Statistical Analysis Of Item Response Theory Models With Missing Data

Item response theory(IRT)models are an essential tool in educational assessment and psychological measurement where study outcomes consist of dichotomous or discrete responses.The response data often come with certain kinds of missingness,especially in large scale assessments.In some timed tests,examinees may fail to reach items at the end of the tests due to time limits,leading to missingness due to not-reached items(NRIs).In other cases,even when items have been presented and examinees have time to consider them,the examinees may choose to omit some items,resulting in missingness due to omitted items(OIs).Previous researches have shown that missingness due to NRIs or OIs is often correlated with examinees' latent ability,making it nonignorable.For such missing responses,if not handled properly,it could lead to incorrect statistical inference and further erode validity of the tests.To account for missingness due to NRIs,Pohl,Ulitzsch,and von Davier(2019)employed van der Linden's hierarchical framework to jointly model response accuracy(RA)and response times(RTs)on reached items.The rationale behind using a joint model for RA and RTs to handle NRIs is as follows: Examinees' latent speeds a?ect how many items they can complete within the time limit and hence contain information about the amount of missingness due to NRIs.The joint model for RA and RTs takes into account this information in speed estimation and,because speed and ability are often correlated,the missingness is also incorporated into the estimation of latent ability and item parameters.However,examinees' first NRIs are informative as the corresponding potential responses are censored when RTs on these items exceed the remaining times on the test.Ignoring this censoring mechanism in parameter estimation can lead to biased estimates of model parameters and inaccurate inferences about examinees.In this thesis,we propose a method to account for NRIs due to time limits.The proposed method is built on top of joint modeling for RA and RT.Compared with the method proposed by Pohl,Ulitzsch,and von Davier(2019),our approach incorporates the mechanism of right censoring for RTs on examinees' first NRIs.Simulation results showed that the proposed approach was able to produce unbiased estimates of model parameters whereas ignoring the NRIs could lead to persistent biases in parameter estimates.The new method was applied to a data set from the Program for International Student Assessment(PISA)2018 Science Test.We also develop a joint model for RA,RT,as well as omission time(OT)to explicitly model missing tendencies due to OIs.Under this approach,the omissions are naturally explained by the competing relationship for RT and OT.That is,shorter response times are more likely to be observed,whereas the longer ones are more likely to be censored.Simulation results showed that not only the model parameters could be recovered well but also the robustness could be verified under the proposed method.The proposed method along with the alternative ones were applied to an empirical data set from the PISA 2015 Test,with results being reported and compared.We further derive a joint model allowing for missing responses resulting from NRIs and/or OIs.Under this model,the missing mechanism of NRIs is explained by the right censoring of potential response times for examinees' first NRIs.And the missing mechanism of OIs is interpreted by the competing relationship for RT and OT.The proposed method and alternative methods that incorporate single missing patterns or ignore missingness were compared through a simulation study.Results showed that only the method accounting for both missing patterns could recover model parameters well.An empirical study based on the PISA 2015 Science Test was further conducted.