Imputation of missing data in life‐history trait datasets: which approach performs the best?

Abstract

Summary1. Despite efforts in data collection, missing values are commonplace in life-history trait databases. Because these values typically are not missing randomly, the common practice of removing missing data not only reduces sample size, but also introduces bias that can lead to incorrect conclusions. Imputing missing values is a potential solution to this problem. Here, we evaluate the performance of four approaches for estimating missing values in trait databases (K-nearest neighbour (kNN), multivariate imputation by chained equations (mice), missForest and Phylopars), and test whether imputed datasets retain underlying allometric relationships among traits. 2. Starting with a nearly complete trait dataset on the mammalian order Carnivora (using four traits), we artificially removed values so that the percent of missing values ranged from 10% to 80%. Using the original values as a reference, we assessed imputation performance using normalized root mean squared error. We also evaluated whether including phylogenetic information improved imputation performance in kNN, mice, and missForest (it is a required input in Phylopars). Finally, we evaluated the extent to which the allometric relationship between two traits (body mass and longevity) was conserved for imputed datasets by looking at the difference (bias) between the slope of the original and the imputed datasets or datasets with missing values removed.3. Three of the tested approaches (mice, missForest and Phylopars), resulted in qualitatively equivalent imputation performance, and all had significantly lower errors than kNN. Adding phylogenetic information into the imputation algorithms improved estimation of missing values for all tested traits. The allometric relationship between body mass and longevity was conserved when up to 60% of data were missing, either with or without phylogenetic information, depending on the approach. This relationship was less biased in imputed datasets compared to datasets with missing values removed, especially when more than 30% of values were missing. 4. Imputations provide valuable alternatives to removing missing observations in trait databases as they produce low errors and retain relationships among traits. Although we must continue to prioritize data collection on species traits, imputations can provide a valuable solution for conducting macroecological and evolutionary studies using life-history trait databases.

Gap-filling a spatially explicit plant trait database: comparing imputation methods and different levels of environmental information

“…Model-based imputation methods use other variables in the dataset to impute missing data, but they substantially alter the univariate trait distributions and the covariance structure of the dataset (Gelman and Hill, 2007). Approaches such as k nearest neighbour (kNN) or machine-learning methods (Stekhoven and Bühlmann, 2012) may be more appropriate to impute multivariate datasets, preserving their covariance structure (Eskelson et al, 2009;Penone et al, 2014). In a multiple imputation framework, m imputed datasets are obtained through simulation and may be jointly analysed to provide parameter estimates that take into account the uncertainty introduced by the imputations themselves (e.g.…”

“…Complex imputation methods such as kNN, MICE or random forests generally outperform overall mean or species mean imputations (Penone et al, 2014;Taugourdeau et al, 2014). In earlier applications of these methods, it has been common to assume that interspecific trait variability was dominant, compared to intraspecific variability.…”

“…The expected declining performance of imputation methods with increasing missingness levels may be trait and dataset dependent (Penone et al, 2014;Taugourdeau et al, 2014). Moreover, the impact of imputations on altering bivariate trait relationships has only been assessed for single relationships (Penone et al, 2014;Schrodt et al, 2015) and not for the multiple relevant relationships within a plant trait dataset. Likewise, there are few studies quantifying how different imputation methods alter the multivariate covariance structure of plant trait datasets .…”

A simple and general method for simultaneously accounting for phylogenetic and species sampling uncertainty via Rubin’s rules in comparative analysis

“…We can easily automate calculations involving the above formulae with currently available R packages for multiple imputation such as mice (reviewed in Nakagawa and Freckleton 2011; see also Penone et al 2014).…”

“…However, Penone et al (2014) recently showed that phylogenetic information could be added to multiple imputation in the form of phylogenetic eigenvectors (Diniz et al 1998; see also Guénard et al 2003), which can be seen as additional predictor variables (for the imputation step not for the analysis step). This means that, to conduct multiple imputation for comparative data, one can use general and flexible packages such as mice (van Buuren and Groothuis-Oudshoorn 2011), as was used for our simulation.…”