How to deal with darkness: Modelling and visualization of zero-inflated personal light exposure data on a logarithmic scale

Abstract

Personal light exposure, the pattern of ocular light levels across time under free-living conditions measured with wearable devices, has become increasingly important in circadian and myopia research. Very small measurement values in light exposure patterns, especially zero, are regularly recorded in field studies. These zero-lux values are problematic for commonly applied logarithmic transformations, and should neither be dismissed nor be unduly influential in visualizations and statistical models. Common approaches used in zero-inflated data sets fail in at least one of these regards. We compare four ways to visualize such data on a linear, logarithmic, hybrid, or symlog scale and we model the light exposure patterns with a generalized additive model by removing zero-lux values, adding a very small or −1 log10 lux value to the dataset, or using the Tweedie error distribution. We show that a symlog-transformed visualization displays relevant features of light exposure across scales, including zero-lux, while at the same time reducing the emphasis on the small values (<1 lux). Symlog is well-suited to visualize differences in light exposure covering heavy-tailed negative values. The open-source software package LightLogR includes the symlog transformation for easy access. We further show that small but not negligible value additions to the light exposure data of -1 log10 lux for statistical modelling allow for acceptable models on a logarithmic scale, while very small values distort results. We also demonstrate the utility of the Tweedie distribution, which does not require prior transformations, models data on a logarithmic scale, and includes zero-lux values, capturing personal light exposure patterns satisfactorily. Data from field studies of personal light exposure requires appropriate handling of zero-lux values in a logarithmic context. Symlog scales for visualizations and an appropriate addition to input values for modelling, or the Tweedie distribution, provide a solid basis.