This function fits model Mtb for closed populations in capture-recapture experiments.

`closedp.Mtb(X, dfreq=FALSE, method = "BFGS", …)`# S3 method for closedp.Mtb
print(x, …)

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.

method

The method to be used by `optim`

. The default is `"BFGS"`

.

…

Further arguments to be passed to `optim`

or `print.default`

.

x

An object, produced by the `closedp.Mtb`

function, to print.

The number of captured units

The total number of capture occasions in the data matrix `X`

.

A table containing, for the fitted model:

`abundance`

:the estimated population size,

`stderr`

:the standard error of the estimated population size,

`deviance`

:the model's deviance,

`df`

:the number of degrees of freedom,

`AIC`

:the Akaike's information criterion,

`BIC`

:the bayesian information criterion,

`infoFit`

:a numerical code giving information about error or warnings encountered when fitting the model (see

`Rcapture-package`

for details).

The output produced by `optim`

from fitting the model.

A vector of character strings. If the `optim`

function generates
one or more warnings when fitting the model, a copy of these warnings are
stored in `optim.warn`

. `NULL`

if `optim`

did not produce
any warnings.

Capture-recapture parameters estimates for model Mtb : the abundance N, \(p_1\) to \(p_t\), the probabilities of first capture for each capture occasion, and \(c_2\) to \(c_t\), the recapture probabilities for each capture occasion.

The Mtb model is non-linear. It is fitted with the `optim`

function instead of the `glm`

function. Therefore, the abundance estimate can be unstable.

For the model to be identifiable, the parameters are constrained in the following way: \(logit(c_i)=logit(p_i)+b\) for i in \(2,\ldots,l\).

Baillargeon, S. and Rivest, L.P. (2007) Rcapture: Loglinear models for capture-recapture in R. *Journal of Statistical Software*, **19**(5), 10.18637/jss.v019.i05.

```
# NOT RUN {
# hare data set
closedp.Mtb(hare)
## Example producing an unstable estimate
# Fourth primary period of mvole data set
period4 <- mvole[, 16:20]
closedp.Mtb(period4)
# }
```

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