Development of a method for addressing various censoring effects in a latent growth curve modeling framework
Censoring effects, including ceiling, floor, and doubly censoring, present significant challenges for social and behavioral science applications, as they can considerably impact the estimation of true score values and lead to biased estimates and misleading inferences. Longitudinal data structures, such as latent growth curve models (LGCMs), are particularly susceptible to these censoring effects, often resulting in distorted relationships between growth factors and external covariates. To address this issue, this study aimed to develop a new method for handling doubly-censored data in the context of longitudinal data analysis. The proposed Generalized Tobit estimator (GBIT) extends the conventional Tobit approach, which typically only considers singly censored data, to handle instances of data with mixed censoring effects, including ceiling, floor, and doubly censoring. The purpose of this study was threefold: (1) to extend Muthén's work on censored multivariate normal data to the case of doubly-censored multivariate normal data in longitudinal designs, (2) to evaluate the estimation of LGCMs that have mixed censored data, particularly doubly censoring effects, considering models both with and without doubly censoring effects taken into account, and (3) to assess the influences of doubly-censored data on the effects of covariates and distal outcomes in the LGCM framework. To validate the proposed GBIT method and investigate its performance in LGCMs, a Monte Carlo simulation study was conducted in two phases. In Phase I, the GBIT was tested under the bivariate doubly-censored normal distribution. In Phase II, the GBIT was applied to the longitudinal data analysis framework with doubly-censored data via the simulation study. The simulation study aimed to provide researchers with an understanding of why doubly censoring matters in longitudinal analysis and to offer a new tool for applied researchers to conduct longitudinal analysis with censored data. The simulation study revealed several important insights regarding the use of GBIT for censoring data analysis. First, it demonstrated that censoring has a significant impact on the data estimation process, particularly on estimates of variances and covariances. Researchers must be aware of whether their data is censored or not and, if so, consider how to handle these censoring effects to avoid misleading and distorted results. Second, the study showed that GBIT is an effective approach for handling censoring effects, providing unbiased estimates under high levels of censoring in bivariate data. This evidence supports the assertion that when a doubly-censoring effect is present within a dataset, it is crucial to treat the data differently from the conventional approach. Finally, GBIT proved to be especially valuable in longitudinal analysis when data are censored. The ability of GBIT to correctly identify growth patterns supports its use in datasets displaying censoring effects, as it can accurately capture the direction of growth over time. In conclusion, the present study offers a valuable contribution to the literature on censoring effects in longitudinal data analysis by proposing and validating the GBIT method for handling doubly-censored data in LGCMs. The findings emphasize the importance of addressing censoring effects in longitudinal studies and suggest that GBIT is a valuable tool for researchers working with censored data. Future research should continue to explore the application of GBIT in various contexts and address potential limitations to further refine the method for a broader range of applications.