A Multidimensional Extension Of Higher-Order DINA Model And Its Application In Geometric Analogies

Considering that most of the tests in the actual testing many kinds of ability,they need a cognitive dignosis model to assess cognitive diagnosis and multidimensional capability.In this paper, A new model(MHO-DINA) is created by combining HO-DINA with MIRT model. Because the parameters of the MHO-DINA model needed to estimate are more than HO-DINA model, so with the traditional MMLE/EM algorithm is difficult to achieve.In this paper, this study is adopted dong bo tu, shu qing qi(2008) introduced an MCMC algorithm: Gibbs sampling under random-shift M-H algorithm(jumping M-H) to realize the MHO-DINA model parameters estimated. There are four studies in this paper, Respectively as follows:Study 1: MHO-DINA model is be created by establishing a theoretical framework.Study 2: The study is about the properties of the multidimensional HO-DINA model and discussed the parameter estimation accuracy and stability. Simulation study found that the accuracy of MHO-DINA model in estimating Participants ability and project parameters(lenta) of the model is not very good but still can be accepted,in an; the estimation accuracy of Participants ability parameter will go worse, when the dimension of the participants’ abilitiy increased; And the pattern of property master of Participants and item parameters s, g parameters estimation precision is more ideal.The influence of each factor of the model are as follows: 1,when the number of the participants or items is larger, parameter estimation of MHO-DINA model will be more accurate and more stable.2, Compared to the number of participants increases, the increase of the item have the greater impact in the estimation accuracy and stability of the parameters of MHO-DINA model;3, Ability dimensions, the parameter estimation accuracy and stability of MHO-DINA model will be poor when the number of ability dimensions(3 d than 2 d ability) is increased.Study 3: MHO-DINA model is compared with MIRT model and HO-DINA model.The main purpose of this experiment is to test if a set of data come from MHO-DINA model, using traditional MIRT model and HO-DINA model and new model(MHO-DINA) to respectively estimate participants parameters and item parameters, which model estimation accuracy and stability will be the most ideal.Thisstudy found that: 1, the result of the traditional model MIRT in assessing the ability of participants parameters is not better than MHO-DINA model.2, the result of the traditional model HO-DINA in the estimated project parameters(s, g) and the master attribute patten of participants is similar with MHO-DINA model.Study 4: MHO-DINA model applied in geometry analogical test data, the new model(MHO-DINA) parameter estimation results and the existing research of HO-DINA model parameter estimation results to make a comparative study, then found that the estimation result of the new model MHO-DINA in participants parameter of geometry analogical test and item parameters have a highly significantly correlated with HO-DINA model parameters. This explain that MHO-DINA model applied to the analysis of the actural data is feasible.And compared with HO-DINA model, MHO- DINA model can provide about the every dimension of participants ability.It is more detailed information, which has reference value.