svabu function

Single visit N-mixture abundance models

Binomial-Poisson, Binomial-NegBin, Binomial-ZIP, and Binomial-ZINB models with single visit.

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

svabu.fit(Y, X, Z, Q = NULL, zeroinfl = TRUE, area = 1, N.max = NULL,
    inits, link.det = "logit", link.zif = "logit", ...)
svabu_nb.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
• distr: character, abundance distribution: "P" for Poisson, "NB" for Negative Binomial.
• ...: 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) and explained in Solymos et a. (2012) and Solymos and Lele (2016).

Returns

An object of class 'svabu'.

References

Royle, J. A. 2004. N-Mixture Models for Estimating Population Size from Spatially Replicated Counts. Biometrics, 60(1) , 108--115. doi:10.1111/j.0006-341X.2004.00142.x

Solymos, P., Lele, S. R. and Bayne, E. 2012. Conditional likelihood approach for analyzing single visit abundance survey data in the presence of zero inflation and detection error. Environmetrics, 23 , 197--205. doi:10.1002/env.1149

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

Denes, F., Solymos, P., Lele, S. R., Silveira, L. & Beissinger, S. 2017. Biome scale signatures of land use change on raptor abundance: insights from single-visit detection-based models. Journal of Applied Ecology, 54 , 1268--1278. doi:10.1111/1365-2664.12818

Author(s)

Peter Solymos and Subhash Lele

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)