Indicator Model of Examination Grades with Latent Parameters

The article proposes to use the indicators of grades 5, 4, 3 to describe the probabilities of an examination grade. It is assumed that the probability of a value of each indicator depends on the latent parameters: the student's readiness to receive a grade corresponding to the indicator and the difficulty of receiving the corresponding grade on the exam. The probabilities of grades are determined depending on the probabilities of indicators. The probabilities of the indicator are determined depending on the values of the student and exam latent parameters. The maximum likelihood method is used to obtain equations linking the latent parameters and observation of indicators. An algorithm for numerically solving equations for finding estimates of latent parameters from an array of grades is described. The adequacy of the model is verified using variance analysis methods. Options for applying the examination grade model to improve the quality of education are described.