Robust and Interpretable Bayesian Quantile Longitudinal Analysis in Social and Behavioral Sciences

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This research project will develop statistical techniques that address robustness and interpretability challenges in longitudinal studies for applied researchers in the social and behavioral sciences. Longitudinal studies help us understand changes in behavior. Although longitudinal research has gained popularity in social and behavioral sciences, it often faces methodological challenges. This project will contribute innovative methods to the longitudinal data analysis literature. The research will increase the scope of applications of longitudinal analysis to areas where data distributions deviate from normality, missing values frequently exist, sample size is small, and data are sparse and irregular. The project has the potential to identify different effective interventions for subjects with different characteristics, potentially benefiting minority groups. Free open-source software will be developed so that technically sophisticated methods can be readily implemented by substantive researchers. The project also will provide training opportunities for the next generation of statisticians and psychologists.Problems associated with longitudinal data include the handling of non-normal and/or missing data, small sample sizes, large measurement errors, high-dimensional variable selection, and population heterogeneity. This project will address these problems by developing a Bayesian quantile growth curve modeling strategy. Instead of modeling the change of conditional means, the new approach will model the change of conditional quantiles, which avoids the distributional assumption of data in general. The investigators will use the Asymmetric Laplace distribution to convert the problem of estimating a quantile growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model so that computationally powerful Bayesian methods can be applied conveniently and missing data can be flexibly addressed. Constraints on the natural shape of the overall change trajectory will be imposed through penalized functional principal component analysis. This approach will yield practical and interpretable estimated growth trajectories for applied researchers. The new methodology will be powerful enough to allow researchers to conduct valid, interpretable, and robust analyses of collected data regardless of the data distribution. In addition, because the method will work well for small-sized samples, the reproducibility problem in social and behavioral sciences may be reduced.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.