Censored data regression: Statistical methods for analyzing Secchi transparency in shallow systems

Secchi depth monitoring in shallow ecosystems occasionally records sight to the bottom and thus the true Secchi depth is larger than the observed. In such cases Secchi depth data are censored. Despite that statistical methods for analyzing such censored data have existed for many decades and have been widely used in other disciplines, the censoring problem has been completely overlooked in aquatic ecology. Here, I have presented and exemplified a statistical regression technique (Censored Data Regression, CDR) that specifically addresses censored data, and compared resulting estimates of mean and standard error of Secchi depth distributions with those of statistical methods commonly applied in the literature. Standard methods increasingly underestimated both mean and standard error of Secchi depths as the proportion of censored data increased. Analysis of measured Secchi depths from four coastal sites in Denmark, representing 29% to 80% censored data, documented substantial biases in distribution means (up to 2 m), and standard errors (50 %) when censoring was not accounted for. This had significant repercussions for the estimation of trends and seasonal patterns of Secchi depths, in the worst case actually reporting no significant trend when a trend was actually present. Consequently, there is a need to introduce CDR as a more appropriate method for analyzing Secchi depths in shallow lakes and coastal ecosystems. More generally, the objective of this study was to raise the awareness of the censoring problem and to promote appropriate statistical methods for analyzing censored ecological data.