Wearable devices such as the ActiGraph are now commonly used in health studies to monitor or track physical activity. This trend aligns well with the growing need to accurately assess the effects of physical activity on health outcomes such as obesity. When accessing the association between these device-based physical activity measures with health outcomes such as body mass index, the device-based data is considered functions, while the outcome is a scalar-valued. The regression model applied in these settings is the scalar-on-function regression (SoFR). Most estimation approaches in SoFR assume that the functional covariates are precisely observed, or the measurement errors are considered random errors. Violation of this assumption can lead to both under-estimation of the model parameters and sub-optimal analysis. The literature on a measurement corrected approach in SoFR is sparse in the non-Bayesian literature and virtually non-existent in the Bayesian literature. This paper considers a fully nonparametric Bayesian measurement error corrected SoFR model that relaxes all the constraining assumptions often made in these models. Our estimation relies on an instrumental variable (IV) to identify the measurement error model. Finally, we introduce an IV quality scalar parameter that is jointly estimated along with all model parameters. Our method is easy to implement, and we demonstrate its finite sample properties through an extensive simulation. Finally, the developed methods are applied to the National Health and Examination Survey to assess the relationship between wearable-device-based measures of physical activity and body mass index among adults living in the United States.
翻译:ActiGraph等可穿的装置现在常用于健康研究,以监测或跟踪物理活动。这一趋势与准确评估物理活动对健康结果(如肥胖)的影响的日益需要完全吻合。当利用这些基于装置的物理活动措施与健康结果(如身体质量指数)之间的联系时,基于装置的数据被视为功能,而结果则被视为是斜度值的。在这些环境中采用的回归模型是卡路里对功能的测量误差(SoFR)。SoFR的大多数估算方法假定功能共变器得到精确的观测,或测量误差被视为随机错误。违反这一假设可能导致低估模型参数和次最佳分析。 SoFRFR的测量方法的文献在非巴耶斯文献中很少,而巴伊西亚文献中几乎不存在。本文认为,在这些模型中应用的完全不相称的巴耶斯测量误差(SoFRFR)模型。我们的估计依据一个工具变量(IV)来确定衡量质量误差的模型,在成人之间使用。在测量误差度模型中,我们采用这一模型时,我们采用一个总的质量比重的模型。最后,我们采用一个质量比重的方法,我们使用一个总的模型。我们使用一个测试的方法是我们的方法。我们使用一个比重的方法。我们的方法。我们使用一个总的质量比重的方法。我们使用一个比重的方法。我们使用一个比重的方法。