Mplus VERSION 6

MUTHEN & MUTHEN

07/31/2014 2:34 PM

INPUT INSTRUCTIONS

TITLE: ipsative_example

DATA: FILE IS 'data.csv';

VARIABLE: ! It is assumed that the input file contains only item responses

! Any additional variables should be added below

Names ARE

i1i2

i1i3

i2i3

i4i5

i4i6

i5i6

i7i8

i7i9

i8i9;

USEVARIABLES ARE i1i2-i8i9;

CATEGORICAL ARE ALL;

ANALYSIS:

ESTIMATOR = ulsmv;

PARAMETERIZATION = theta;

MODEL:

Trait1 BY

i1i2*1 (L1)

i1i3*1 (L1)

i4i5*1 (L4)

i4i6*1 (L4)

i7i8*-1 (L7)

i7i9*-1 (L7);

Trait2 BY

i1i2*-1 (L2_n)

i2i3*1 (L2)

i4i5*1 (L5_n)

i5i6*-1 (L5)

i7i8*-1 (L8_n)

i8i9*1 (L8);

Trait3 BY

i1i3*1 (L3_n)

i2i3*1 (L3_n)

i4i6*-1 (L6_n)

i5i6*-1 (L6_n)

i7i9*-1 (L9_n)

i8i9*-1 (L9_n);

! variances for all traits are set to 1

Trait1-Trait3@1;

! starting values for correlations between traits

Trait1 WITH Trait2*0.3 Trait3*-0.3;

Trait2 WITH Trait3*0.5;

! declare uniquenesses and set their starting values

i1i2*2 (e1e2);

i1i3*2 (e1e3);

i2i3*2 (e2e3);

i4i5*2 (e4e5);

i4i6*2 (e4e6);

i5i6*2 (e5e6);

i7i8*2 (e7e8);

i7i9*2 (e7e9);

i8i9*2 (e8e9);

! declare correlated uniqunesses and set their starting values

i1i2 WITH i1i3*1 (e1);

i1i2 WITH i2i3*-1 (e2_n);

i1i3 WITH i2i3*1 (e3);

i4i5 WITH i4i6*1 (e4);

i4i5 WITH i5i6*-1 (e5_n);

i4i6 WITH i5i6*1 (e6);

i7i8 WITH i7i9*1 (e7);

i7i8 WITH i8i9*-1 (e8_n);

i7i9 WITH i8i9*1 (e9);

MODEL CONSTRAINT:

!factor loadings relating to the same item are equal in absolute value

L2_n = -L2;

L5_n = -L5;

L8_n = -L8;

! pair's uniqueness is equal to sum of 2 utility uniqunesses

e1e2 = e1 - e2_n;

e1e3 = e1 + e3;

e2e3 = -e2_n + e3;

e4e5 = e4 - e5_n;

e4e6 = e4 + e6;

e5e6 = -e5_n + e6;

e7e8 = e7 - e8_n;

e7e9 = e7 + e9;

e8e9 = -e8_n + e9;

! fix one uniqueness per block for identification

e1=1;

e4=1;

e7=1;

SAVEDATA: ! trait scores for individuals are estimated and saved in a file

FILE IS 'ipsative_example_fscore';

SAVE = FSCORES;

INPUT READING TERMINATED NORMALLY

ipsative_example

SUMMARY OF ANALYSIS

Number of groups 1

Number of observations 1000

Number of dependent variables 9

Number of independent variables 0

Number of continuous latent variables 3

Observed dependent variables

Binary and ordered categorical (ordinal)

I1I2 I1I3 I2I3 I4I5 I4I6 I5I6

I7I8 I7I9 I8I9

Continuous latent variables

TRAIT1 TRAIT2 TRAIT3

Estimator ULSMV

Maximum number of iterations 1000

Convergence criterion 0.500D-04

Maximum number of steepest descent iterations 20

Parameterization THETA

Input data file(s)

data.csv

Input data format FREE

UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES

I1I2

Category 1 0.494 494.000

Category 2 0.506 506.000

I1I3

Category 1 0.511 511.000

Category 2 0.489 489.000

I2I3

Category 1 0.519 519.000

Category 2 0.481 481.000

I4I5

Category 1 0.501 501.000

Category 2 0.499 499.000

I4I6

Category 1 0.522 522.000

Category 2 0.478 478.000

I5I6

Category 1 0.493 493.000

Category 2 0.507 507.000

I7I8

Category 1 0.487 487.000

Category 2 0.513 513.000

I7I9

Category 1 0.489 489.000

Category 2 0.511 511.000

I8I9

Category 1 0.475 475.000

Category 2 0.525 525.000

THE MODEL ESTIMATION TERMINATED NORMALLY

WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE.

THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED

VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED

VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES.

CHECK THE RESULTS SECTION FOR MORE INFORMATION.

PROBLEM INVOLVING VARIABLE I2I3.

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 14.277*

Degrees of Freedom 18

P-Value 0.7109

* The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used

for chi-square difference testing in the regular way. MLM, MLR and WLSM

chi-square difference testing is described on the Mplus website. MLMV, WLSMV,

and ULSMV difference testing is done using the DIFFTEST option.

Chi-Square Test of Model Fit for the Baseline Model

Value 1928.950

Degrees of Freedom 36

P-Value 0.0000

CFI/TLI

CFI 1.000

TLI 1.004

Number of Free Parameters 27

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.000

MODEL RESULTS

Two-Tailed

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

TRAIT1 BY

I1I2 1.914 0.654 2.929 0.003

I1I3 1.914 0.654 2.929 0.003

I4I5 0.638 0.120 5.339 0.000

I4I6 0.638 0.120 5.339 0.000

I7I8 -0.762 0.153 -4.981 0.000

I7I9 -0.762 0.153 -4.981 0.000

TRAIT2 BY

I1I2 -0.558 0.237 -2.355 0.019

I2I3 0.558 0.237 2.355 0.019

I4I5 1.112 0.139 7.989 0.000

I5I6 -1.112 0.139 -7.989 0.000

I7I8 -1.189 0.219 -5.424 0.000

I8I9 1.189 0.219 5.424 0.000

TRAIT3 BY

I1I3 1.088 0.286 3.805 0.000

I2I3 1.088 0.286 3.805 0.000

I4I6 -0.435 0.084 -5.163 0.000

I5I6 -0.435 0.084 -5.163 0.000

I7I9 -1.814 0.264 -6.863 0.000

I8I9 -1.814 0.264 -6.863 0.000

TRAIT1 WITH

TRAIT2 0.351 0.093 3.782 0.000

TRAIT3 -0.323 0.066 -4.889 0.000

TRAIT2 WITH

TRAIT3 0.492 0.100 4.933 0.000

I1I2 WITH

I1I3 1.000 0.000 Infinity 0.000

I2I3 -1.023 0.635 -1.610 0.107

I1I3 WITH

I2I3 1.253 0.781 1.603 0.109

I4I5 WITH

I4I6 1.000 0.000 Infinity 0.000

I5I6 -1.027 0.324 -3.172 0.002

I4I6 WITH

I5I6 0.520 0.177 2.934 0.003

I7I8 WITH

I7I9 1.000 0.000 Infinity 0.000

I8I9 -0.751 0.352 -2.133 0.033

I7I9 WITH

I8I9 1.003 0.591 1.699 0.089

Thresholds

I1I2$1 -0.034 0.091 -0.375 0.708

I1I3$1 0.066 0.095 0.691 0.490

I2I3$1 0.100 0.086 1.156 0.248

I4I5$1 0.005 0.081 0.063 0.950

I4I6$1 0.084 0.060 1.386 0.166

I5I6$1 -0.033 0.074 -0.441 0.659

I7I8$1 -0.068 0.083 -0.819 0.413

I7I9$1 -0.062 0.088 -0.698 0.485

I8I9$1 -0.131 0.084 -1.552 0.121

Variances

TRAIT1 1.000 0.000 999.000 999.000

TRAIT2 1.000 0.000 999.000 999.000

TRAIT3 1.000 0.000 999.000 999.000

Residual Variances

I1I2 2.023 0.635 3.184 0.001

I1I3 2.253 0.781 2.883 0.004

I2I3 2.276 1.361 1.673 0.094

I4I5 2.027 0.324 6.259 0.000

I4I6 1.520 0.177 8.575 0.000

I5I6 1.547 0.418 3.701 0.000

I7I8 1.751 0.352 4.976 0.000

I7I9 2.003 0.591 3.392 0.001

I8I9 1.754 0.837 2.097 0.036

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix 0.267E-03

(ratio of smallest to largest eigenvalue)

SAMPLE STATISTICS FOR ESTIMATED FACTOR SCORES

SAMPLE STATISTICS

Means

TRAIT1 TRAIT2 TRAIT3

________ ________ ________

1 -0.001 0.002 0.004

Covariances

TRAIT1 TRAIT2 TRAIT3

________ ________ ________

TRAIT1 0.564

TRAIT2 0.260 0.574

TRAIT3 -0.171 0.321 0.574

Correlations

TRAIT1 TRAIT2 TRAIT3

________ ________ ________

TRAIT1 1.000

TRAIT2 0.458 1.000

TRAIT3 -0.301 0.560 1.000

SAVEDATA INFORMATION

Order and format of variables

I1I2 F10.3

I1I3 F10.3

I2I3 F10.3

I4I5 F10.3

I4I6 F10.3

I5I6 F10.3

I7I8 F10.3

I7I9 F10.3

I8I9 F10.3

TRAIT1 F10.3

TRAIT2 F10.3

TRAIT3 F10.3

Save file

ipsative_example_fscore

Save file format

12F10.3

Save file record length 5000

Beginning Time: 14:34:44

Ending Time: 14:34:44

Elapsed Time: 00:00:00

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