# fit.ns: Fitting a Neyman-Scott point process model In b-steve/nspp: Fitting point process models via the Palm likelihood

## Description

Estimates parameters for a Neyman-Scott point process by maximising the Palm likelihood. This approach was first proposed by Tanaka et al. (2008) for two-dimensional Thomas processes. Further generalisations were made by Stevenson, Borchers, and Fewster (in prep) and Jones-Todd (2017).

## Usage

 ```1 2 3``` ```fit.ns(points, lims, R, disp = "gaussian", child.dist = "pois", child.info = NULL, sibling.list = NULL, edge.correction = "pbc", start = NULL, bounds = NULL, trace = FALSE) ```

## Arguments

 `points` A matrix containing locations of observed points, where each row corresponds to a point and each column corresponds to a dimension. `lims` A matrix with two columns, corresponding to the upper and lower limits of each dimension, respectively. `R` Truncation distance for the difference process. `disp` A character string indicating the distribution of children around their parents. Use `"gaussian"` for multivariate normal dispersion with standard deviation `sigma`, or `"uniform"` for uniform dispersion within distance `tau` of the parent. `child.dist` The distribution of the number of children generated by a randomly selected parent. For a Poisson distribution, use `"pois"`; for a binomial distribution, use `"binomx"`, where `"x"` is replaced by the fixed value of the number of independent trials (e.g., `"binom5"` for a Binomial(5, p) distribution, and `"binom50"` for a Binomial(50, p) distribution); and `"twoplane"` for a child distribution appropriate for a two-plane aerial survey. `child.info` A list of further information that is required about the distribution for the number of children generated by parents. See ‘Details’. `sibling.list` An optional list that comprises (i) a component named `sibling.mat`, containing a matrix such that the jth entry in the ith row is `TRUE` if the ith and jth points are known siblings, `FALSE` if they are known nonsiblings, and `NA` if their sibling status is not known; (ii) alpha, providing the probability that a sibling is successfully identified as a sibling; and (iii) beta, providing the probability that a nonsibling is successfully identified as a nonsibling. `edge.correction` The method used for the correction of edge effects. Either `"pbc"` for periodic boundary conditions, or `"buffer"` for a buffer-zone correction. `start` A named vector of starting values for the model parameters. `bounds` A list with named components. Each component should be a vector of length two, giving the upper and lower bounds for the named parameter. `trace` Logical; if `TRUE`, parameter values are printed to the screen for each iteration of the optimisation procedure.

## Details

The parameter `D` is the density of parent points, which is always estimated. Possible additional parameters are

• `lambda`, the expected number of children generated per parent (when `child.dist = "pois"`).

• `p`, the proportion of the `x` possible children are generated (when `child.dist = "binomx"`).

• `kappa`, the average length of the surface phase of a diving cetacean (when `child.dist = "twoplane"`; see Stevenson, Borchers, and Fewster, in prep).

• `sigma`, the standard deviation of dispersion along each dimension (when `disp` = "gaussian").

• `tau`, the maximum distance a child can be from its parent (when `disp` = "uniform")

The `"child.info"` argument is required when `child.dist` is set to `"twoplane"`. It must be a list that comprises (i) a component named `w`, providing the halfwidth of the detection zone; (ii) a component named `b`, providing the halfwidth of the survey area; (iii) a component named `l`, providing the time lag between planes (in seconds); and (iv) a component named `tau`, providing the mean dive-cycle duration. See Stevenson, Borchers, and Fewster (in prep) for details.

## Value

An R6 reference class object. Extraction of the information held within is best handled by functions coef.nspp, confint.nspp, summary.nspp, and plot.nspp.

## References

Tanaka, U., Ogata, Y., and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott point processes. Biometrical Journal, 50: 43–57.

Stevenson, B. C., Borchers, D. L., and Fewster, R. M. (in prep) Trace-contrast methods to account for identification uncertainty on aerial surveys of cetacean populations.

Jones-Todd, C. M. (2017) Modelling complex dependencies inherent in spatial and spatio-temporal point pattern data. PhD thesis, University of St Andrews.

## Examples

 ```1 2 3 4 5 6``` ```## Fit model. fit <- fit.ns(example.2D, lims = rbind(c(0, 1), c(0, 1)), R = 0.5) ## Print estimates. coef(fit) ## Plot the estimated Palm intensity. plot(fit) ```

b-steve/nspp documentation built on June 4, 2017, 12:10 a.m.