IRT 2

Question 1

assumptions of maximum likelihood (ML)

Answer 1

1. unidimensionality
   > items only correlate because they measure the same single latent variable
2. local independence
   > conditional on theta, all items are independent

Question 2

joint ML

Answer 2

+ all parameters are estimated simultaneously

• all/none items correct = infinite/-infinite theta
• everybody/nobody has an item correct = infinite/-infinite b
• undesirable asymptotic properties (can create an infinite number of parameters in large sample sizes)

Question 3

conditional ML (eRm)

Answer 3

estimates easiness instead of difficulty

+ conditional on sum score, theta disappears, so you only have item parameters
(so does not assume a standard normal distribution for theta)

• only applicable to rasch model

Question 4

marginal ML (ltm)

Answer 4

+ applicable to all IRT models

• assumes normal distribution of theta (mean = 0, sd = 1)

Question 5

identification

Answer 5

marginal ML
- variance theta = 1
- mean theta = 0

conditional ML
- mean b = 0

Question 6

model fit

Answer 6

unidimensionality
> eigenvalues

equal a parameters
> item rest/item test correlations

absence of guessing
1. test on basis of theta estimates
2. test on basis of sum scores
3. 3 parameter model

model predictions
> Pij - E(Pij)

Question 7

model comparison - likelihood ratio test

conditions

Answer 7

1. models have to be nested
2. constraints cannot be boundary constraints

Question 8

significant likelihood ratio test

Answer 8

if the LRT is significant, the most complex model fits best

> e.g., the constraints in the Rasch model deteriorate the likelihood