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Item Addressing missing data in specification search in measurement invariance testing with Likert-type scale variables: A comparison of two approaches(Springer, 2020-12) Chen, Po-Yi; Wu, Wei; Brandt, Holger; Jia, Fan; Psychology, School of ScienceIn measurement invariance testing, when a certain level of full invariance is not achieved, the sequential backward specification search method with the largest modification index (SBSS_LMFI) is often used to identify the source of non-invariance. SBSS_LMFI has been studied under complete data but not missing data. Focusing on Likert-type scale variables, this study examined two methods for dealing with missing data in SBSS_LMFI using Monte Carlo simulation: robust full information maximum likelihood estimator (rFIML) and mean and variance adjusted weighted least squared estimator coupled with pairwise deletion (WLSMV_PD). The result suggests that WLSMV_PD could result in not only over-rejections of invariance models but also reductions of power to identify non-invariant items. In contrast, rFIML provided good control of type I error rates, although it required a larger sample size to yield sufficient power to identify non-invariant items. Recommendations based on the result were provided.Item Estimation of Covariate-Speci c Time-Dependent ROC Curves in the Presence of Missing Biomarkers(Wiley, 2015-09) Li, Shanshan; Ning, Yang; Department of Biostatistics, Richard M. Fairbanks School of Public HealthCovariate-specific time-dependent ROC curves are often used to evaluate the diagnostic accuracy of a biomarker with time-to-event outcomes, when certain covariates have an impact on the test accuracy. In many medical studies, measurements of biomarkers are subject to missingness due to high cost or limitation of technology. This article considers estimation of covariate-specific time-dependent ROC curves in the presence of missing biomarkers. To incorporate the covariate effect, we assume a proportional hazards model for the failure time given the biomarker and the covariates, and a semiparametric location model for the biomarker given the covariates. In the presence of missing biomarkers, we propose a simple weighted estimator for the ROC curves where the weights are inversely proportional to the selection probability. We also propose an augmented weighted estimator which utilizes information from the subjects with missing biomarkers. The augmented weighted estimator enjoys the double-robustness property in the sense that the estimator remains consistent if either the missing data process or the conditional distribution of the missing data given the observed data is correctly specified. We derive the large sample properties of the proposed estimators and evaluate their finite sample performance using numerical studies. The proposed approaches are illustrated using the US Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset.Item Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques(Taylor & Francis, 2020) Chen, Po-Yi; Wu, Wei; Garnier-Villarreal, Mauricio; Kite, Benjamin Arthur; Jia, Fan; Psychology, School of ScienceOrdinal missing data are common in measurement equivalence/invariance (ME/I) testing studies. However, there is a lack of guidance on the appropriate method to deal with ordinal missing data in ME/I testing. Five methods may be used to deal with ordinal missing data in ME/I testing, including the continuous full information maximum likelihood estimation method (FIML), continuous robust FIML (rFIML), FIML with probit links (pFIML), FIML with logit links (lFIML), and mean and variance adjusted weight least squared estimation method combined with pairwise deletion (WLSMV_PD). The current study evaluates the relative performance of these methods in producing valid chi-square difference tests (Δχ2) and accurate parameter estimates. The result suggests that all methods except for WLSMV_PD can reasonably control the type I error rates of Δχ2 tests and maintain sufficient power to detect noninvariance in most conditions. Only pFIML and lFIML yield accurate factor loading estimates and standard errors across all the conditions. Recommendations are provided to researchers based on the results.