
    U2                 1.062      0.157      6.780      0.000
    U3                 0.916      0.141      6.482      0.000
    U4                 1.155      0.161      7.190      0.000
    U5                 0.980      0.151      6.471      0.000
    U6                 0.519      0.121      4.298      0.000
    U7                 1.128      0.159      7.085      0.000
    U8                 1.043      0.148      7.050      0.000
    U9                 1.021      0.150      6.827      0.000
    U10                0.969      0.141      6.852      0.000
    U11                1.235      0.165      7.484      0.000
    U12                0.982      0.148      6.651      0.000
    U13                1.007      0.146      6.900      0.000
    U14                0.760      0.127      5.990      0.000
    U15                0.791      0.128      6.203      0.000
    U16                0.950      0.141      6.739      0.000
    U17                1.144      0.161      7.119      0.000
    U18                1.125      0.154      7.323      0.000
    U19                0.781      0.131      5.942      0.000
    U20                1.094      0.151      7.223      0.000

 Item Difficulties
    U1$1              -0.359      0.113     -3.176      0.001
    U2$1              -0.417      0.112     -3.721      0.000
    U3$1              -0.357      0.122     -2.913      0.004
    U4$1              -0.288      0.101     -2.841      0.004
    U5$1              -0.451      0.120     -3.748      0.000
    U6$1              -0.833      0.253     -3.296      0.001
    U7$1              -0.402      0.107     -3.747      0.000
    U8$1              -0.403      0.114     -3.540      0.000
    U9$1              -0.428      0.116     -3.698      0.000
    U10$1             -0.464      0.122     -3.816      0.000
    U11$1              0.480      0.105      4.555      0.000
    U12$1              0.562      0.129      4.374      0.000
    U13$1              0.462      0.120      3.833      0.000
    U14$1              0.366      0.143      2.560      0.010
    U15$1              0.354      0.138      2.566      0.010
    U16$1              0.420      0.123      3.403      0.001
    U17$1              0.524      0.113      4.626      0.000
    U18$1              0.409      0.109      3.766      0.000
    U19$1              0.843      0.176      4.778      0.000
    U20$1              0.435      0.112      3.882      0.000

 Variances
    F                  1.000      0.000      0.000      1.000


QUALITY OF NUMERICAL RESULTS

     Condition Number for the Information Matrix              0.125E+00
       (ratio of smallest to largest eigenvalue)


TECHNICAL 1 OUTPUT


     PARAMETER SPECIFICATION


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
 1                 21            22            23            24            25


           TAU
              U6$1          U7$1          U8$1          U9$1          U10$1
              ________      ________      ________      ________      ________
 1                 26            27            28            29            30


           TAU
              U11$1         U12$1         U13$1         U14$1         U15$1
              ________      ________      ________      ________      ________
 1                 31            32            33            34            35


           TAU
              U16$1         U17$1         U18$1         U19$1         U20$1
              ________      ________      ________      ________      ________
 1                 36            37            38            39            40


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           NU
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
 1                  0             0             0             0             0


           LAMBDA
              F
              ________
 U1                 1
 U2                 2
 U3                 3
 U4                 4
 U5                 5
 U6                 6
 U7                 7
 U8                 8
 U9                 9
 U10               10
 U11               11
 U12               12
 U13               13
 U14               14
 U15               15
 U16               16
 U17               17
 U18               18
 U19               19
 U20               20


           THETA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1                 0
 U2                 0             0
 U3                 0             0             0
 U4                 0             0             0             0
 U5                 0             0             0             0             0
 U6                 0             0             0             0             0
 U7                 0             0             0             0             0
 U8                 0             0             0             0             0
 U9                 0             0             0             0             0
 U10                0             0             0             0             0
 U11                0             0             0             0             0
 U12                0             0             0             0             0
 U13                0             0             0             0             0
 U14                0             0             0             0             0
 U15                0             0             0             0             0
 U16                0             0             0             0             0
 U17                0             0             0             0             0
 U18                0             0             0             0             0
 U19                0             0             0             0             0
 U20                0             0             0             0             0


           THETA
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
 U6                 0
 U7                 0             0
 U8                 0             0             0
 U9                 0             0             0             0
 U10                0             0             0             0             0
 U11                0             0             0             0             0
 U12                0             0             0             0             0
 U13                0             0             0             0             0
 U14                0             0             0             0             0
 U15                0             0             0             0             0
 U16                0             0             0             0             0
 U17                0             0             0             0             0
 U18                0             0             0             0             0
 U19                0             0             0             0             0
 U20                0             0             0             0             0


           THETA
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
 U11                0
 U12                0             0
 U13                0             0             0
 U14                0             0             0             0
 U15                0             0             0             0             0
 U16                0             0             0             0             0
 U17                0             0             0             0             0
 U18                0             0             0             0             0
 U19                0             0             0             0             0
 U20                0             0             0             0             0


           THETA
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
 U16                0
 U17                0             0
 U18                0             0             0
 U19                0             0             0             0
 U20                0             0             0             0             0


           ALPHA
              F
              ________
 1                  0


           BETA
              F
              ________
 F                  0


           PSI
              F
              ________
 F                  0


     STARTING VALUES


           TAU
              U1$1          U2$1          U3$1          U4$1          U5$1
              ________      ________      ________      ________      ________
 1             -0.298        -0.356        -0.274        -0.257        -0.364


           TAU
              U6$1          U7$1          U8$1          U9$1          U10$1
              ________      ________      ________      ________      ________
 1             -0.405        -0.356        -0.339        -0.356        -0.372


           TAU
              U11$1         U12$1         U13$1         U14$1         U15$1
              ________      ________      ________      ________      ________
 1              0.464         0.464         0.389         0.249         0.249


           TAU
              U16$1         U17$1         U18$1         U19$1         U20$1
              ________      ________      ________      ________      ________
 1              0.339         0.481         0.372         0.584         0.389


           NU
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           NU
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
 1              0.000         0.000         0.000         0.000         0.000


           LAMBDA
              F
              ________
 U1             1.000
 U2             1.000
 U3             1.000
 U4             1.000
 U5             1.000
 U6             1.000
 U7             1.000
 U8             1.000
 U9             1.000
 U10            1.000
 U11            1.000
 U12            1.000
 U13            1.000
 U14            1.000
 U15            1.000
 U16            1.000
 U17            1.000
 U18            1.000
 U19            1.000
 U20            1.000


           THETA
              U1            U2            U3            U4            U5
              ________      ________      ________      ________      ________
 U1             1.000
 U2             0.000         1.000
 U3             0.000         0.000         1.000
 U4             0.000         0.000         0.000         1.000
 U5             0.000         0.000         0.000         0.000         1.000
 U6             0.000         0.000         0.000         0.000         0.000
 U7             0.000         0.000         0.000         0.000         0.000
 U8             0.000         0.000         0.000         0.000         0.000
 U9             0.000         0.000         0.000         0.000         0.000
 U10            0.000         0.000         0.000         0.000         0.000
 U11            0.000         0.000         0.000         0.000         0.000
 U12            0.000         0.000         0.000         0.000         0.000
 U13            0.000         0.000         0.000         0.000         0.000
 U14            0.000         0.000         0.000         0.000         0.000
 U15            0.000         0.000         0.000         0.000         0.000
 U16            0.000         0.000         0.000         0.000         0.000
 U17            0.000         0.000         0.000         0.000         0.000
 U18            0.000         0.000         0.000         0.000         0.000
 U19            0.000         0.000         0.000         0.000         0.000
 U20            0.000         0.000         0.000         0.000         0.000


           THETA
              U6            U7            U8            U9            U10
              ________      ________      ________      ________      ________
 U6             1.000
 U7             0.000         1.000
 U8             0.000         0.000         1.000
 U9             0.000         0.000         0.000         1.000
 U10            0.000         0.000         0.000         0.000         1.000
 U11            0.000         0.000         0.000         0.000         0.000
 U12            0.000         0.000         0.000         0.000         0.000
 U13            0.000         0.000         0.000         0.000         0.000
 U14            0.000         0.000         0.000         0.000         0.000
 U15            0.000         0.000         0.000         0.000         0.000
 U16            0.000         0.000         0.000         0.000         0.000
 U17            0.000         0.000         0.000         0.000         0.000
 U18            0.000         0.000         0.000         0.000         0.000
 U19            0.000         0.000         0.000         0.000         0.000
 U20            0.000         0.000         0.000         0.000         0.000


           THETA
              U11           U12           U13           U14           U15
              ________      ________      ________      ________      ________
 U11            1.000
 U12            0.000         1.000
 U13            0.000         0.000         1.000
 U14            0.000         0.000         0.000         1.000
 U15            0.000         0.000         0.000         0.000         1.000
 U16            0.000         0.000         0.000         0.000         0.000
 U17            0.000         0.000         0.000         0.000         0.000
 U18            0.000         0.000         0.000         0.000         0.000
 U19            0.000         0.000         0.000         0.000         0.000
 U20            0.000         0.000         0.000         0.000         0.000


           THETA
              U16           U17           U18           U19           U20
              ________      ________      ________      ________      ________
 U16            1.000
 U17            0.000         1.000
 U18            0.000         0.000         1.000
 U19            0.000         0.000         0.000         1.000
 U20            0.000         0.000         0.000         0.000         1.000


           ALPHA
              F
              ________
 1              0.000


           BETA
              F
              ________
 F              0.000


           PSI
              F
              ________
 F              1.000


TECHNICAL 8 OUTPUT


   E STEP  ITER  LOGLIKELIHOOD    ABS CHANGE   REL CHANGE  ALGORITHM
              1 -0.62863564D+04    0.0000000    0.0000000  EM
              2 -0.62661906D+04   20.1657817    0.0032079  EM
              3 -0.62653912D+04    0.7994457    0.0001276  EM
              4 -0.62653242D+04    0.0670496    0.0000107  EM
              5 -0.62653166D+04    0.0075983    0.0000012  EM
              6 -0.62653152D+04    0.0013361    0.0000002  EM
              7 -0.62653149D+04    0.0003687    0.0000001  EM


SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES


     SAMPLE STATISTICS


           Means
              F             F_SE
              ________      ________
 1              0.000         0.455


           Covariances
              F             F_SE
              ________      ________
 F              0.791
 F_SE           0.001         0.001


           Correlations
              F             F_SE
              ________      ________
 F              1.000
 F_SE           0.033         1.000


PLOT INFORMATION

The following plots are available:

  Histograms (sample values, estimated factor scores)
  Scatterplots (sample values, estimated factor scores)
  Sample proportions and estimated probabilities
  Item characteristic curves
  Information curves
  Latent variable distribution plots

     Beginning Time:  17:48:44
        Ending Time:  17:48:45
       Elapsed Time:  00:00:01



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