R: Pseudoscore Diagnostic For Fitted Model against General...

psst {spatstat.core} | R Documentation

## Pseudoscore Diagnostic For Fitted Model against General Alternative

### Description

Given a point process model fitted to a point pattern dataset, and any choice of functional summary statistic, this function computes the pseudoscore test statistic of goodness-of-fit for the model.

### Usage

    psst(object, fun, r = NULL, breaks = NULL, ...,
         model=NULL,
         trend = ~1, interaction = Poisson(), rbord = reach(interaction),
         truecoef=NULL, hi.res=NULL, funargs = list(correction="best"),
         verbose=TRUE)

### Arguments

`object` | Object to be analysed. Either a fitted point process model (object of class `"ppm"`) or a point pattern (object of class `"ppp"`) or quadrature scheme (object of class `"quad"`).
`fun` | Summary function to be applied to each point pattern.
`r` | Optional. Vector of values of the argument r at which the function S(r) should be computed. This argument is usually not specified. There is a sensible default.
`breaks` | Optional alternative to `r` for advanced use.
`...` | Ignored.
`model` | Optional. A fitted point process model (object of class `"ppm"`) to be re-fitted to the data using `update.ppm`, if `object` is a point pattern. Overrides the arguments `trend,interaction,rbord`.
`trend,interaction,rbord` | Optional. Arguments passed to `ppm` to fit a point process model to the data, if `object` is a point pattern. See `ppm` for details.
`truecoef` | Optional. Numeric vector. If present, this will be treated as if it were the true coefficient vector of the point process model, in calculating the diagnostic. Incompatible with `hi.res`.
`hi.res` | Optional. List of parameters passed to `quadscheme`. If this argument is present, the model will be re-fitted at high resolution as specified by these parameters. The coefficients of the resulting fitted model will be taken as the true coefficients. Then the diagnostic will be computed for the default quadrature scheme, but using the high resolution coefficients.
`funargs` | List of additional arguments to be passed to `fun`.
`verbose` | Logical value determining whether to print progress reports during the computation.

### Details

Let x be a point pattern dataset consisting of points x[1],...,x[n] in a window W. Consider a point process model fitted to x, with conditional intensity lambda(u,x) at location u. For the purpose of testing goodness-of-fit, we regard the fitted model as the null hypothesis. Given a functional summary statistic S, consider a family of alternative models obtained by exponential tilting of the null model by S. The pseudoscore for the null model is

V(r) = sum( Delta S(x[i], x, r)) - integral( Delta S(u,x, r) lambda(u,x) du)

where the Delta operator is

Delta S(u,x, r) = S(x union u, r) - S(x setminus u, r)

the difference between the values of S for the point pattern with and without the point u.

According to the Georgii-Nguyen-Zessin formula, V(r) should have mean zero if the model is correct (ignoring the fact that the parameters of the model have been estimated). Hence V(r) can be used as a diagnostic for goodness-of-fit.

This algorithm computes V(r) by direct evaluation of the sum and integral. It is computationally intensive, but it is available for any summary statistic S(r).

The diagnostic V(r) is also called the pseudoresidual of S. On the right hand side of the equation for V(r) given above, the sum over points of x is called the pseudosum and the integral is called the pseudocompensator.

### Value

A function value table (object of class `"fv"`), essentially a data frame of function values.

Columns in this data frame include `dat` for the pseudosum, `com` for the compensator and `res` for the pseudoresidual.

There is a plot method for this class. See `fv.object`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Ege Rubak rubak@math.aau.dk and Jesper Moller.

### References

Baddeley, A., Rubak, E. and Moller, J. (2011) Score, pseudo-score and residual diagnostics for spatial point process models. Statistical Science 26, 613–646.

### See Also

Special cases: `psstA`, `psstG`.

Alternative functions: `Kres`, `Gres`.

### Examples

        if(live <- interactive()) {
          fit0 <- ppm(cells ~ 1)
        } else {
          fit0 <- ppm(cells ~ 1, nd=8)
        }
        G0 <- psst(fit0, Gest)
        G0
        if(live) plot(G0)

[Package spatstat.core version 2.4-4 Index]