Resource Selection (Probability) Functions for use-availability wildlife data as described in Lele and Keim (2006) and Lele (2009).

rsf(formula, data, m, B = 99, inits, method = "Nelder-Mead",
control, model = TRUE, x = FALSE, ...)

rspf(formula, data, m, B = 99, link = "logit", inits,
method = "Nelder-Mead", control, model = TRUE, x = FALSE, ...)

rsf.fit(X, Y, m, link = "logit", B = 99,
inits, method = "Nelder-Mead", control, ...)

rsf.null(Y, m, inits, ...)

## Arguments

formula two sided model formula of the form y ~ x, where y is a vector of observations, x is the set of covariates. argument describing the matching of use and available points, see Details. data. number of bootstrap iterations to make. character, type of link function to be used. initial values, optional. method to be used in optim for numerical optimization. control options for optim. a logical value indicating whether model frame should be included as a component of the returned value logical values indicating whether the model matrix used in the fitting process should be returned as components of the returned value. vector of observations. covariate matrix. other arguments passed to the functions.

## Details

The rsf function fits the Exponential Resource Selection Function (RSF) model to presence only data.

The rspf function fits the Resource Selection Probability Function (RSPF) model to presence only data Link function "logit", "cloglog", and "probit" can be specified via the link argument.

The rsf.fit is the workhorse behind the two functions. link="log" leads to Exponential RSF.

The rsf.null function fits the 'no selection' version of the Exponential Resource Selection Function (RSF) model to presence only data.

LHS of the formula data must be binary, ones indicating used locations, while zeros indicating available location.

All available points are used for each use points if m=0 (global availability). If m is a single value, e.g. m=5, it is assumed that available data points are grouped in batches of 5, e.g. with IDs c(1,2) for used point locations and c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2) for available locations (local availability, matched use-available design). Similarly, a vector of matching IDs can also be provided, e.g. c(1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2) by combining the above two. This potentially could allow for unbalanced matching (e.g. c(1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2)) and for easier subsetting of the data, but comes with an increased computing time. Note, the response in the LHS of the formula should be coded as c(1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) for all of the above examples. When m is defined as a mapping vector or the value is 0, the order of course does not matter. However, ordering matters when m is constant because that implies a certain structure.

For model description and estimation details, see Lele and Keim (2006), Lele (2009), and Solymos and Lele (2016).

## Value

A list with class "rsf", "rsf.null", or "rspf" containing the following components:

call

the matched call.

y

vector from LHS of the formula.

coefficients

a named vector of coefficients.

std.error

a named vector of standard errors for the coefficients.

loglik

the maximized pseudo log-likelihood according to Lele 2009.

results

optim results.

character, value of the link function used.

control

control parameters for optim.

inits

initial values used in optimization.

m

value of the m argument with possibly matched use-available design.

np

number of active parameters.

fitted.values

vector of fitted values. These are relative selection values for RSF models, and probability of selection for RSPF models.

nobs

number of used locations.

bootstrap

component to store bootstrap results if B>0.

converged

logical, indicating convergence of the optimization.

formula

the formula supplied.

terms

the terms object used.

levels

a record of the levels of the factors used in fitting.

contrasts

the contrasts used.

model

if requested, the model frame.

x

if requested, the model matrix.

## References

Lele, S.R. (2009) A new method for estimation of resource selection probability function. Journal of Wildlife Management 73, 122--127.

Lele, S. R. & Keim, J. L. (2006) Weighted distributions and estimation of resource selection probability functions. Ecology 87, 3021--3028.

Solymos, P. & Lele, S. R. (2016) Revisiting resource selection probability functions and single-visit methods: clarification and extensions. Methods in Ecology and Evolution 7, 196--205.

## Examples

## --- Simulated data example ---

## settings
n.used <- 1000
m <- 10
n <- n.used * m
set.seed(1234)
x <- data.frame(x1=rnorm(n), x2=runif(n))
cfs <- c(1.5,-1,0.5)
## fitting Exponential RSF model
dat1 <- simulateUsedAvail(x, cfs, n.used, m, link="log")
m1 <- rsf(status ~ .-status, dat1, m=0, B=0)
summary(m1)#>
#> Call:
#> rsf(formula = status ~ . - status, data = dat1, m = 0, B = 0)
#>
#> Resource Selection Function (Exponential RSF) model
#> Non-matched Used-Available design
#> Maximum Likelihood estimates
#>
#> Fitted values:
#>     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
#>  0.03444  0.67639  1.34572  2.34955  2.75012 40.08155
#>
#>    Estimate Std. Error z value Pr(>|z|)
#> x1  -1.0036         NA      NA       NA
#> x2   0.4506         NA      NA       NA
#>
#> Log-likelihood: -8714
#> BIC = 1.744e+04
#>
#> Hosmer and Lemeshow goodness of fit (GOF) test:
#> X-squared = 6.293, df = 8, p-value 0.6145
#> ## fitting Logistic RSPF model
dat2 <- simulateUsedAvail(x, cfs, n.used, m, link="logit")
m2 <- rspf(status ~ .-status, dat2, m=0, B=0)
summary(m2)#>
#> Call:
#> rspf(formula = status ~ . - status, data = dat2, m = 0, B = 0)
#>
#> Resource Selection Probability Function (Logistic RSPF) model
#> Non-matched Used-Available design
#> Maximum Likelihood estimates
#>
#> Fitted probabilities:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
#>  0.1158  0.8306  0.9151  0.8712  0.9604  0.9986
#>
#>             Estimate Std. Error z value Pr(>|z|)
#> (Intercept)   1.7294     0.8221   2.104   0.0354 *
#> x1           -1.1667     0.5352  -2.180   0.0293 *
#> x2            1.2669     1.0942   1.158   0.2469
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Log-likelihood: -9197
#> BIC = 1.841e+04
#>
#> Hosmer and Lemeshow goodness of fit (GOF) test:
#> X-squared = 4.256, df = 8, p-value 0.8334
#>
## --- Real data analysis from Lele & Keim 2006 ---

if (FALSE) {
goats$exp.HLI <- exp(goats$HLI)
goats$sin.SLOPE <- sin(pi * goats$SLOPE / 180)
goats$ELEVATION <- scale(goats$ELEVATION)
goats$ET <- scale(goats$ET)
goats$TASP <- scale(goats$TASP)

## Fit two RSPF models:
## global availability (m=0) and bootstrap (B=99)
m1 <- rspf(STATUS ~ TASP + sin.SLOPE + ELEVATION, goats, m=0, B = 99)
m2 <- rspf(STATUS ~ TASP + ELEVATION, goats, m=0, B = 99)

## Inspect the summaries
summary(m1)
summary(m2)

## Compare models: looks like m1 is better supported
CAIC(m1, m2)

## Visualize the relationships
plot(m1)
mep(m1) # marginal effects similar to plot but with CIs
kdepairs(m1) # 2D kernel density estimates
plot(m2)
kdepairs(m2)
mep(m2)

## fit and compare to null RSF model (not available for RSPF)
m3 <- rsf(STATUS ~ TASP + ELEVATION, goats, m=0, B = 0)
m4 <- rsf.null(Y=goats\$STATUS, m=0)
CAIC(m3, m4)
}