Risk of Metropolis-Hastings Robbins-Monro algorithm in multidimensional models of item-response theory in binary data considering test length

The present study was conducted with the aim of investigating the risk of MHRM algorithm in multi-dimensional models of item-response theory in binary data, taking into account different test dimensions and lengths. The research method used was a real experiment using a multi-group post-test design. The studied sample was created based on simulation studies under different conditions of independent variables in 27 modes with 100 repetitions for each. The model used was the two-parameter multidimensional model of logistics and the investigated parameters were the slope and difficulty of the items. In order to check the risk of each of the parameters in different experimental conditions, the average squared error index was used. R statistical software packages mirt, interactions, car and psych were used for data generation and analysis. The results of the research showed that the MHRM algorithm has less risk compared to the EM and MCEM algorithms. This issue was especially evident under the conditions of high dimensional data (5 dimensions) and short test length (15 questions). Also, the results of the research showed that when the dimensions of the test increase and the length of the test decreases, the risk of parameter estimation increases significantly. As a result, it can be said that the application of the MHRM algorithm in data with a high number of dimensions and a short test length is necessary, and researchers are advised to use it in the analysis of data with a complex structure such as a high number of dimensions