Dear all,
I have an English Listening Comprehension test consisting of 50 items taken by about 400 students. I would like to score the test using the TOEFL scale (max 58 I think), and it is claimed that TOEFL is scored using IRT (3PL model). I am using MIRT package in R to obtain three parameters, as I used 3PL model.
library(readxl)
TOEFL006
Hello Faisal,
The formula you give only refers to the likelihood of success on a single item. I think you're asking how to form ability estimates for each of the dimensions in your measure.
Have a look at this thread, as I think it gives the information you're after: https://groups.google.com/g/mirt-package/c/eIG8-n7t7zA
Good luck with your work.
Hi David,
Thank you very much for your reply. Now I understand that I have been mislead.
I have now calculated the factor score.
> fscores(data)
and I obtained the factor scores:
[1,] 2.1839888
[2,] 1.8886260
[3,] 0.6791995
[4,] 1.2761837
[5,] 0.8195919
[6,] -1.5257231
I am still confused how to convert these scores into TOEFL score for listening section (31-68). Thank you very much for your kind help.
Hello again Faisal,
What you're now asking is, how to equate/adjust the scores from your sample, with the items that sample responded to, to appropriately reside on the ETS scale for TOEFL scores. To do this perfectly would require that you knew the original linkage between the (original) calibration of TOEFL items to the arbitrary 31-68 scale _and_ be positive that your item calibrations were not biased from those of ETS's original data set with respect to the nature of the sample (distribution of ability).
If you simply want to present scores on that scale, and you don't care about comparability with respect to ETS's published norms, then you could arbitrarily set the limits to either scores of 0 and 100% of items (= 31 & 68, respectively--which is tricky, because IRT models can't use cases with zero or perfect scores for item calibration purposes...there has to be some variation), or set the limits for the lowest observed factor score and highest observed factor scores to those values, then use linear interpolation for the remainder of scale values, then round each factor score to the nearest (interpolated) scale value.
Good luck with your work.
This essay may be of interest for your research showing that IRT theta-parameter is not ability measure although they are positively correlated to each other:
Preprint Item Response Theory and Its General Total Score
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