trainGLM {enmSdmX}

Calibrate a generalized linear model (GLM)

Description

This function constructs a generalized linear model. By default, the model is constructed in a two-stage process. First, the "construct" phase generates a series of simple models with univariate, quadratic, or 2-way-interaction terms. These simple models are then ranked based on their AICc. Second, the "select" phase creates a "full" model from the simple models such that there is at least presPerTermInitial presences (if the response is binary) or data rows (if not) for each coefficient to be estimated (not counting the intercept). Finally, it selects the best model using AICc from all possible subsets of this "full" model, while respecting marginality (i.e., all lower-order terms of higher-order terms appear in the model).

The function outputs any or all of: a table with AICc for all evaluated models; all models evaluated in the "selection" phase; and/or the single model with the lowest AICc.

Usage

trainGLM(
  data,
  resp = names(data)[1],
  preds = names(data)[2:ncol(data)],
  scale = NA,
  construct = TRUE,
  select = TRUE,
  quadratic = TRUE,
  interaction = TRUE,
  interceptOnly = TRUE,
  method = "glm.fit",
  presPerTermInitial = 10,
  presPerTermFinal = 10,
  maxTerms = 8,
  w = TRUE,
  family = stats::binomial(),
  out = "model",
  cores = 1,
  verbose = FALSE,
  ...
)

Arguments

data

Data frame.

resp

Response variable. This is either the name of the column in data or an integer indicating the column in data that has the response variable. The default is to use the first column in data as the response.

preds

Character list or integer list. Names of columns or column indices of predictors. The default is to use the second and subsequent columns in data.

scale

Either NA (default), or TRUE or FALSE. If TRUE, the predictors will be centered and scaled by dividing by subtracting their means then dividing by their standard deviations. The means and standard deviations will be returned in the model object under an element named "scales". For example, if you do something like model <- trainGLM(data, scale=TRUE), then you can get the means and standard deviations using model$scales$mean and model$scales$sd. If FALSE, no scaling is done. If NA (default), then the function will check to see if non-factor predictors have means ~0 and standard deviations ~1. If not, then a warning will be printed, but the function will continue to do its operations.

construct

Logical. If TRUE (default) then construct model from individual terms entered in order from lowest to highest AICc up to limits set by presPerTermInitial or maxTerms is met. If FALSE then the "full" model consists of all terms allowed by quadratic and interaction.

select

Logical. If TRUE (default) then calculate AICc for all possible subsets of models and return the model with the lowest AICc of these. This step if performed after model construction (if any).

quadratic

Logical. Used only if construct is TRUE. If TRUE (default) then include quadratic terms in model construction stage for non-factor predictors.

interaction

Logical. Used only if construct is TRUE. If TRUE (default) then include 2-way interaction terms (including interactions between factor predictors).

interceptOnly

If TRUE (default) and model selection is enabled, then include an intercept-only model.

method

Character: Name of function used to solve the GLM. For "normal" GLMs, this can be 'glm.fit' (default), 'brglmFit' (from the brglm2 package), or another function.

presPerTermInitial

Positive integer. Minimum number of presences needed per model term for a term to be included in the model construction stage. Used only is construct is TRUE.

presPerTermFinal

Positive integer. Minimum number of presence sites per term in initial starting model. Used only if select is TRUE.

maxTerms

Maximum number of terms to be used in any model, not including the intercept (default is 8). Used only if construct is TRUE.

w

Weights. Any of:

• TRUE: Causes the total weight of presences to equal the total weight of absences (if family='binomial')

• FALSE: Each datum is assigned a weight of 1.

• A numeric vector of weights, one per row in data.

• The name of the column in data that contains site weights.

family

Name of family for data error structure (see family). Default is to use the 'binomial' family.

out

Character vector. One or more values:

• 'model': Model with the lowest AICc.

• 'models': All models evaluated, sorted from lowest to highest AICc (lowest is best).

• 'tuning': Data frame with tuning parameters, one row per model, sorted by AICc.

cores

Integer >= 1. Number of cores to use when calculating multiple models. Default is 1. If you have issues when cores > 1, please see the troubleshooting_parallel_operations guide.

verbose

Logical. If TRUE then display progress.

...

Arguments to pass to glm.

Value

The object that is returned depends on the value of the out argument. It can be a model object, a data frame, a list of models, or a list of all two or more of these. If scale is TRUE, any model object will also have an element named $scale, which contains the means and standard deviations for predictors that are not factors.

See Also

glm

Examples

# NB: The examples below show a very basic modeling workflow. They have been 
# designed to work fast, not produce accurate, defensible models. They can
# take a few minutes to run.

library(mgcv)
library(sf)
library(terra)
set.seed(123)

### setup data
##############

# environmental rasters
rastFile <- system.file('extdata/madClim.tif', package='enmSdmX')
madClim <- rast(rastFile)

# coordinate reference system
wgs84 <- getCRS('WGS84')

# lemur occurrence data
data(lemurs)
occs <- lemurs[lemurs$species == 'Eulemur fulvus', ]
occs <- vect(occs, geom=c('longitude', 'latitude'), crs=wgs84)

occs <- elimCellDuplicates(occs, madClim)

occEnv <- extract(madClim, occs, ID = FALSE)
occEnv <- occEnv[complete.cases(occEnv), ]
	
# create 10000 background sites (or as many as raster can support)
bgEnv <- terra::spatSample(madClim, 20000)
bgEnv <- bgEnv[complete.cases(bgEnv), ]
bgEnv <- bgEnv[1:min(10000, nrow(bgEnv)), ]

# collate occurrences and background sites
presBg <- data.frame(
  presBg = c(
    rep(1, nrow(occEnv)),
    rep(0, nrow(bgEnv))
  )
)

env <- rbind(occEnv, bgEnv)
env <- cbind(presBg, env)

predictors <- c('bio1', 'bio12')

### calibrate models
####################

# Note that all of the trainXYZ functions can made to go faster using the
# "cores" argument (set to just 1, by default). The examples below will not
# go too much faster using more cores because they are simplified, but
# you can try!
cores <- 1

# MaxEnt
mx <- trainMaxEnt(
	data = env,
	resp = 'presBg',
	preds = predictors,
	regMult = 1, # too few values for reliable model, but fast
	verbose = TRUE,
	cores = cores
)

# MaxNet
mn <- trainMaxNet(
	data = env,
	resp = 'presBg',
	preds = predictors,
	regMult = 1, # too few values for reliable model, but fast
	verbose = TRUE,
	cores = cores
)

# generalized linear model (GLM)
gl <- trainGLM(
	data = env,
	resp = 'presBg',
	preds = predictors,
	scale = TRUE, # automatic scaling of predictors
	verbose = TRUE,
	cores = cores
)

# generalized additive model (GAM)
ga <- trainGAM(
	data = env,
	resp = 'presBg',
	preds = predictors,
	verbose = TRUE,
	cores = cores
)

# natural splines
ns <- trainNS(
	data = env,
	resp = 'presBg',
	preds = predictors,
	scale = TRUE, # automatic scaling of predictors
	df = 1:2, # too few values for reliable model(?)
	verbose = TRUE,
	cores = cores
)

# boosted regression trees
envSub <- env[1:1049, ] # subsetting data to run faster
brt <- trainBRT(
	data = envSub,
	resp = 'presBg',
	preds = predictors,
	learningRate = 0.001, # too few values for reliable model(?)
	treeComplexity = c(2, 3), # too few values for reliable model, but fast
	minTrees = 1200, # minimum trees for reliable model(?), but fast
	maxTrees = 1200, # too small for reliable model(?), but fast
	tryBy = 'treeComplexity',
	anyway = TRUE, # return models that did not converge
	verbose = TRUE,
	cores = cores
)

# random forests
rf <- trainRF(
	data = env,
	resp = 'presBg',
	preds = predictors,
	numTrees = c(100, 500), # using at least 500 recommended, but fast!
	verbose = TRUE,
	cores = cores
)

### make maps of models
#######################

# NB We do not have to scale rasters before predicting GLMs and NSs because we
# used the `scale = TRUE` argument in trainGLM() and trainNS().

mxMap <- predictEnmSdm(mx, madClim)
mnMap <- predictEnmSdm(mn, madClim) 
glMap <- predictEnmSdm(gl, madClim)
gaMap <- predictEnmSdm(ga, madClim)
nsMap <- predictEnmSdm(ns, madClim)
brtMap <- predictEnmSdm(brt, madClim)
rfMap <- predictEnmSdm(rf, madClim)

maps <- c(
	mxMap,
	mnMap,
	glMap,
	gaMap,
	nsMap,
	brtMap,
	rfMap
)

names(maps) <- c('MaxEnt', 'MaxNet', 'GLM', 'GAM', 'NSs', 'BRTs', 'RFs')
fun <- function() plot(occs, col='black', pch=3, add=TRUE)
plot(maps, fun = fun, nc = 4)

### compare model responses to BIO12 (mean annual precipitation)
################################################################

# make a data frame holding all other variables at mean across occurrences,
# varying only BIO12
occEnvMeans <- colMeans(occEnv, na.rm=TRUE)
occEnvMeans <- rbind(occEnvMeans)
occEnvMeans <- as.data.frame(occEnvMeans)
climFrame <- occEnvMeans[rep(1, 100), ]
rownames(climFrame) <- NULL

minBio12 <- min(env$bio12)
maxBio12 <- max(env$bio12)
climFrame$bio12 <- seq(minBio12, maxBio12, length.out=100)

predMx <- predictEnmSdm(mx, climFrame)
predMn <- predictEnmSdm(mn, climFrame)
predGl <- predictEnmSdm(gl, climFrame)
predGa <- predictEnmSdm(ga, climFrame)
predNat <- predictEnmSdm(ns, climFrame)
predBrt <- predictEnmSdm(brt, climFrame)
predRf <- predictEnmSdm(rf, climFrame)


plot(climFrame$bio12, predMx,
xlab='BIO12', ylab='Prediction', type='l', ylim=c(0, 1))

lines(climFrame$bio12, predMn, lty='solid', col='red')
lines(climFrame$bio12, predGl, lty='dotted', col='blue')
lines(climFrame$bio12, predGa, lty='dashed', col='green')
lines(climFrame$bio12, predNat, lty=4, col='purple')
lines(climFrame$bio12, predBrt, lty=5, col='orange')
lines(climFrame$bio12, predRf, lty=6, col='cyan')

legend(
   'topleft',
   inset = 0.01,
   legend = c(
	'MaxEnt',
	'MaxNet',
	'GLM',
	'GAM',
	'NS',
	'BRT',
	'RF'
   ),
   lty = c(1, 1:6),
   col = c(
	'black',
	'red',
	'blue',
	'green',
	'purple',
	'orange',
	'cyan'
   ),
   bg = 'white'
)