Summary
Given the prevalence of missing data on species’ traits – Raunkiaeran shorfall — and its importance for theoretical and empirical investigations, several methods have been proposed to fill sparse databases. Despite its advantages, imputation of missing data can introduce biases. Here, we evaluate the bias in descriptive statistics, model parameters, and phylogenetic signal estimation from imputed databases under different missing and imputing scenarios.
We simulated coalescent phylogenies and traits under Brownian Motion and different Ornstein-Uhlenbeck evolutionary models. Missing values were created using three scenarios: missing completely at random, missing at random but phylogenetically structured and missing at random but correlated with some other variable. We considered four methods for handling missing data: delete missing values, imputation based on observed mean trait value, Phylogenetic Eigenvectors Maps and Multiple Imputation by Chained Equations. Finally, we assessed estimation errors of descriptive statistics (mean, variance), regression coefficient, Moran’s correlogram and Blomberg’s K of imputed traits.
We found that percentage of missing data, missing mechanisms, Ornstein-Uhlenbeck strength and handling methods were important to define estimation errors. When data were missing completely at random, descriptive statistics were well estimated but Moran’s correlogram and Blomberg’s K were not well estimated, depending on handling methods. We also found that handling methods performed worse when data were missing at random, but phylogenetically structured. In this case adding phylogenetic information provided better estimates. Although the error caused by imputation was correlated with estimation errors, we found that such relationship is not linear with estimation errors getting larger as the imputation error increases.
Imputed trait databases could bias ecological and evolutionary analyses. We advise researchers to share their raw data along with their imputed database, flagging imputed data and providing information on the imputation process. Thus, users can and should consider the pattern of missing data and then look for the best method to overcome this problem. In addition, we suggest the development of phylogenetic methods that consider imputation uncertainty, phylogenetic autocorrelation and preserve the level of phylogenetic signal of the original data.
