#' Sensitivity Analysis Species Sampling - Phylogenetic Logistic Regression
#'
#' Performs analyses of sensitivity to species sampling by randomly removing
#' species and detecting the effects on parameter estimates in phylogenetic
#' logistic regression.
#'
#' @param formula The model formula
#' @param data Data frame containing species traits with row names matching tips
#' in \code{phy}.
#' @param phy A phylogeny (class 'phylo') matching \code{data}.
#' @param n.sim The number of times species are randomly deleted for each
#' \code{break}.
#' @param breaks A vector containing the percentages of species to remove.
#' @param btol Bound on searching space. For details see \code{phyloglm}
#' @param track Print a report tracking function progress (default = TRUE)
#' @param ... Further arguments to be passed to \code{phyloglm}
#' @details
#'
#' This function randomly removes a given percentage of species (controlled by
#' \code{breaks}) from the full phylogenetic logistic regression, fits a phylogenetic
#' logistic regression model without these species using \code{\link[phylolm]{phyloglm}},
#' repeats this many times (controlled by \code{n.sim}), stores the results and
#' calculates the effects on model parameters.
#'
#' Only logistic regression using the "logistic_MPLE"-method from
#' \code{phyloglm} is implemented.
#'
#' Currently, this function can only implement simple logistic models (i.e. \eqn{trait~
#' predictor}). In the future we will implement more complex models.
#'
#' Output can be visualised using \code{sensi_plot}.
#' @return The function \code{samp_phylm} returns a list with the following
#' components:
#' @return \code{formula}: The formula
#' @return \code{full.model.estimates}: Coefficients, aic and the optimised
#' value of the phylogenetic parameter (e.g. \code{lambda} or \code{kappa}) for
#' the full model without deleted species.
#' @return \code{sensi.estimates}: A data frame with all simulation
#' estimates. Each row represents a model rerun with a given number of species
#' \code{n.remov} removed, representing \code{n.percent} of the full dataset.
#' Columns report the calculated regression intercept (\code{intercept}),
#' difference between simulation intercept and full model intercept (\code{DIFintercept}),
#' the percentage of change in intercept compared to the full model (\code{intercept.perc})
#' and intercept p-value (\code{pval.intercept}). All these parameters are also reported
#' for the regression slope (\code{DIFestimate} etc.). Additionally, model aic value
#' (\code{AIC}) and the optimised value (\code{optpar}) of the phylogenetic
#' parameter (e.g. \code{kappa} or \code{lambda}, depending on the phylogenetic model
#' used) are reported. Lastly we reported the standardised difference in intercept
#' (\code{sDIFintercept}) and slope (\code{sDIFestimate}).
#' @return \code{sign.analysis} For each break (i.e. each percentage of species
#' removed) this reports the percentage of statistically significant (at p<0.05)
#' intercepts (\code{perc.sign.intercept}) over all repetitions as well as the
#' percentage of statisticaly significant (at p<0.05) slopes (\code{perc.sign.estimate}).
#' @return \code{data}: Original full dataset.
#' @note Please be aware that dropping species may reduce power to detect
#' significant slopes/intercepts and may partially be responsible for a potential
#' effect of species removal on p-values. Please also consult standardised differences
#' in the (summary) output.
#' @author Gustavo Paterno & Gijsbert D.A. Werner
#' @seealso \code{\link[phylolm]{phyloglm}}, \code{\link{samp_phylm}},
#' \code{\link{influ_phyglm}}, \code{\link{sensi_plot}}
#' @references
#'
#' Paterno, G. B., Penone, C. Werner, G. D. A.
#' \href{http://doi.wiley.com/10.1111/2041-210X.12990}{sensiPhy:
#' An r-package for sensitivity analysis in phylogenetic
#' comparative methods.} Methods in Ecology and Evolution
#' 2018, 9(6):1461-1467.
#'
#' Werner, G.D.A., Cornwell, W.K., Sprent, J.I., Kattge, J. & Kiers, E.T. (2014).
#' A single evolutionary innovation drives the deep evolution of symbiotic N2-fixation
#' in angiosperms. Nature Communications, 5, 4087.
#'
#' #' Ho, L. S. T. and Ane, C. 2014. "A linear-time algorithm for
#' Gaussian and non-Gaussian trait evolution models". Systematic Biology 63(3):397-408.
#' @examples
#'# Simulate Data:
#'set.seed(6987)
#'phy = rtree(100)
#'x = rTrait(n=1,phy=phy)
#'X = cbind(rep(1,100),x)
#'y = rbinTrait(n=1,phy=phy, beta=c(-1,0.5), alpha=.7 ,X=X)
#'dat = data.frame(y, x)
#'# Run sensitivity analysis:
#'samp <- samp_phyglm(y ~ x, data = dat, phy = phy, n.sim = 10)
#'# To check summary results and most influential species:
#'summary(samp)
#'\dontrun{
#'# Visual diagnostics for clade removal:
#'sensi_plot(samp)
#'}
#' @export
samp_phyglm <- function(formula,
data,
phy,
n.sim = 30,
breaks = seq(.1, .5, .1),
btol = 50,
track = TRUE,
...)
{
if (!inherits(formula, "formula"))
stop("formula must be class 'formula'")
if (!inherits(data, "data.frame"))
stop("data must be class 'data.frame'")
if (!inherits(phy, "phylo"))
stop("phy must be class 'phylo'")
if (length(breaks) < 2)
stop("Please include more than one break,
e.g. breaks=c(.3,.5)")
else
# Check match between data and phy
data_phy <- match_dataphy(formula, data, phy, ...)
full.data <- data_phy$data
phy <- data_phy$phy
N <- nrow(full.data)
mod.0 <- phylolm::phyloglm(
formula,
data = full.data,
phy = phy,
method = "logistic_MPLE",
btol = btol
)
if (isTRUE(mod.0$convergence != 0))
stop("Full model failed to converge,
consider changing btol. See ?phyloglm")
intercept.0 <- mod.0$coefficients[[1]]
estimate.0 <- mod.0$coefficients[[2]]
optpar.0 <- mod.0$alpha
pval.intercept.0 <-
phylolm::summary.phyloglm(mod.0)$coefficients[[1, 4]]
pval.estimate.0 <-
phylolm::summary.phyloglm(mod.0)$coefficients[[2, 4]]
aic.0 <- mod.0$aic
#Creates empty data frame to store model outputs
sensi.estimates <-
data.frame(
"n.remov" = numeric(),
"n.percent" = numeric(),
"intercept" = numeric(),
"DIFintercept" = numeric(),
"intercept.perc" = numeric(),
"pval.intercept" = numeric(),
"estimate" = numeric(),
"DIFestimate" = numeric(),
"estimate.perc" = numeric(),
"pval.estimate" = numeric(),
"AIC" = numeric(),
"optpar" = numeric()
)
#Loops over breaks, remove percentage of species determined by 'breaks
#and repeat determined by 'n.sim'.
counter = 1
limit <- sort(round((breaks) * nrow(full.data), digits = 0))
NL <- length(breaks) * n.sim
if (track == TRUE)
pb <- utils::txtProgressBar(min = 0, max = NL, style = 3)
for (i in limit) {
for (j in 1:n.sim) {
exclude <- sample(1:N, i)
crop.data <- full.data[-exclude,]
crop.phy <- ape::drop.tip(phy, phy$tip.label[exclude])
mod <- try(phylolm::phyloglm(
formula,
data = crop.data,
phy = crop.phy,
method = "logistic_MPLE",
btol = btol
),
TRUE)
if (isTRUE(class(mod) == "try-error")) {
next
}
else {
intercept <- mod$coefficients[[1]]
estimate <- mod$coefficients[[2]]
pval.intercept <-
phylolm::summary.phyloglm(mod)$coefficients[[1, 4]]
pval.estimate <-
phylolm::summary.phyloglm(mod)$coefficients[[2, 4]]
aic <- mod$aic
DIFintercept <- intercept - intercept.0
DIFestimate <- estimate - estimate.0
intercept.perc <- round((abs(DIFintercept / intercept.0)) * 100, digits = 1)
estimate.perc <- round((abs(DIFestimate / estimate.0)) * 100, digits = 1)
aic <- mod$aic
optpar <- mod$alpha
n.remov <- i
n.percent <- round((n.remov / N) * 100, digits = 0)
rep <- j
if (track == TRUE)
utils::setTxtProgressBar(pb, counter)
# Stores values for each simulation
estim.simu <-
data.frame(
n.remov,
n.percent,
intercept,
DIFintercept,
intercept.perc,
pval.intercept,
estimate,
DIFestimate,
estimate.perc,
pval.estimate,
aic,
optpar,
stringsAsFactors = F
)
sensi.estimates[counter,] <- estim.simu
counter = counter + 1
}
}
}
if (track == TRUE)
on.exit(close(pb))
#Calculates Standardized DFbeta and DIFintercept
sDIFintercept <- sensi.estimates$DIFintercept /
stats::sd(sensi.estimates$DIFintercept)
sDIFestimate <- sensi.estimates$DIFestimate /
stats::sd(sensi.estimates$DIFestimate)
sensi.estimates$sDIFintercept <- sDIFintercept
sensi.estimates$sDIFestimate <- sDIFestimate
#Calculates percentages of signficant intercepts & slopes within breaks.
res <- sensi.estimates
n.sim <- table(res$n.remov)
breaks <- unique(res$n.percent)
sign.intercept <- res$pval.intercept > .05
sign.estimate <- res$pval.estimate > .05
res$sign.intercept <- sign.intercept
res$sign.estimate <- sign.estimate
perc.sign.intercept <-
1 - (with(res, tapply(sign.intercept, n.remov, sum))) / n.sim
perc.sign.estimate <-
1 - (with(res, tapply(sign.estimate, n.remov, sum))) / n.sim
mean.sDIFestimate <-
with(res, tapply(sDIFestimate, n.remov, mean))
mean.sDIFintercept <- with(res, tapply(sDIFintercept, n.remov, mean))
mean.perc.intercept <- with(res, tapply(intercept.perc, n.remov, mean))
mean.perc.estimate <-
with(res, tapply(estimate.perc, n.remov, mean))
perc.sign.tab <- data.frame(
percent_sp_removed = breaks,
perc.sign.intercept = as.numeric(perc.sign.intercept),
mean.perc.intercept = as.numeric(mean.perc.intercept),
mean.sDIFintercept = as.numeric(mean.sDIFintercept),
perc.sign.estimate = as.numeric(perc.sign.estimate),
mean.perc.estimate = as.numeric(mean.perc.estimate),
mean.sDIFestimate = as.numeric(mean.sDIFestimate)
)
#Creates a list with full model estimates:
param0 <- list(
coef = phylolm::summary.phyloglm(mod.0)$coefficients,
aic = phylolm::summary.phyloglm(mod.0)$aic,
optpar = mod.0$alpha
)
#Generates output:
res <- list(
call = match.call(),
model = "logistic_MPLE",
formula = formula,
full.model.estimates = param0,
sensi.estimates = sensi.estimates,
sign.analysis = perc.sign.tab,
data = full.data
)
class(res) <- "sensiSamp"
return(res)
}
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