Applying Lasso Regularization To Detect Differential Item Functioning In Cognitive Diagnosis Models

In recent years,cognitive diagnosis(CD)has been widely studied because it can provide detailed information about the internal cognitive process and processing mechanism of individuals.Cognitive diagnosis models(CDMs)play an important role in cognitive diagnosis assessments(CDAs).By analyzing examinees’ response data and response processes,CDMs can explore examinees’ underlying cognitive structures and provide diagnostic information on examinees’ strengths,weaknesses and development potentials.To ensure the accuracy and fairness of CDAs,detecting differential item functioning(DIF)is one of the important statistical routines.In order to boost the potency of CDAs,developing an efficient DIF detection method is indispensable.However,most of the existing CD-DIF detection methods are slightly modified according to DIF assessment methods within the framework of classical test theory(CTT)and item response theory(IRT).The differences of theoretical backgrounds and research ideas in different fields are ignored.Some CDMs-based DIF detection methods are highly dependent on specific models.In addition,these specific models have strong assumptions and restrictions,which leads to the inflexibility and narrow application range.Traditional CD-DIF detection methods also need the tedious process of variable matching,item by item assessment and iterative identification of anchor items,which makes the detection process complicated and inefficient.According to the findings and limitations of previous studies,in this paper,we aim to propose a DIF detection method based on Lasso regularization procedure within the difference cognitive diagnosis models(D-CDMs)framework.In order to verify the effectiveness and feasibility of this method,three studies,namely theoretical study,simulation study and empirical study,were conducted.Specifically,the theoretical study detailed why and how the D-CDMs framework was established.This part used the Lasso regularization procedure to solve the possible overfitting problem.Therefore,we also illustrated the process of evaluating DIF state of all items directly by parameter estimation including Lasso regularization procedure.The simulation study evaluated the DIF detection performance of the Lasso regularization method under simulated experimental conditions,while the empirical study examined the application performance of the Lasso regularization method.The results show that:(1)Lasso regularization method can simultaneously investigate the DIF state of all items,and make up for the limitations of traditional CD-DIF detection method to a certain extent.(2)Compared with existing commonly used CD-DIF detection methods(MH,LR,LR-FS,Wald and Wald-FS method),Lasso regularization method has better detection performance under various experimental conditions,with lower Type I error rate and higher power.(3)MH,Wald,Wald-FS,LR-FS and Lasso regularization method all agree that the mathematical item PM985Q02 of PISA 2012 is most likely a DIF item,at least this item is unfair among 15-year-old male and female students in Bulgaria.After controlling the examinees’ attribute mastery pattern,it is found that only in the item PM985Q02,the female group has a higher success probability than the male group,and the difference is significant.