Research On Longitudinal Multidimensional IRT Growth Model And Parameter Estimation Method

This study mainly combines the multidimensional item response theory(IRT)model with the latent growth curve(LGC)model to provide a longitudinal multidimensional IRT model.Firstly,the equivalence transformation of multidimensional compensatory IRT model and longitudinal IRT model is introduced;Secondly,the parameters of the longitudinal multidimensional compensatory IRT model are estimated.the Maximum Likelihood Estimation method is used to carry out theoretical deduction of the individual ability parameters.Then,the marginal maximum likelihood Estimation(MMLE)is used to estimate the overall ability distribution and item parameters.The covariance matrix of uniform covariance and first-order autoregressive(AR(1))covariance is selected to adapt to the correlation of overall ability parameters over time.Finally,Expectation maximization(EM)algorithm is used to simulate the model.The results show that:(1)In the longitudinal multidimensional compensatory IRT model in the three time tests under the same item,the overall ability changes nonlinearly over time;(2)High estimation accuracy of the overall ability distribution and item parameter estimation by EM algorithm.,indicating that the EM algorithm of this model provides a good estimation;(3)The larger the sample size of the subjects,the higher the parameter estimation accuracy of the EM algorithm;The estimators under uniform covariance matrix and AR(1)covariance matrix are relatively approximate and have good results.