This presentation covers the intricacies of the Item Response Theory. I made this presentation to explain the concepts of IRT to my lab research group at the University of Minnesota. I have taken the contents from various sources so apologies for the poor design of the presentation.

1. Item Response Theory
Rahul Bhojwani
rahulbhojwani2003@gmail.com
bhojw005@umn.edu

2. Different Test Theories:
● Classical Test Theory
● Item Response Theory

4. Let’s start with IRT Terminologies:
● Item
● Ability and Difficulty
● Scale

5. Type of Items:
● Dichotomous (True or False)
● Polytomous (Multiple Choice)

15. IRT entails 3 assumptions:
● A unidimensional trait denoted by 𝛉
● Local independence of items;
● The response of a person to an item can be
modeled by a mathematical item response
function (IRF).

27. Adding more parameters
● 1 PL model ( Difficulty)
● 2 PL model ( Difficulty and Discrimination)
● 3 PL model ( Difficulty, Discrimination and
Guessing)

43. Item Calibration:
● How to generate item and test taker difficulty from
the response matrix:
○ Joint Maximum Likelihood (UCON)
○ PROX
■ http://www.winsteps.com/winman/estimation.htm
■ https://conservancy.umn.edu/bitstream/handle/11299/98553/v01n2p
281.pdf?sequence=1

44. Item Calibration:
● How to add new items to the scale:
○ Same students → New items
○ New students → New items
○ New students → Old items
● How to match two different scales:

45. Get scale of new test taker:
● Maximum Likelihood
● Bayesian model
● Link: https://www.rasch.org/memo23c.pdf
● Test Characteristic curve

52. Questions??

53. Sources:
Item difficulty calibration:
https://conservancy.umn.edu/bitstream/handle/11299/98553/v01n2p281.pdf?sequ
ence=1

54. Extras: