Final - Item Response Theory (Reise et al.)

Question 1

What are 2 key limitations of classical test theory?

Answer 1

• interpretation of true score is test and sample dependent
• reliability of true score is a function of items used (assumes all items are interchangeable which we can’t rly assume)

Question 2

What are the 4 assumptions of IRT?

Answer 2

• true score defined on latent trait dimension rather than observed score
• knowing the properties of the item a person endorses tells us the trait level the person possesses (items characterized using same latent trait dimension used to characterize ppl)
• properties of item don’t change if we administer item using different samples
• true score does not change regardless of which set of items is administered

Question 3

IRT is a family of _____ that describe the probability of _____ as a function of _____

Answer 3

• family of mathematical models
• prob of a given response to an item as a function of certain item properties and respondent true score

Question 4

The probability of an item endorsement across the range of true scores is represented by a function called _____

Answer 4

item response function

Question 5

What is the item characteristic curve (ICC)?

Answer 5

• plot of IRF (equation relating theta/true score to prob of endorsing an item)
• x-axis = theta/latent trait
• y-axis = probability of item endorsement

Question 6

What does it mean that the item characteristic curve is monotonic?

Answer 6

• prob of item endorsement increases w increases in theta

Question 7

In the middle of the ICC, changes in theta correspond to (large/small) changes in probability relative to the ends of ICC

Answer 7

LARGE (steeper in middle)

Question 8

ICC is limited by ___ and ___

Answer 8

0 and 1 (probability is bound by 0-1)

Question 9

What is item difficulty (b)?

Answer 9

• point on theta where probability of item endorsement is 50%
• draw a horizontal line from 0.5, b is where line intersects w curve

Question 10

Item difficulty (b) typically ranges between __ and __

Answer 10

-2 and 2

Question 11

What does it mean if:
- b is negative
- b is positive
- theta > b
- theta < b
- theta = b

Answer 11

• b is negative: easier item (more freq endorsed)
• b is positive: difficult item (less freq endorsed)
• theta > b: item more likely to be endorsed
• theta < b: item less likely to be endorsed
• theta = b: 50% chance of item being endorsed

Question 12

What is item discrimination (a)?

Answer 12

• value of slope at steepest point of curve

Question 13

item discrimination (a) typically ranges between __ and __

Answer 13

.5 and 1.5

Question 14

Highly discriminating items have (smaller/steeper) slopes
Poorly discriminating items have (smaller/steeper) slopes

Answer 14

• highly: steeper slopes
• poorly: smaller slopes

Question 15

What is the ITEM information curve?

Answer 15

• how well an item differentiates among respondents who are at diff levels of latent variable
• basically how well are items doing their job at assessing the true score
• item diff: location on latent trait where info is maximized
• item discr: how much info item provides

Question 16

What is the TEST information curve (TIC)?

Answer 16

• relative precision of scale across diff locations of theta
• height proportional to SEM (inversely related)
• want curve high for entire range of theta (think table)

Question 17

(T/F) SEM is the same across all latent trait values

Answer 17

FALSE, different for every value of theta

Question 18

in IRT, what are the 2 ways items vary?

Answer 18

difficulty and discrimination

Question 19

the location on the curve where items provide the most information is at ____

Answer 19

theta = b

Question 20

What are the 5 ways IRT helps us improve psychological tests?

Answer 20

• IDENTIFY item characteristics (eg difficulty, discr.)
• CHOOSE items w higher discrimination covering entire range of latent continuum
• INCREASE reliability w fewer items
• COMPARE items across diff measures of same construct
• COMPARE group differences

Question 21

What are the 2 primary applications of IRT?

Answer 21

• improving existing measures
• detecting differential item functioning

Question 22

What is differential item functioning (DIF)?

Answer 22

• assesses whether there is measurement equivalency btw 2 or more groups
• examination of group diffs in item responses when controlling for latent trait (groups should be equal on theta)