Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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`object` |
Object to be analysed.
Either a fitted point process model (object of class |

`fun` |
Summary function to be applied to each point pattern. |

`r` |
Optional.
Vector of values of the argument |

`breaks` |
Optional alternative to |

`...` |
Ignored. |

`model` |
Optional. A fitted point process model (object of
class |

`trend,interaction,rbord` |
Optional. Arguments passed to |

`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` |
Optional. List of parameters passed to |

`funargs` |
List of additional arguments to be passed to |

`verbose` |
Logical value determining whether to print progress reports during the computation. |

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**.

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`

.

and Jesper Moller.

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

Alternative functions:
`Kres`

,
`Gres`

.

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