svocc function

ZI Binomial model with single visit

svocc(formula, data, link.sta = "cloglog", link.det = "logit",
    penalized = FALSE, method = c("optim", "dc"), inits,
    model = TRUE, x = FALSE, ...)
svocc.fit(Y, X, Z, link.sta = "cloglog", link.det = "logit",
    penalized = FALSE, auc = FALSE, method = c("optim", "dc"),
    inits, ...)

extractMLE(object, ...)
svocc.step(object, model, trace = 1, steps = 1000,
    criter = c("AIC", "BIC", "cAUC"), test = FALSE, k = 2,
    control, ...)

Arguments

• formula: formula of the form y ~ x | z, where y is a vector of observations, x is the set of covariates for the occurrence model, z is the set of covariates for the detection model
• Y, X, Z: vector of observation, design matrix for occurrence model, and design matrix for detection model
• data: data
• link.sta, link.det: link function for the occurrence (true state) and detection model
• penalized: logical, if penalized likelihood estimate should be computed
• method: optimization or data cloning to be used as optimization
• inits: initial values
• model: a logical value indicating whether model frame should be included as a component of the returned value, or true state or detection model
• x: logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value
• auc: logical, if AUC should be calculated
• object: a fitted model object
• trace: info returned during the procedure
• steps: max number of steps
• criter: criterion to be minimized (cAUC=1-AUC)
• test: logical, if decrease in deviance should be tested
• k: penalty to be used with AIC
• control: controls for optimization, if missing taken from object
• ...: other arguments passed to the functions

Details

See Examples.

The right hand side of the formula must contain at least one continuous (i.e. non discrete/categorical) covariate. This is the necessary condition for the single-visit method to be valid and parameters to be identifiable. See References for more detailed description.

Returns

An object of class 'svocc'.

References

Lele, S.R., Moreno, M. and Bayne, E. 2011. Dealing with detection error in site occupancy surveys: What can we do with a single survey? Journal of Plant Ecology, 5(1) , 22--31. doi:10.1093/jpe/rtr042

Moreno, M. and Lele, S. R. 2010. Improved estimation of site occupancy using penalized likelihood. Ecology, 91 , 341--346. doi:10.1890/09-1073.1

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. doi:10.1111/2041-210X.12432

Author(s)

Peter Solymos and Monica Moreno

Examples

data(datocc)
## MLE
m00 <- svocc(W ~ x1 | x1 + x3, datocc)
## PMLE
m01 <- svocc(W ~ x1 | x1 + x3, datocc, penalized=TRUE)

## print
m00
## summary
summary(m00)
## coefficients
coef(m00)
## state (occupancy) model estimates
coef(m00, "sta")
## detection model estimates
coef(m00, "det")
## compare estimates
cbind(truth=c(0.6, 0.5, 0.4, -0.5, 0.3),
mle=coef(m00), pmle=coef(m01))

## AIC, BIC
AIC(m00)
BIC(m00)
## log-likelihood
logLik(m00)
## variance-covariance matrix
vcov(m00)
vcov(m00, model="sta")
vcov(m00, model="det")
## confidence intervals
confint(m00)
confint(m00, model="sta")
confint(m00, model="det")

## fitted values
## (conditional probability of occurrence given detection history:
## if W=1, fitted=1,
## if W=0, fitted=(phi*(1-delta)) / ((1-delta) + phi * (1-delta))
summary(fitted(m00))
## estimated probabilities: (phi*(1-delta)) / ((1-delta) + phi * (1-delta))
summary(m00$estimated.probabilities)
## probability of occurrence (phi)
summary(m00$occurrence.probabilities)
## probability of detection (delta)
summary(m00$detection.probabilities)

## Not run:

## model selection
m02 <- svocc(W ~ x1 | x3 + x4, datocc)
m03 <- drop1(m02, model="det")
## dropping one term at a time, resulting change in AIC
m03
## updating the model
m04 <- update(m02, . ~ . | . - x4)
m04
## automatic model selection
## part of the model (sta/det) must be specified
m05 <- svocc.step(m02, model="det")
summary(m05)

## nonparametric bootstrap
m06 <- bootstrap(m01, B=25)
attr(m06, "bootstrap")
extractBOOT(m06)
summary(m06, type="mle")
summary(m06, type="pmle") ## no SEs! PMLE!!!
summary(m06, type="boot")
## vcov
#vcov(m06, type="mle") ## this does not work with PMLE
vcov(m06, type="boot") ## this works
## confint
confint(m06, type="boot") ## quantile based

## parametric bootstrap
## sthis is how observations are simulated
head(simulate(m01, 5))
m07 <- bootstrap(m01, B=25, type="param")
extractBOOT(m07)
summary(m07)

data(oven)
ovenc <- oven
ovenc[, c(4:8,10:11)][] <- lapply(ovenc[, c(4:8,10:11)], scale)
ovenc$count01 <- ifelse(ovenc$count > 0, 1, 0)
moven <- svocc(count01 ~ pforest | julian + timeday, ovenc)
summary(moven)
drop1(moven, model="det")
moven2 <- update(moven, . ~ . | . - timeday)
summary(moven)

BIC(moven, moven2)
AUC(moven, moven2)
rocplot(moven)
rocplot(moven2, col=2, add=TRUE)
## End(Not run)