Linking item parameters to a base scale

Abstract

This paper compares three methods of item calibration—concurrent calibration, separate calibration with linking, and fixed item parameter calibration—that are frequently used for linking item parameters to a base scale. Concurrent and separate calibrations were implemented using BILOG-MG. The Stocking and Lord in Appl Psychol Measure 7:201–210, (1983) characteristic curve method of parameter linking was used in conjunction with separate calibration. The fixed item parameter calibration (FIPC) method was implemented using both BILOG-MG and PARSCALE because the method is carried out differently by the two programs. Both programs use multiple EM cycles, but BILOG-MG does not update the prior ability distribution during FIPC calibration, whereas PARSCALE updates the prior ability distribution multiple times. The methods were compared using simulations based on actual testing program data, and results were evaluated in terms of recovery of the underlying ability distributions, the item characteristic curves, and the test characteristic curves. Factors manipulated in the simulations were sample size, ability distributions, and numbers of common (or fixed) items. The results for concurrent calibration and separate calibration with linking were comparable, and both methods showed good recovery results for all conditions. Between the two fixed item parameter calibration procedures, only the appropriate use of PARSCALE consistently provided item parameter linking results similar to those of the other two methods.

Appendix

• 1. Concurrent Calibration for both base and target groups (BILOG-MG)

>COMMENT

>GLOBAL DFNAME = ’BLMcom200.dat’,NPARM = 3,SAVE;

>SAVE PARM = ’BLMcom200.par’;

>LENGTH NITEMS = 60;

>INPUT NTOT = 60, NID = 4, NGROUP = 2, NFNAME = ’c:\FIPC\simu\keynot.txt’;

>ITEMS INUM = (1(1)60),INAMES = (OL01(1)OL10, CO01(1)CO40, NE01(1)NE10);

>TEST TNAME = Math;

>GROUP1 GNANE = ’BASE’, LENGTH = 50, INUM = (1(1)50);

>GROUP2 GNANE = ’TARGET’, LENGTH = 50, INUM = (21(1)60);

(4A1,1X,I1,1X,60A1)

>CALIB NQPT = 11, cycles = 3000, CRIT = 0.001, REF = 1, TPRIOR;

>SCORE NOPRINTS;

• 2. Separate Calibration for a target group (BILOG-MG)

>COMMENT

>GLOBAL DFNAME = ’new200.dat’,NPARM = 3,SAVE;

>SAVE PARM = ’BLMnew200.par’;

>LENGTH NITEMS = 50;

>INPUT NTOT = 50, NALT = 5, NID = 4;

>ITEMS INUM = (1(1)50),INAMES = (CO01(1)CO40, NE01(1)NE10);

>TEST TNAME = Simulation;

(4A1,T1,50A1)

>CALIB NQPT = 11, cycles = 3000, CRIT = 0.001, TPRIOR;

>SCORE NOPRINTS;

• 3. Fixed Item Parameter Calibration for a target group (BILOG-MG)

>COMMENT

>GLOBAL DFNAME = ’new200.dat’, PRNAME = ’BLMOLD200.PRM’, NPARM = 3, SAVE;

>SAVE PARM = ’BLMfix200.par’;

>LENGTH NITEMS = 50;

>INPUT NTOT = 50, NALT = 5, NID = 4;

>ITEMS INUM = (1(1)50),INAMES = (CO01(1)CO40, NE01(1)NE10);

>TEST TNAME = Math, FIX = (1(0)40,0(0)10);

(4A1,T1,50A1)

>CALIB NQPT = 11, cycles = 3000, CRIT = 0.001, TPRIOR, NOADJUST;

>SCORE NOPRINTS;

• 4. Fixed Item Parameter Calibration for a target group (PARSCALE)

>COMMENT

>FILE DFNAME = ’new200.dat’, IFNAME = ’PSLold200.prm’, SAVE;

>SAVE PARM = ’fix200.par’;

>INPUT NIDCH = 4, NTOTAL = 50, NTEST = 1, LENGTH = 50, NFMT = 1;

(4A1, T1, 50A1)

>TEST TNAME = Math, ITEM = (01(1)50), NBLOCK = 50,

 INAMES = (

 CO01, CO02, CO03, CO04, CO05, CO06, CO07, CO08, CO09, CO10,

 CO11, CO12, CO13, CO14, CO15, CO16, CO17, CO18, CO19, CO20,

 CO21, CO22, CO23, CO24, CO25, CO26, CO27, CO28, CO29, CO30,

 CO31, CO32, CO33, CO34, CO35, CO36, CO37, CO38, CO39, CO40,

 NE01, NE02, NE03, NE04, NE05, NE06, NE07, NE08, NE09, NE10);

>BLOCK1 BNAME = COMMON, NITEM = 1, NCAT = 2,

 ORI = (0,1), MOD = (1,2), GPARM = 0.2, GUESS = (2, EST), REP = 40, SKIP;

>BLOCK2 BNAME = UNIQUE, NITEM = 1, NCAT = 2,

 ORI = (0,1), MOD = (1,2), GPARM = 0.2, GUESS = (2, EST), REP = 10;

>CALIB PARTIAL, LOGISTIC, SCALE = 1.7, NQPT = 41, CYCLE = (3000,1,1,1,1),

 FREE = (NOADJUST, NOADJUST), POSTERIOR, NEWTON = 0, CRIT = 0.001, ITEMFIT = 10, SPRIOR, GPRIOR;

>SCORE;