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The Research of Item Response Theory 3PLM Parameter Estimation Based on Improved Particle Swarm Otpimization

Author: YuanZhou
Tutor: FengTie
School: Jilin University
Course: Computer Software and Theory
Keywords: Item Response Theory Three - Parameter Logistic Model Newton - Raphson iteration Particle swarm optimization Simulated annealing algorithm Extinction mechanism Monte Carlo experiment
CLC: TP301.6
Type: Master's thesis
Year: 2011
Downloads: 69
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Abstract


Item response theory (IRT) is based on a novel psychometric theory, have a large difference with the classical test theory, it is more truly reflect the level of competence of the testers. With the development of item response theory, scholars have put forward a number of mathematical models, one of the most widely used for the three-parameter Logistic Model (3PLM). 3PLM given the topic of discrimination, the relationship between the difficulty, guessing factor, the ability of the tester, and the correct answers probability to determine questions of parameters and the test's ability to provide a theoretical basis. A long time in item response theory 3PLM, mainly through higher mathematics iterative method for solving nonlinear equations solution through knowledge of mathematical statistics to determine the unknown parameters, but the use of these methods is often some fatal defects: not converge in a limited and reasonable time or get a large deviation in the parameter estimates, therefore urgently a new viable, efficient solution. Particle Swarm Optimization Dr. Kennedy and Dr. Eberhart in 1995 by the research groups of birds and schools of fish movement behavior and proposed a new swarm intelligence algorithm. It is based on the particle smart evolution, population search strategy optimization algorithm. Particle swarm optimization algorithm is simple, practical, commonly used to solve a number of large-scale, complex, non-linear, non-differentiable optimization problems and has a good effect. In this paper, the application of particle swarm algorithm to solve the item response theory parameters of 3PLM in estimated to do a feasibility analysis to confirm the feasibility of the particle swarm algorithm in 3PLM parameter estimation, but also pointed out that the direct use of the particle swarm algorithm application in 3PLM parameters estimated in inadequate: as premature because the basic particle swarm algorithm, and later in the algorithm is easy to fall into local extremum, thus resulting parameter estimates have relatively large errors, parameter estimation results are often unsatisfactory. In order to eliminate these shortcomings of the basic particle swarm algorithm, this paper proposes a new and improved hybrid particle swarm algorithm. The algorithm first introduces annular subgroup topology of the whole particle groups are divided into six subgroups six sub-group, form a ring, and mutual transmission of information between the subgroup, in the iterative process, each sub-group to find their own subgroup of the optimal solution regularly exchanged with the adjacent subgroups, and enhance the global search search accuracy, but also speed up the convergence rate of the particle swarm algorithm; introduced simulated annealing population extinction mechanisms, simulated annealing, in theory to the probability of convergence to a global optimal solution, particle swarm and simulated annealing algorithm to escape from local optima, making it easier to find the global optimum, when groups of particle swarm optimal solution for a long time does not update, the improved algorithm using simulated annealing the fine search algorithm, can help to jump out of the local extrema, when the end of the simulated annealing process, the use of populations of extinction mechanism, allowing the particles to re-initialized, thereby increasing the diversity of particle groups, so that the improved algorithm has a better search accuracy. Compared with basic particle swarm algorithm, improved particle swarm algorithm has greatly enhanced the ability to search the optimal solution. The computer simulation results show that the improved particle swarm algorithm greatly improves the accuracy of the algorithm, particle swarm optimization is more useful in practical applications. The papers will be new and improved hybrid particle swarm algorithm is applied to item response theory 3PLM parameters estimated them. First, determine the parameters estimated in project parameters for each project and each of the test's ability parameters are unknown cases, this is the most common situation in reality, in this case using the improved particle swarm algorithm 3PLM parameter estimation is the most meaningful; Second, for each project, with each test to determine the objective function in 3PLM likelihood function is the likelihood function as the objective function of the logarithm of the number of get the objective function to calculate the optimal solution for each particle; once again, determine the improved particle swarm algorithm parameters and population size, their value will algorithm running efficiency have an important impact, the appropriate value will be greatly enhanced algorithm performance; Finally, determine the improved algorithm in the the item response the theory 3PLM parameter estimation step, the use of new and improved algorithms to find the optimal solution in the solution space as the estimates of the various parameters. Finally, the use of Monte Carlo experiments to verify the performance of the new hybrid particle swarm algorithm. To compare the improvement the parameter estimates commercial software BILOG particle swarm algorithm to get the parameter estimates designed eight typical crossover experiment; projects speculation coefficient distribution at different intervals, the results tend to be estimated have great influence, guess coefficient is divided into three intervals to conduct a separate experiment. The experimental results with two ABSE with RMSE statistics measure through statistical analysis proved that the improved particle swarm algorithm in 3PLM parameter estimation to improve the resilience of the parameter estimates of the true value, and the results do not depend on the estimated choice of initial parameter values, the new and improved hybrid particle swarm algorithm the response theory 3PLM parameters in the project estimation is feasible and efficient.

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