The Research Of Item Response Theory 3PLM Parameter Estimation Based On Improved Particle Swarm Otpimization

Item response theory (IRT) is a relatively new theory which is based on psychology measurement. By contrast with classical test theory, it better reflects the true level of ability of those people who take part in test. With the development of the IRT. the scholars bring forward many mathematical models, and the three parameters logistic model has a more widely application. The three parameters logistic model shows a logical relationship of the disturb, the difference, guess coefficient of the item, the ability of people who join in the test and the probability of getting the correct answer. The relationship provides the basis of the determination of every item's parameters and the testers' ability. For a long time, in the three parameters model, the determination of every parameter is based on some higher mathematics methods, but those methods always have some fatal flaws, they often don't converge in the reasonable time or the estimate results have a large deviation from the real results, so a new feasible, more efficient solution is necessary.Particle Swarm Optimization is a new type of swarm intelligence algorithm which is brought out by Dr.Eberhart and Dr.Kennedy in 1995, the algorithm is derived from the research about the movement behavior of birds and fish group. It is an optimization algorithm which is based on particle intelligent evolution and group search strategy. It is often used to solve some large-scale, complex, nonlinear, nondifferentiable. optimization problems.The thesis makes a feasibility analysis of whether particle swarm optimization can get the fit parameter estimation values in 3PLM of item response theory, and the conclusion proves that the PSO can get the fit estimation values. It is not satisfied if we use the basic PSO to get the estimation values in 3PLM, because the basic PSO has some deficiencies:the algorithm is prematurity easily and easy to fall into local optimum in the latter. In order to eliminate these shortcomings of the basic PSO, the thesis provides an improved new hybrid particle swarm algorithm, which introduced the sub-group of the ring topology firstly, and each sub-group can exchange the optimal solution regularly, so that the algorithm has a faster convergence and the more accuracy global search results. The enhanced algorithm also introduces the simulated annealing and species extinction mechanism. In theory, simulated annealing converge to the global optimal solution with probability 1, and the combination of PSO and simulated annealing can make algorithm escape the local optima and to find the global optimal solution. Extinct species mechanism increases the diversity of particles, it can make the algorithm has a more sophisticated search. The improved PSO algorithm is more excellent than the basic PSO algorithm. Computer simulations show that the improved PSO algorithm improves the accuracy greatly, and the new algorithm is more feasible.The thesis applies the new enhanced PSO algorithm to parameter estimation in the three parameters of the item response theory. First, the circumstance that we study is the each item parameters and the ability parameter of each tester are all unknown, and this is the most common situation in reality. In this case, it is also the most significant to use the improved PSO to estimate the parameter values in 3PLM. Second, we determine the objective function for each tester and each item. We let the log-likelihood function as the objective function and find out the best solution by the objective function. Third, we determine the parameters value domain and the population size of the enhanced algorithm, their values will have a great influence to the algorithm efficiency, the proper value will enhance the performance of the algorithm greatly. At last, we determine the steps of how to use improved pso algorithm in 3PLM parameters estimate of item response theory.Finally, the thesis uses Monte Carlo experiments to test new hybrid particle swarm optimization algorithm. To compare the estimate value of improved PSO algorithm and the BILOG software, we design the eight typical cross experiments. If the guess coefficient is in different range, the estimate result is also different, so we design another experiment which divides the guess coefficient into three different ranges. We use the two statistics:RMSE and ABSE to evaluate the experiment results. The statistical analysis proves that the improved PSO can improve the recovery of the true value of estimate parameters in 3PLM parameter estimation of item response theory, and the estimated results are not dependent on the choice of initial parameter values, so the new improved PSO algorithm is feasible and efficient.