Step-by-Step Model with Latent Parameters for Student Assessments

The article discusses the disadvantages of traditional approaches to statistical processing of assessments of intermediate attestations of students. We proposed a model in which the obtaining of the k grade on an ordinal scale is associated with the successful completion of k certification steps. By analogy with Item Response Theory used for processing test results the probability of a successful step is determined by latent parameters — the student's ability and the difficulty of the step. Methods for determining latent parameters from the estimates obtained and statistical procedures for checking the adequacy of the model are proposed. The data of processing the array of estimates are presented. The processing results confirmed the possibility of using the proposed mo­del for a more accurate assessment of students' ability and the difficulty of attestations.