A fully Bayesian semi-parametric scalar-on-function regression (SoFR) with measurement error using instrumental variables
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利用工具变量校正测量误差的全贝叶斯半参数标量对函数回归
- 研究问题
- 当可穿戴设备记录的函数型活动指标存在测量误差时，如何校正其与标量健康结果的回归关系，并评估工具变量的质量？
- 方法与思路
- 作者提出贝叶斯测量误差校正的标量对函数回归，利用工具变量识别误差模型，联合估计工具质量参数，并开展模拟和美国健康调查应用。
- 材料陈述的贡献
- 摘要称方法放宽常见限制并引入可联合估计的工具质量标量，以模拟展示有限样本性质，应用于身体活动与体重指数关系分析。
- 阅读关注点
- 应核对工具变量有效性及误差模型的识别条件、质量参数的含义，并厘清题名的半参数与摘要的全非参数表述及模拟覆盖范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未获核验；摘要未说明放宽了哪些完整假设，使用工具变量也不足以确认应用具有因果解释。
原文摘要
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.