The EM Algorithm For Skew Normal Item Response Theory

With the explosive growth of global data and the increase in analysis of latent traits requirements through the observable data,the item response theory(IRT)has become the popular theory in the field of statistics recently,and it has been researched and applied widely in education,psychology,health care,etc.It is generally assumed that underlying hidden variable follows normally distribut-ed when estimating IRT model parameters.However,there are many situations where the data may not be normally distributed.Therefore,this paper mainly studies the IRT model when the underlying hidden variable follows skew normal distribution.The skew normal IRT model was proposed through reasonable assumptions,and the skewed EM algorithm was given,and a reasonable analysis was performed in the med-ical datasets.First,this paper introduces the popular MCMC algorithm and EM algorithm under the IRT model.Second,the skew IRT model was proposed based on the skew normal distribution.Further,this paper deduces the specific form of the skewed EM algorith-m,proves the convergence of the skewed EM algorithm theoretically and calculates its convergence rate as O(log(1/c)),time complexity as O(A J2).Finally,numerical sim-ulation and empirical analysis are performed in this paper.The results show that the skew IRT model can better fit the real data,and the skewed EM algorithm is superior to the traditional MCMC algorithm in terms of computational time and accuracy.