Response variable selection in principal response curves using permutation testing

Abstract

Principal response curves analysis (PRC) is widely applied to experimental multivariate longitudinal data for the study of time-dependent treatment effects on the multiple outcomes or response variables (RVs). Often, not all of the RVs included in such a study are affected by the treatment and RV-selection can be used to identify those RVs and so give a better estimate of the principal response. We propose four backward selection approaches, based on permutation testing, that differ in whether coefficient size is used or not in ranking the RVs. These methods are expected to give a more robust result than the use of a straightforward cut-off value for coefficient size. Performance of all methods is demonstrated in a simulation study using realistic data. The permutation testing approach that uses information on coefficient size of RVs speeds up the algorithm without affecting its performance.This most successful permutation testing approach removes roughly 95 % of the RVs that are unaffected by the treatment irrespective of the characteristics of the data set and, in the simulations, correctly identifies up to 97 % of RVs affected by the treatment.

Forest understorey plant responses to long‐term experimental warming, light and nitrogen addition

“…We tested which species were driving the observed community changes in response to the treatments, by means of principal response curves (PRC) based on cover data. PRC is a special case of redundancy analysis (RDA) and describes the timedependent overall response of the community to the treatment relative to the control treatment (Van den Brink & Ter Braak, 1999;Vendrig et al, 2017). This is done by plotting the canonical coefficients of one principal component (the 'site scores') as a function of time.…”

“…In this way, the community composition of the treatment and control group can be compared at the same moment in time. In addition, species scores indicate, for each of the species, whether their response is positively or negatively correlated to the overall response and to what extent (Vendrig et al, 2017). Note that a species score of zero could mean that the species response is either different from the community response, or there is no response to the treatment.…”

Resampling-based methods for biologists

“…We find the bootstrap particularly attractive for decision analysis because it can provide a distribution of possible outcomes across a set of potential management actions while accounting for model and parameter uncertainty (e.g., Ellner & Fieberg, 2003). Ecologists have a long history of using resampling-based methods to analyze multivariate response data using ordination methods (ter Braak, 1990;Vendrig, Hemerik & ter Braak, 2017;Van den Brink & ter Braak, 1999;ter Braak & Smilauer, 2018). The vegan and permute packages provide methods for restricted permutations (e.g., permuting observations within blocks for randomized complete block designs) that can be used with multivariate data (e.g., Anderson & ter Braak, 2003;Oksanen et al, 2019;Simpson, 2019); the mvabund package also provides methods for bootstrapping generalized linear models fit to multivariate response data (Wang et al, 2019;Wang et al, 2012).…”

Peer Review #1 of "Resampling-based methods for biologists (v0.1)"

“…We find the bootstrap particularly attractive for decision analysis because it can provide a distribution of possible outcomes across a set of potential management actions while accounting for model and parameter uncertainty (e.g., Ellner and Fieberg, 2003). Ecologists have a long history of using resampling-based methods to analyze multivariate response data using ordination methods (ter Braak, 1990;Vendrig et al, 2017; Van den Brink and ter Braak, 1999;ter Braak and Smilauer, 2018). The vegan and permute packages provide methods for restricted permutations (e.g., permuting observations within blocks for randomized complete block designs) that can be used with multivariate data (e.g., Anderson and ter Braak, 2003;Oksanen et al, 2019;Simpson, 2019); the mvabund package also provides methods for bootstrapping generalized linear models fit to multivariate response data (Wang et al, 2019(Wang et al, , 2012.…”