1. The Impact of Item Response Theory in Educational Assessment: A Practical Point of View Cees A.W. Glas University of Twente, The Netherlands
University of Twente

2. Measuring body height with a questionnaire
1. I bump my head quite often
2. For school pictures I was always asked to stand in the first row
3. In bed, I often suffer from cold feet
4. When walking down the stairs, I often take two steps at a time
5. I think I would do well in a basket ball team
6. As a police officer, I would not make much of an impression
7. In most cars I sit uncomfortably
8. I literally look up to most of my friends
9. Etc.

3. Test of Body Height 3 7 5 9 11 13 1 18 2 4 8 6 21 6 16
Jim
Ann Jo

4. The Rasch model

5. Item Response Curve Rasch model
Probability
Correct
Response
Latent Ability Scale

6. Item Response Function
Discrimination
Probability of Success
Guessing
Difficulty
Ability

7. Applications Local reliability and optimal test construction
Test Equating
Multilevel item response theory in school effectiveness research

8. Item and Test Information
Information is a local measure of reliability
Item and test information function
In Adaptive Testing items are selected to maximize information at the estimated ability of examinee.

9. Adaptive Item Selection
Information

10. Adaptive Item Selection Cont’d
Information
Item 1

11. Adaptive Item Selection Cont’d
Test
Item 2
Item 1
Information

12. Adaptive Item Selection Cont’d
Test
Information
Item 3
Item 2
Item 1

13. Item and Test Information Cont’d
Items
Ability

14. Adaptive Testing with Content Constraints
Psychometrically optimal adaptive individualized testing
Test content specifications
Psychometrically optimal within content constraints and practical constraints
Discrete optimization problem

15. Adaptive Testing with Content Constraints
Law School Admission Test
content constraints
item type constraints
word count constraints
answer key constraints
gender / minority orientation
clusters of items (testlets)
some items contain clues to each other

16. Test Constraints
Constraints are imposed by Linear - Programming techniques
For every item i a variable is defined

17. Test assembly model Maximize information in the test
Item i is selected for the test or not.
At most 5 items on statistics
Items 12 and 35 contain clues to each other
Time available is 60 minutes

18. Equating of Examinations
Problem: level of students and difficulty of examinations fluctuate over the years
Objective: to determine pass/fail cut-off scores on examinations in such a way that it reflects the same level of proficiency on the latent scale,
taking into account the difficulty level of the examinations
and differences in proficiency level over years

20. Simple Deterministic Model
Important feature of the model: Parameter Separation: distinct parameters for persons and items
University of Twente

22. Model for Item with 5 response categories
Probability
Response
Category
X=0
X=4
X=1
X=3
X=2
Latent Ability Scale

23. Multidimensional IRT model
University of Twente

24. Anchor Item Equating Design

25. Problems Anchor Item Design
Student ability increases between test administrations due to learning
Difference in ability and item ordering between anchor test and examination due to low motivation of students
If anchor test becomes known, the test functions different over the years
All these effects violate the model and bias the estimated cut-off scores

26. Equating Design Central Examinations, the Netherlands

27. Equating Design SweSat

28. Measurement model: GPCM
Alternatives to GPCM (Muraki):
Graded Response Model (Samejima)
Sequential Model (Tutz)

29. Structural Model Takane and de Leeuw (1987)
Model is equivalent with a factor analysis model:
Discrimination parameters are factor loadings
Ability parameters are factor scores

30. IRT structural modeling

31. Problems with “ordinary” regression and analysis of variance models
Different aggregation levels: school level and student level
Variance structure: students within schools are more similar than students from different schools
Old unsatisfactory solutions:
aggregating to school level
disaggregating to student level
Newer solutions: multilevel models: Bryk & Raudenbush, Longford, Goldstein

33. Motivation for this approach All the niceties of IRT are available in Multilevel Analysis
Method to model unreliability in the dependent and independent variables
Hetroscedasticity: reliability is defined locally
Incomplete test administration and calibration design (possibility to include selection models)
No assumption of normally distributed scores
Less ceiling problems

34. An Example (Shalabi, Fox, Glas, Bosker)
3384 grade seven pupils in 119 schools in the West Bank
Mathematics test
Gender
SES IQ
School Leadership
School Climate

35. Intra-class correlation:
Model:
Intra-class correlation:

38. Conclusions IRT is based on the idea of parameter separation
An IRT measurement model can be combined with a structural model
The combined model is equivalent with factor analysis and latent variable models and as such a generalization of other well-known regression models
Applications of IRT
Local reliability and optimal test construction
Test Equating
Multilevel IRT in school effectiveness research