closedpCI {Rcapture} | R Documentation |
The closedpCI.t
and closedpCI.0
functions fit a loglinear model specified by the user and computes the multinomial profile likelihood confidence interval for the adundance estimation. The model can be given as a design matrix mX
or identified trougth arguments m
, h
and theta
. These functions extand closedp.t
and closedp.0
as they broaden the range of model one can fit and they computes confidence interval. Unlike the closedp
functions, it fits only one model at a time.
closedpCI.t(X, dfreq=FALSE, m=c("M0","Mt","Mh","Mth"), h=c("Chao","Poisson","Darroch","Gamma"), theta=2, mX=NULL, mname, neg=TRUE, alpha=0.05) closedpCI.0(X, dfreq=FALSE, dtype=c("hist","nbcap"), t, t0=t, m=c("M0","Mh"), h=c("Chao","Poisson","Darroch","Gamma"), theta=2, mX=NULL, mname, neg=TRUE, alpha=0.05) ## S3 method for class 'closedpCI': print(x, ...) plotCI(x, ...) ## S3 method for class 'closedpCI': plotCI(x, main="Profile Likelihood Confidence Interval", ...) ## S3 method for class 'closedpCI': boxplot(x, main="Boxplots of Pearson Residuals", ...) ## S3 method for class 'closedpCI': plot(x, main="Scatterplot of Pearson Residuals", ...)
X |
The matrix of the observed capture histories (see Rcapture-package for a description of the accepted formats). |
dfreq |
A logical. By default FALSE, which means that X has one row per unit. If TRUE, it indicates that the matrix X contains frequencies in its last column. |
dtype |
A characters string, either "hist" or "nbcap", to specify the type of data. "hist", the default, means that X contains complete observed capture histories. "nbcap" means that X contains numbers of captures (see Rcapture-package for details on data formats). |
t |
Requested only if dtype="nbcap" . A numeric specifying the total number of capture occasions in the experiment. |
t0 |
A numeric. Models are fitted considering only the frequencies of units captured 1 to t0 times. By default t0=t . |
m |
A character string indicating the model to fit. For closedpCI.0 it can be either "M0"=M0 model or "Mh"=Mh model. For closedpCI.t it can also be "Mt"=Mt model or "Mth"=Mth model. |
h |
A character string ("Chao", "Poisson", "Darroch" or "Gamma") or a numerical R function specifying the form of the column for heterogeneity in the design matrix. "Chao" represents Chao's model, "Poisson" represents the function f(k)=theta^k-1, where k is the number of captures, "Darroch" represents the function f(k)=k^2/2, and "Gamma" represents the function f(k)=-log(theta + k) + log(theta). If an R function is given, it is the implemantation of any convex mathematical function f(k). It has only one argument. |
theta |
The value of the parameter for a Poisson or Gamma model. |
mX |
The design matrix of the loglinear model. In this matrix, the order of the capture histories is as defined in the histpos.t or histpos.0 function. |
mname |
A character string specifying the name of the customized model. |
neg |
If this option is set to TRUE, negative eta parameters in Chao's models are set to zero. |
alpha |
A confidence interval with confidence level 1-alpha is constructed. The value of alpha must be between 0 and 1; the default is 0.05. |
x |
An object, produced by the closedpCI.t function, to print. |
main |
A main title for the plot |
... |
Further arguments to be passed to methods (see print.default , plot.default or boxplot.default ). |
The closedpCI.t
function fits models using the frequencies of the observable capture histories (vector of size 2^t-1), whereas closedp.0
uses the number of units capture i times, for i=1,...,t (vector of size t). Thus, closedpCI.0
can be used with data sets larger than those for closedpCI.t
.
This function does not work for closed population models featuring a behavioral effect, such as Mb and Mbh. The abundance estimation is calculated as the number of captured units plus the exponential of the Poisson regression intercept. However, models with a behavioral effect can by fitted with closedp.t
(Mb and Mbh), closedp.Mtb
and closedp.bc
.
An intercept is added to the model. Therefore, the mX
matrix must not contain a column of ones.
The plotCI.closedpCI
function produces a plot of the multinomial profile likelihood for N. The value of N maximizing the profile likelihood and the bounds of the confidence interval are identified.
The boxplot.closedpCI
function produces a boxplot of the Pearson residuals of the customized model.
The plot.closedpCI
function traces the scatterplot of the Pearson residuals in terms of fi (number of units captured i times) for the customized model.
n |
The number of captured units |
t |
The number of capture occasions in the data matrix X |
results |
A table containing the estimated population size, the standard error of estimation, the deviance, the number of degrees of freedom and the Akaike criteria. |
glm |
The 'glm' object obtained from fitting the model. |
CI |
A table containing the abundance estimation and its confidence interval. |
alpha |
1-the confidence level of the interval. |
NCI |
The x-coordinates for plot.closedpCI.t |
loglikCI |
The y-coordinates for plot.closedpCI.t |
t0 |
A copy of the t0 argument given in the function call. |
This function uses the optimize
and the uniroot
functions of the stats
package.
Sophie Baillargeon Sophie.Baillargeon@mat.ulaval.ca and
Louis-Paul Rivest Louis-Paul.Rivest@mat.ulaval.ca
Baillargeon, S. and Rivest, L.P. (2007) Rcapture: Loglinear models for capture-recapture in R. Journal of Statistical Software, 19(5), http://www.jstatsoft.org/v19/i05.
Rivest, L.P. and Baillargeon, S. (2007) Applications and extensions of Chao's moment estimator for the size of a closed population. Biometrics, 63(4), 999–1006.
Cormack, R. M. (1992) Interval estimation for mark-recapture studies of closed populations. Biometrics, 48, 567–576.
data(hare) CI<-closedpCI.t(hare, m = "Mth", h = "Poisson", theta = 2) CI plotCI(CI) data(HIV) mat<-histpos.t(4) mX2<-cbind(mat,mat[,1]*mat[,2]) closedpCI.t(HIV,dfreq=TRUE,mX=mX2,mname="Mt interaction 1,2") data(BBS2001) CI0<-closedpCI.0(BBS2001,dfreq=TRUE,dtype="nbcap",t=50,t0=20, m="Mh",h="Gamma",theta=3.5) CI0 plot(CI0) plotCI(CI0) ### As an alternative to a gamma model, one can fit a negative Poisson model. ### It is appropriate in experiments where very small capture probabilities ### are likely. It can lead to very large estimators of abundance. data(mvole) period3<-mvole[,11:15] psi <- function(x) { 0.5^x - 1 } closedpCI.t(period3, m = "Mh", h = psi)