IRT

Question 1

Item Response Theory

Answer 1

• measurement theory that describes how an item is related to a construct
• measured by item characteristic curve

Question 2

Theta

Answer 2

person’s construct score (theta/ability) in IRT

Question 3

Empirical ICC

Answer 3

• Plots probability of an item response by their level on a construct
• IRT

Question 4

Model-Implied ICC

Answer 4

-fit a logistic (sigmoid) curve to each item’s probability (think of this as the prettier graph)
IRT

Question 5

Test

Answer 5

ICCs can be summed across items to get the TCC

Question 6

IRT Utility

Answer 6

Helps us to select fewer items, be more succinct (reduce redundancy)

Question 7

IRT Parameters

Answer 7

1. Difficulty/severity
2. Discrimination
3. Guessing
4. Careless Errors

Question 8

Difficulty

Answer 8

• corresponds to item location on the latent construct

- meaning, where on the x-axis the point at which 50% probability of that item falls

Question 9

Discrimination

Answer 9

□ How well the item can distinguish between those higher or lower on the construct
□ AKA, how strongly the item is correlated with the construct/latent factor
□ Determined by slope at steepest point
–Steeper = fine distinction; less difference needed to make the individual switch from unlikely to likely
–Less steep = less precise and less info, low discrimination; more difference needed to make an individual switch from less to more likely

Question 10

Guessing

Answer 10

□ How likely a person would get the correct answer even if guessing
□ Determined by lower asymptote
—If lower asymptote is above zero, it suggests that person’s probability of getting the item correct never reaches zero (think: 50% on true/false, 25% on 4-chice multiple choice)

Question 11

Careless Errors

Answer 11

□Determined by upper asymptote
–If upper asymptote is below 1, the probability of getting the item correct/endorsing the item never reaches 1 for any level on the construct

Question 12

IRT Models

Answer 12

1. 1-Parameter: difficulty
   
   • No crossed lines
2. 2-Parameter: difficulty, discrimination
   
   • Cross lines, lower asymp of 0, higher of 1
3. 3-Parameter: difficulty, discrimination, guessing
   
   • Crossed lines, random lower asymp, higher of 1
4. 4-Parameter: difficulty, discrimination, guessing, carless error
   
   • Crossed lines, random lower and upper asymp

Question 13

Polytomous Data

Answer 13

Likert scale

• if 5 items, there’s 4 thresholds (k-1)
• if 5 items, tells us as much as 4 dichotomous variables