MLE Scoring with a Graded Model

In this example, the item parameter estimates from previous example, saved in the exampl01.par file, are used in scoring the simulated examinees by the maximum likelihood method (MLE).

EXAMPLE 2:  ARTIFICIAL EXAMPLE (MONTE CARLO DATA)
            GRADED MODEL - MLE SCALE SCORES
>COMMENTS
>FILES  DFNAME='EXAMPL01.DAT', IFNAME='EXAMPL01.PAR', SAVE;
>SAVE   SCORE='EXAMPL02.SCO';
>INPUT  NIDCH=4, NTOTAL=20, LENGTH=20;
(4A1,10X,20A1)
>TEST1  TNAME=SCALE1, ITEM=(1(1)20), NBLOCK=1;
>BLOCK1 BNAME=SBLOCK1, NITEMS=20, NCAT=4;
>CALIB  NOCALIB;
>SCORE  MLE, SMEAN=0.0, SSD=1.0, NAME=MLE, PFQ=5;

The syntax file above is very similar to that of the example in previous example.

Note that the item parameter file from the previous example is used as input (IFNAME keyword on the FILES command) and that calibration is suppressed by the NOCALIB option of the CALIB command.

Comparison of the results in files example03.ph3 (see Phase 3 output below) and exampl02.ph3 (not shown here) show that, when the scores are scaled to match the mean and standard deviation of the generating distribution, both the EAP and MLE estimates recover the generating values with good accuracy.

EAP Scores with Generalized Partial Credit Model

This example scores and calibrates the data of the previous example assuming the partial credit model with standard scoring function. The syntax file is shown below.

EXAMPLE 3:  ARTIFICIAL EXAMPLE (MONTE CARLO DATA)
            GENERALIZED PARTIAL CREDIT MODEL - EAP SCALE SCORES
>COMMENTS
>FILES   DFNAME='EXAMPL01.DAT', SAVE;
>SAVE    SCORE='EXAMPL03.SCO';
>INPUT   NIDCH=4, NTOTAL=20, NTEST=1, LENGTH=20;
(4A1,10X,20A1)
>TEST    TNAME='SCALE1', ITEM=(1(1)20), NBLOCK=2;
>BLOCK1  BNAME='SBLOCK1', NITEMS=10, NCAT=4, SCORING=(1,2,3,4);
>BLOCK2  BNAME='SBLOCK2', NITEMS=10, NCAT=4, MODIFIED=(1,1,2,2),
         SCORE=(1,2);
>CALIB   PARTIAL, LOGISTIC, NQPTS=15, CYCLE=(100,1,1,1,1), NEWTON=2,
         CRIT=0.01;
>SCORE   MLE, SMEAN=0.0, SSD=1.0, NAME='PCR_MLE', PFQ=5;

To illustrate the situation where two types of items are involved, the four categories for the second ten items are collapsed into two categories, thus making those items effectively binary. Two blocks are required (each with ten items), and the MODIFIED list in the BLOCK2 command specifies the collapsing.

The standard score function assumes 4 is the high category, so no response modification is required in BLOCK1. In BLOCK2, the scoring function is used to specify scoring function values.

CADJUST is not used with the partial credit model, nor is SCALE in the CALIB command (see example 4-1 and example 4-2 for use of these keywords).

Because the data are now less informative, the number of quadrature points for calibration can be reduced (NQPT=15 instead of the 30 previously used).

Despite the different model and the partition of the items into two blocks, the estimated trait scores in exampl03.sco agree well with the estimates from previous examples after rescaling in the sample.