This function computes various demographic parameters using a loglinear model for open populations in capture-recapture experiments.

`openp(X, dfreq=FALSE, m=c("up","ep"), neg=TRUE, keep=rep(TRUE,2^I-1))`# S3 method for openp
print(x, …)

# S3 method for openp
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.

m

This argument is a character string taking the value "up" (up = unconstrained probabilities) or "ep" (ep = equal
probabilities). If `m`

is set to "up" (the default), no constraint is set on the loglinear parameters. Therefore
some loglinear and demographic parameters are not estimable. On the other hand, when `m`

takes the value "ep",
the capture probabilities are set to a common value; this enables the estimation of all the parameters.

keep

This option is useful to fit the model on a subset of the possible capture histories. `keep`

is a logical
vector of length \(2^I-1\) taking the value TRUE for a history kept and FALSE for a history put aside. In this
vector, the order of the capture histories is as defined in the `histpos.t`

function. By default, every capture
history is kept.

neg

If this option is set to TRUE, relevant negative gamma parameters are set to zero. This insures that the estimated survival probabilities belong to [0, 1] and that the births are positive.

x

An object, produced by the `openp`

function, to print or to plot.

main

A main title for the plot

…

Further arguments to be passed to methods (see `print.default`

and `plot.default`

).

The number of captured units

A table containing the deviance, degrees of freedom and AIC of the fitted model.

A table containing, for the models with an added trap effect, the deviance, degrees of freedom and AIC.

The estimated trap effect parameters and their standard errors. For m="up", the \(I-3\) first rows of
`trap.param`

are estimations of the differences \(logit\)(capture probability after a capture)-
\(logit\)(capture probability after a miss) for periods 3 to \(I-1\). The last row gives a pooled
estimate of these differences calculated under the assumption that they are homogeneous.

The estimated capture probabilities per period and their standard errors.

The estimated survival probabilities between periods and their standard errors.

The estimated population sizes per period and their standard errors.

The estimated number of new arrivals in the population between periods and their standard errors.

The estimated total number of units who ever inhabited the survey area and its standard error.

The 'glm' object obtained from fitting the loglinear model

The loglinear model parameters estimations and their standard errors, calculated by the `glm`

function.

The Ui statistics, useful for the survival probabilities calculation, and their standard errors

The Vi statistics, useful for the population sizes estimation, and their standard errors

The covariance matrix of all the demographic parameters estimates.

The position of the gamma parameters set to zero in the loglinear parameter vector.

The function `openp`

generates statistics to test the presence of a trap effect.

The `plot.openp`

function produces a scatterplot of the Pearson residuals of the model versus the frequencies of capture.

If the data matrix `X`

was obtained through the `periodhist`

function, the `dfreq`

argument must be set to TRUE.

Standard errors are calculated by linearization.

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 Daigle, G. (2004) Loglinear models for the robust design in mark-recapture experiments. *Biometrics*, **60**, 100--107.

```
# NOT RUN {
# duck data set
op.m1 <- openp(duck, dfreq = TRUE)
plot(op.m1)
# To remove the capture history 111111.
keep2 <- apply(histpos.t(6), 1, sum) != 6
op.m2 <- openp(duck, dfreq = TRUE, keep = keep2)
op.m2
# To remove the capture histories with 5 captures or more
keep3 <- apply(histpos.t(6), 1, sum) < 5
op.m3 <- openp(duck, dfreq = TRUE, keep = keep3)
op.m3
# mvole data set aggregated per primary period
mvole.op <- periodhist(mvole, vt = rep(5, 6))
openp(mvole.op, dfreq = TRUE)
# }
```

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