Recently developed accelerometer devices have been used in large epidemiological studies for continuous and objective monitoring of physical activities. Typically, physical movements are summarized as minutes in light, moderate, and vigorous physical activities in each wearing day. Because of preponderance of zeros, zero‐inflated distributions have been used for modeling the daily moderate or higher levels of physical activity. Yet, these models do not fully account for variations in daily physical activity and cannot be extended to model weekly physical activity explicitly, while the weekly physical activity is considered as an indicator for a subject's average level of physical activity. To overcome these limitations, we propose to use a zero‐inflated Poisson mixture distribution that can model daily and weekly physical activity in same family of mixture distributions. Under this method, the likelihood of an inactive day and the amount of exercise in an active day are simultaneously modeled by a joint random effects model to incorporate heterogeneity across participants. If needed, the method has the flexibility to include an additional random effect to address extra variations in daily physical activity. Maximum likelihood estimation can be obtained through Gaussian quadrature technique, which is implemented conveniently in an R package GLMMadaptive. Method performances are examined using simulation studies. The method is applied to data from the Hispanic Community Health Study/Study of Latinos to examine the relationship between physical activity and BMI groups and within a participant the difference in physical activity between weekends and weekdays.

中文翻译：

---

使用零膨胀混合泊松分布对每日和每周的中等和剧烈身体活动进行建模。


最近开发的加速度计设备已用于大型流行病学研究，以连续、客观地监测身体活动。通常，身体运动被概括为每个佩戴日中轻度、中度和剧烈身体活动的分钟数。由于零占主导地位，零膨胀分布已用于对每日中等或更高水平的体力活动进行建模。然而，这些模型没有完全考虑日常身体活动的变化，并且不能扩展到明确地模拟每周身体活动，而每周身体活动被认为是受试者平均身体活动水平的指标。为了克服这些限制，我们建议使用零膨胀泊松混合分布，它可以在同一混合分布族中模拟每日和每周的身体活动。在这种方法下，通过联合随机效应模型同时对不活动日的可能性和活动日的运动量进行建模，以纳入参与者之间的异质性。如果需要，该方法可以灵活地包含额外的随机效应，以解决日常身体活动的额外变化。最大似然估计可以通过高斯求积技术获得，该技术在 R 包GLMAdaptive中可以方便地实现。使用模拟研究检查方法性能。该方法应用于西班牙裔社区健康研究/拉丁裔研究的数据，以检查身体活动与体重指数组之间的关系，以及参与者周末和工作日之间身体活动的差异。