| Cognitive diagnosis models(CDM)are multidimensional discrete latent variable models that classify examinees as masters or non-masters of different skills.Those skills(such as knowledge,skills,strategy,personality traits,or psychological disorders)are often referred to as attributes.A Q-matrix identifies the subset of attributes measured by each item in CDM.The Q-matrix might be misspecified because it usually specified by domain experts.Some Q-matrix validation methods such as Wald-IC and Hull methods could provide a better result on Q-matrix recovery rat,but they are not sensitive to the misspecified q-entry.The information matrix for the maximum likelihood estimates of model parameters in CDM plays a key role in statistical inference,including the estimation of model parameters’ standard errors,detection of differential item functioning,item-level comparison of the saturated and reduced models,the Q-matrix estimation or validation and attribute hierarchy exploration.The main focus of this dissertation is the applications of complete information matrix for Q-matrix estimation or validation.This dissertation is organized as follows.First,various Q-matrix validation and estimation approaches developed by previous researchers are introduced,and information matrix estimation methods proposed in literature are introduced.Then,simulation studies are designed to evaluate and compare the performance of the Wald-XPD method under a wide range of conditions,followed by real data examples to illustrate the practical applications of these testing methods.In the first study,a Q-matrix validation method was introduced that constructed a Wald test with a complete empirical cross-product information matrix(XPD).How the Wald-XPD method was extended for Q-matrix estimation under partially known Q-matrix conditions was explained in this study.In the second study,a simulation study was conducted to compare the Wald-XPD method with the GDI method,LR method and Wald-IC method in validating Q-matrix in terms of Q-matrix recovery rat,the true positive rate and true negative rate.Simulation results showed that:(1)the Wald-XPD method provided better overall performance than other testing methods,especially in the aspect of true negative rate.(2)The LR method was the worst performer on all dependent variables.In the third study,the Wald-XPD and Hull methods were extended for Q-matrix estimation.Besides,we conducted the Wald-XPD procedure using the Q-matrix estimation and Q-matrix validation.The purpose of the study is twofold: to explore the difference between Q-matrix estimation and Q-matrix validation;and to examine how the performance of the Wald-XPD procedure using the Q-matrix estimation and Q-matrix validation compares to that of the Hull,LR and Wald-XPD methods under a wide range of realistic conditions.Simulation results indicated that:(1)the Wald-XPD method implemented in this manner showed a better performance than other methods.(2)The Wald-XPD procedure using the Q-matrix estimation and Q-matrix validation showed a low tendency to under-specification and over-specification errors.In the fourth study,two real data examples were provided to illustrate the utilities of the Wald-XPD,GDI,LR,Wald-IC method and Hull methods.The data stemmed from a learning experiment at the University of Tuebingen in Germany was used to demonstrate that the LR,Wald-IC and Wald-XPD methods could be used for the purpose of Q-matrix validation.The fraction subtraction data set was used to illustrate that the LR,Hull,Wald-XPD methods and the Wald-XPD method using the Q-matrix estimation and Q-matrix validation could be used for Q-matrix estimation.The results showed that:(1)according to the results of the model-data fit,the G-DINA model based on the suggested Q-matrix provided by Wald-XPD validation method obtained the best relative and absolute fit.(2)As in the second simulation study,the Wald-XPD method performed very well under partial known Q-matrix conditions,and the Wald-XPD procedure using the Q-matrix estimation and Q-matrix validation showed a better performance than that of the Wald-XPD method.In conclusion,the Wald-XPD method is a powerful method that can serve as a comprehensive solution for the Q-matrix validation,which should be used with intent to provide ancillary information to assist experts in their decision-making processes. |
