where p(x|θ, ϑ) is the probability of a response vector x given the subject ability θ and the vector of item parameters ϑ. The number of item parameters depends on the model used (1PL, 2PL, or 3PL).
where g(θ|ν) is the distribution of the subjects and ν is a vector of the population location and scale parameters. The normal distribution with mean 0 and standard deviation 1 is used for g(θ|ν) in JMP.
There are 2L patterns of responses for L items. The ability level for each pattern can be calculated by finding the ability level with the highest probability for the response pattern by applying the following until θ converges:
θ maximizes the likelihood of obtaining the response pattern
t is the number of iterations
L is the number of items
Xi is the observed score
pij is the probability of a correct response on the jth item by the ith person based on the item parameters.

Help created on 7/12/2018