svabu: Binomial-Poisson and Binomial-ZIP models with single visit

In detect: Analyzing Wildlife Data with Detection Error

Description

Binomial-Poisson and Binomial-ZIP models with single visit

Usage

svabu(formula, data, zeroinfl = TRUE, area = 1, N.max = NULL, 
    inits, link.det = "logit", link.zif = "logit", 
    model = TRUE, x = FALSE, ...)

svabu.fit(Y, X, Z, Q = NULL, zeroinfl = TRUE, area = 1, N.max = NULL, 
    inits, link.det = "logit", link.zif = "logit", ...)

zif(x)
is.present(object, ...)
predictMCMC(object, ...)
svabu.step(object, model, trace = 1, steps = 1000, 
    criter = c("AIC", "BIC"), 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. x can further expanded as x1 + zif(x2) into terms for the nonzero count data part (x1) and the zero inflation component (zif(x2)) using the zif special.
Y, X, Z, Q	vector of observation, design matrix for abundance model, design matrix for detection and design matrix for zero inflation model
data	data
area	area
N.max	maximum of true count values (for calculating the integral)
zeroinfl	logical, if the Binomial-ZIP model should be fitted
inits	initial values used by link{optim}
link.det, link.zif	link function for the detection and zero inflation parts of the model
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. For the function zif it is any object to be returned.
object	a fitted 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.

The Binomial-Poisson model is the single visit special case of the N-mixture model proposed by Royle (2004).

Value

An object of class 'svabu'.

Author(s)

Peter Solymos and Subhash Lele

References

Royle, J. A. 2004. N-Mixture Models for Estimating Population Size from Spatially Replicated Counts. Biometrics, 60(1), 108–115.

Solymos, P., Lele, S. R and Bayne, E. 2011. Conditional likelihood approach for analyzing single visit abundance survey data in the presence of zero inflation and detection error. Environmetrics, 23, 197–205.

Solymos, P., Lele, S. R and Bayne, E. 2011. Abundance estimation in the presence of zero inflation and detection error using single visit data. Alberta Biodiversity Monitoring Institute, Alberta, Canada. Technical Report No. ABMI-20061, August 24, 2011. Available at: http://www.abmi.ca

Examples

data(databu)

## fit BZIP and BP models
m00 <- svabu(Y ~ x1 + x5 | x2 + x5, databu[1:200,])

## print method
m00
## summary: CMLE
summary(m00)
## coef
coef(m00)
coef(m00, model="sta") ## state (abundance)
coef(m00, model="det") ## detection
coef(m00, model="zif") ## zero inflation (this is part of the 'true state'!)

## Not run: 
## Diagnostics and model comparison

m01 <- svabu(Y ~ x1 + x5 | x2 + x5, databu[1:200,], zeroinfl=FALSE)
## compare estimates (note, zero inflation is on the logit scale!)
cbind(truth=c(2,-0.8,0.5, 1,2,-0.5, plogis(0.3)),
"B-ZIP"=coef(m00), "B-P"=c(coef(m01), NA))

## fitted
plot(fitted(m00), fitted(m01))
abline(0,1)

## compare models
AIC(m00, m01)
BIC(m00, m01)
logLik(m00)
logLik(m01)
## diagnostic plot
plot(m00)
plot(m01)

## Bootstrap

## non parametric bootstrap
## - initial values are the estimates
m02 <- bootstrap(m00, B=25)
attr(m02, "bootstrap")
extractBOOT(m02)
summary(m02)
summary(m02, type="cmle")
summary(m02, type="boot")
## vcov
vcov(m02, type="cmle")
vcov(m02, type="boot")
vcov(m02, model="sta")
vcov(m02, model="det")
## confint
confint(m02, type="cmle") ## Wald-type
confint(m02, type="boot") ## quantile based
## parametric bootstrap
simulate(m00, 5)
m03 <- bootstrap(m00, B=5, type="param")
extractBOOT(m03)
summary(m03)

## Model selection

m04 <- svabu(Y ~ x1 + x5 | x2 + x5 + x3, databu[1:200,], phi.boot=0)
m05 <- drop1(m04, model="det")
m05
m06 <- svabu.step(m04, model="det")
summary(m06)
m07 <- update(m04, . ~ . | . - x3)
m07

## Controls

m00$control
getOption("detect.optim.control")
getOption("detect.optim.method")
options("detect.optim.method"="BFGS")
m08 <- svabu(Y ~ x1 + x5 | x2 + x5, databu[1:100,])
m08$control ## but original optim method is retained during model selection and bootstrap
## fitted models can be used to provide initial values
options("detect.optim.method"="Nelder-Mead")
m09 <- svabu(Y ~ x1 + x5 | x2 + x5, databu[1:100,], inits=coef(m08))

## Ovenbirds dataset

data(oven)
ovenc <- oven
ovenc[, c(4:8,10:11)][] <- lapply(ovenc[, c(4:8,10:11)], scale)
moven <- svabu(count ~ pforest | observ + pforest + julian + timeday, ovenc)
summary(moven)
drop1(moven, model="det")
moven2 <- update(moven, . ~ . | . - timeday)
summary(moven2)
moven3 <- update(moven2, . ~ . | ., zeroinfl=FALSE)
summary(moven3)
BIC(moven, moven2, moven3)

## End(Not run)

detect documentation built on May 2, 2019, 4:50 p.m.