fit.cr: Capture-recapture estimation
In david-borchers/mt5751a: Functions for the first part of MT5751

Estimates abundance using capture-recapture methods. Five methods are implemented: M0, Mt, Mb, Mtb and Mh (see argument model.)

fit.cr(
  ch,
  model,
  alpha = 0.05,
  start.n0 = NULL,
  start.p = NULL,
  start.b = NULL,
  start.mu1 = NULL,
  start.mu2 = NULL,
  start.phi = NULL
)

`ch`	Binary capture history matrix, with rows being individuals and columns being occasions.
`model`	One of 'M0' Model with constant capture probability. 'Mt' Model with differewnt capture probability on each occasion. 'Mb' Model with behavioural response to capture that increases or decreases capture probability after first capture. 'Mtb' Model with differewnt capture probability on each occasion and behavioural response to capture that increases or decreases capture probability after first capture. 'Mh2' Model a finite 2-part mixture capture probability, i.e. 2 levels of latent capture probability.
`alpha`	The significance level for confidence intervals (defaults to `alpha`=0.05 for 95% level)
`start.n0`	Starting value for number of undetected animals for numerical optimisation of likelihood.
`start.p`	Starting value for detection probability for numerical optimisation of likelihood. For model Mt all probabilities are assumed to be the same to start with.
`start.b`	Starting value for the behavioural effect of capture. Positive means capture increases detection probability, negative decreases. (`start.b` is the multiplicative effect of previous capture on the ODDS of capture, i.e. on p/(1-p).)
`start.mu1`	Starting value for number of undetected animals for numerical optimisation of likelihood.
`start.mu2`	Starting value for the second latent capture probability in model Mh2.
`start.phi`	Starting value for the proportion of the population that has the first level of the latent capture probability.

The function returns a list with the following elements:

$model : Just reflects the model argument passed to the function.
$Nhat : Estimated abundance and 95% confidence interval.
$phat : Estimated detection probabilities and 95% confidence interval(s). NOTE: in the case of models Mb and Mtb, 'b(odds)' is given - this is the multiplicative effect of previous capture on the ODDS of capture, i.e. on p/(1-p).
$beta.point.ests: Point estimates of the model parameters (on the log scale in the case of abundance, and on the logit scale in the case of probabilities.).
$beta.varcovar.ests: The estimated variance-covariance matrix of the model parameters (on the log scale in the case of abundance, and on the logit scale in the case of probabilities.)
$$beta.corrmatrix: The estimated correlation matrix of the model parameters (on the log scale in the case of abundance, and on the logit scale in the case of probabilities.).
$nobs: Number of unique captures.
$loglik: The log-likelihood at the MLE.
$AIC: Akaike's information criterion for the model.