In the basic local independence model (BLIM), the conditional probability of the response pattern R given the knowledge state K is based on the assumption of local stochastic independence between the responses given this knowledge state. The following app illustrates the building blocks of the probability P(R|K).

Now it's your turn! Test your knowledge in the following exercises.


Select the appropriate expression for each of the stated empirical interpretations.

Lucky guess
Careless error
Correct response
(item mastered)
Incorrect response
(item not mastered)

Sarah takes part in a test with five items: a, b, c, d, and e. She only masters items a and b. But she answers items b, c, and e correctly. The response pattern R contains Sarah's correct responses, the knowledge state K contains the items she masters.

Venn diagram

Set representation

Select the subset in which each item is to be placed.

Item a is element of
Item b is element of
Item c is element of
Item d is element of
Item e is element of

Now classify Sarah's answers to each item. If your choice is correct, the corresponding expression will appear in the formula below. If your choice is wrong, a question mark will appear instead.








The probability of the response pattern R given the knowledge state K is:

R = {b,c,e} and K = {a,b}

P(R|K) =

⋅

⋅

⋅

⋅




The probability of the response pattern R given the knowledge state K is:

R = {b,c,e} and K = {a,b}
P(R|K) = βa ⋅ (1 - βb) ⋅ ηc ⋅ (1 - ηd) ⋅ ηe

Select parameter values and see how P(R|K) changes.