# Scores to Measures with SPSS

"How can I get the logit measures corresponding to raw scores from each of three forms using pre-calibrated items? Ideally I would like to construct a table that associated every raw score on each of the three forms to an interval-level measure, and I would like all of these measures to be on a common metric."
Karon Cook

Here is an SPSS routine that automates the process. You provide an initial starting ability estimate that is at about the mean of your pre-calibrated item difficulties. The routine then computes the estimated raw score (sum of p) for the specified set of pre-calibrated items, as well as the sum of p(1-p). For the next iteration, it use the Newton-Raphson method to adjust the estimated ability by adding (target raw score - sum of p)/(sum of p(1-p)). Change 20 in the following to your test length, L:

TITLE
INPUT PROGRAM
+ LOOP RS = 1 TO 19 [insert the range of raw scores from 1 to L-1]
+ COMPUTE ABIL = 0 [Insert your starting ability value here]
+ COMPUTE DISC = 0
+ LOOP
+ COMPUTE ABIL = ABIL + DISC
+ DO REPEAT PROB = P1 TO P20/DIFF = [insert your string of L difficulties]
+ COMPUTE PROB = ((EXP(ABIL - DIFF)))/(1 + EXP(ABIL - DIFF))
+ END REPEAT
+ DO REPEAT PQ = PQ1 TO PQ20 / PROB = P1 TO P20 [change 20 to your L ]
+ COMPUTE PQ = (PROB) * (1 - PROB)
+ END REPEAT
+ COMPUTE DISC = (RS - SUM(P1 TO P20))/(SUM(PQ1 TO PQ20))
+ END LOOP IF (ABS(DISC) LT .01) [my criterion for convergence = .01]
+ END CASE
+ END FILE
END INPUT PROGRAM
LIST VAR = RS ABIL

Mark Daniel
American Guidance Service

Scores to Measures with SPSS.Daniel M. … Rasch Measurement Transactions, 1998, 12:2 p. 637.

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