In arives/rr2: R2s for Regression Models

knitr::opts_chunk$set(echo = TRUE)

Goal

This package provides three R^2^s for statistical models with correlated errors including classes: 'lmerMod' (LMM), 'glmerMod' (GLMM), 'phylolm' (Phylogenetic GLS), and 'binaryPGLMM/phyloglm/communityPGLMM' (Phylogenetic Logistic Regression). Detailed technical descriptions can be found in Ives 2018.

Installation

This package can be installed with:

install.packages("rr2")

# or install the latest version
# install.packages("devtools")
devtools::install_github("arives/rr2")

Package structure

This package has three main functions: R2.resid(), R2.lik(), and R2.pred(). You can use them individually in the form of, e.g., R2.resid(mod, mod.r) where mod is the full model and mod.r is the reduced model for partial R2s. If you do not include the reduced model mod.r, then the appropriate model with just the intercept is used to give the total R^2^. When using R2.resid and R2.pred with PGLS, you need to include the phylo object containing a phylogenetic tree, e.g., R2.resid(mod, mod.r, phy = phy).

You can calculate all three R^2^s at the same time with R2(mod, mod.r). You can also specify which R^2^(s) to calculate within this function by turning off unwanted methods, e.g., R2(mod, mod.r, resid = FALSE) or R2(mod, mod.r, pred = FALSE).

This package also has some helper functions such as inv.logit(), partialR2(), and partialR2adj().

| Models | Available.R2s | | :------------------------------- | :------------------------- | | LM | partialR2, partialR2adj | | LM | R2.pred, R2.resid, R2.lik | | GLM | R2.pred, R2.resid, R2.lik | | LMM: lmerMod | R2.pred, R2.resid, R2.lik | | GLMM: glmerMod | R2.pred, R2.resid, R2.lik | | PGLS: phylolm | R2.pred, R2.resid, R2.lik | | PGLMM: binaryPGLMM | R2.pred, R2.resid, ------- | | PGLMM: phyloglm | -------, --------, R2.lik | | PGLMM: communityPGLMM (gaussian) | R2.pred, --------, R2.lik | | PGLMM: communityPGLMM (binomial) | R2.pred, --------, ------- |

Usage: calculating R^2^s for regression models

First, let's simulate data that will be used to fit various models.

# data 
set.seed(123)
p1 <- 10; nsample <- 10; n <- p1 * nsample
d <- data.frame(x1 = rnorm(n = n), 
                x2 = rnorm(n = n), 
                u1 = rep(1:p1, each = nsample), 
                u2 = rep(1:p1, times = nsample))
d$u1 <- as.factor(d$u1); d$u2 <- as.factor(d$u2)

# LMM: y with random intercept
b1 <- 1; b2 <- -1; sd1 <- 1.5
d$y_re_intercept <- b1 * d$x1 + b2 * d$x2 + 
  rep(rnorm(n = p1, sd = sd1), each = nsample) +  # random intercept u1
  rep(rnorm(n = p1, sd = sd1), times = nsample) + # random intercept u2
  rnorm(n = n)

# LMM: y with random slope
b1 <- 0; sd1 <- 1; sd.x1 <- 2
d$y_re_slope <- b1 * d$x1 + 
  rep(rnorm(n = p1, sd = sd1), each = nsample) + # random intercept u1
  d$x1 * rep(rnorm(n = p1, sd = sd.x1), times = nsample) + # random slope u1
  rnorm(n = n)

# GLMM
b1 <- 1; sd1 <- 1.5
prob <- rr2::inv.logit(b1 * d$x1 + rep(rnorm(n = p1, sd = sd1), each = nsample)) 
# random intercept u1
d$y_binary <- rbinom(n = n, size = 1, prob = prob)

# PGLS
b1 <- 1.5; signal <- 0.7
phy <- ape::compute.brlen(ape::rtree(n = n), method = "Grafen", power = 1)
phy.x <- ape::compute.brlen(phy, method = "Grafen", power = .0001)
x_trait <- ape::rTraitCont(phy.x, model = "BM", sigma = 1)
e <- signal^0.5 * ape::rTraitCont(phy, model = "BM", sigma = 1) + (1-signal)^0.5 * rnorm(n=n)
d$x_trait <- x_trait[match(names(e), names(x_trait))]
d$y_pgls <- b1 * x_trait + e
rownames(d) <- phy$tip.label    

# Phylogenetic Logistic Regression
b1 <- 1.5; signal <- 2
e <- signal * ape::rTraitCont(phy, model = "BM", sigma = 1)
e <- e[match(phy$tip.label, names(e))]
d$y_phy_binary <- rbinom(n = n, size = 1, prob = rr2::inv.logit(b1 * d$x1 + e))

head(d)

Then, let's fit some models and calculate their R^2^s.

LM

library(rr2)
z.f.lm <- lm(y_re_intercept ~ x1 + x2, data = d)
z.x.lm <- lm(y_re_intercept ~ x1, data = d)
z.0.lm <- lm(y_re_intercept ~ 1, data = d)

R2(mod = z.f.lm, mod.r = z.x.lm)
partialR2(mod = z.f.lm, mod.r = z.x.lm)
partialR2adj(mod = z.f.lm, mod.r = z.x.lm)

LMM

z.f.lmm <- lme4::lmer(y_re_intercept ~ x1 + x2 + (1 | u1) + (1 | u2), data = d, REML = F)
z.x.lmm <- lme4::lmer(y_re_intercept ~ x1 + (1 | u1) + (1 | u2), data = d, REML = F)
z.v.lmm <- lme4::lmer(y_re_intercept ~ 1 + (1 | u2), data = d, REML = F)
z.0.lmm <- lm(y_re_intercept ~ 1, data = d)

R2(mod = z.f.lmm, mod.r = z.x.lmm)
R2(mod = z.f.lmm, mod.r = z.v.lmm)
R2(mod = z.f.lmm, mod.r = z.0.lmm)
R2(mod = z.f.lmm) # if omit mod.r, default will be the simplest model, such as z.0.lmm here.

GLMM

z.f.glmm <- lme4::glmer(y_binary ~ x1 + (1 | u1), data = d, family = "binomial")
z.x.glmm <- lme4::glmer(y_binary ~ 1 + (1 | u1), data = d, family = "binomial")
z.v.glmm <- glm(y_binary ~ x1, data = d, family = "binomial")

R2(mod = z.f.glmm, mod.r = z.x.glmm)
R2(mod = z.f.glmm, mod.r = z.v.glmm)
R2(mod = z.f.glmm)
# specify sigma2_d for R2.resid()
R2.resid(mod = z.f.glmm, mod.r = z.v.glmm, sigma2_d = "s2w")
R2.resid(mod = z.f.glmm, mod.r = z.v.glmm, sigma2_d = "NS") 
R2.resid(mod = z.f.glmm, mod.r = z.v.glmm, sigma2_d = "rNS")

PGLS

z.f.pgls <- phylolm::phylolm(y_pgls ~ x_trait, phy = phy, data = d, model = "lambda")
z.v.lm <- lm(y_pgls ~ x_trait, data = d)

# phy is needed for phylogenetic models' R2.resid and R2.pred
R2(mod = z.f.pgls, mod.r = z.v.lm, phy = phy)
R2(mod = z.f.pgls, phy = phy)

# This also works for models fit with nlme::gls()
z.f.gls <- nlme::gls(y_pgls ~ x_trait, data = d, correlation = ape::corPagel(1, phy), method = "ML")
z.x.gls <- nlme::gls(y_pgls ~ 1, data = d, correlation = ape::corPagel(1, phy), method = "ML")
R2(mod = z.f.gls, mod.r = z.v.lm)
R2(mod = z.f.gls)

Phylogenetic Logistic Regression

Note: we modified ape::binaryPGLMM to return necessary components for rr2::R2().

z.f.plog <- rr2::binaryPGLMM(y_phy_binary ~ x1, data = d, phy = phy)
z.x.plog <- rr2::binaryPGLMM(y_phy_binary ~ 1, data = d, phy = phy)
z.v.plog <- glm(y_phy_binary ~ x1, data = d, family = "binomial")

# R2.lik can't be used with binaryPGLMM because it is not a ML method
R2(mod = z.f.plog, mod.r = z.x.plog)
R2(mod = z.f.plog)

z.f.plog2 <- phylolm::phyloglm(y_phy_binary ~ x1, data = d, start.alpha = 1, phy = phy)
z.x.plog2 <- phylolm::phyloglm(y_phy_binary ~ 1, data = d, phy = phy, 
                               start.alpha = min(20, z.f.plog2$alpha))
z.v.plog2 <- glm(y_phy_binary ~ x1, data = d, family = "binomial")

# R2.resid and R2.pred do not apply for phyloglm
R2(z.f.plog2, z.x.plog2) 
# alternate
R2.lik(z.f.plog2, z.x.plog2)

Contributions of predictors

We can use rr2::R2() to calculate partial R^2^s and compare contributions of different predictors. Here is an example using phylolm::phyloglm(). The same comparisons can be also applied to other types of models.

z.f <- phylolm::phyloglm(y_phy_binary ~ x1 + x2, data = d, start.alpha = 1, phy = phy)
z.r1 <- phylolm::phyloglm(y_phy_binary ~ x1, data = d, start.alpha = 1, phy = phy)
z.r2 <- phylolm::phyloglm(y_phy_binary ~ x2, data = d, start.alpha = 1, phy = phy)
# total R2
R2(z.f)
# contribution of x1
R2(z.f, z.r2)
# contribution of x2
R2(z.f, z.r1)

It is also possible to estimate the "contribution" of correlation structrues in the model. For the above example, we can replace the phylogeny with a star phylogeny and then compare the R^2^s of the two models.

# see the first chunk R code for the build of phy.x, a star phylogeny
z.r3 <- phylolm::phyloglm(y_phy_binary ~ x1 + x2, data = d, start.alpha = 1, phy = phy.x)
R2(z.f, z.r3)

Citation

Please cite the following papers if you find this package useful:

• Anthony R. Ives. 2018. R2s for Correlated Data: Phylogenetic Models, LMMs, and GLMMs. Systematic Biology, Volume 68, Issue 2, March 2019, Pages 234-251.
• Anthony R. Ives and Daijiang Li (2018). rr2: An R package to calculate R^2s for regression models. The Journal of Open Source Software, 3(30), 1028.

Contributing

Contributions are welcome. You can either provide comments and feedback by filing an issue on Github here or making pull requests. It may be easier if you first open an issue outlining what you will do in the pull request.

Questions about the package can also be posted as issues on Github.

arives/rr2 documentation built on Aug. 20, 2023, 3:24 a.m.