Using the maximum likelihood method to estimate test complexity levels

Consideration was given to the problem of estimating the levels of complexity of the test tasks for the remote education system. It was assumed that the random responses of the subjects obey the logistic distribution and the levels of student readiness are not known in advance. An algorithm based on the methods of maximum likelihood and Broyden–Fletcher–Goldfarb–Shanno was proposed to calculate the task complexity. Strict concavity of the logarithmic likelihood function was established, and an example was considered.