ppSmooth: Generalized linear point process modeling using smoothing...
In ppstat: Point Process Statistics

Description Usage Arguments Details Value Note Author(s) See Also

The function ppSmooth fits a generalized linear point process model based on a B-spline basis expansion of smooth terms.

1 2	ppSmooth(formula, data, family, support = 1, knots = 'log', N = 200, Delta, lambda, coefficients, fit = TRUE, varMethod = 'Fisher', ...)

`formula`	an object of class `formula`. A symbolic description of the model to be fitted. Smooth terms are treated in a special way and other terms are treated as in `pointProcessModel`. See ‘Details’.
`data`	an object of class `MarkedPointProcess` containing the point process data as well as any continuous process data.
`family`	an object of class `Family`. Specification of the general model family containing the specification of the phi function, which links the linear predictor process to the predictable intensity process.
`support`	a `numeric` vector. Specifies the support of the filter functions as the interval from `support[1]` to `support[2]`. If `support` is of length 1 the support is the interval from 0 to `support[1]`. The default value is 1.
`knots`	a `character` or `numeric`. The number or value of knots to use. The default value, `'log'`, means that an algorithm similar to the one in `smoothing.spline` is used to adaptively select the number of knots. Other possible values are `'all'` (not recommended), an `integer` specifying the precise number of adaptive knots that are used, or a numeric vector of length 2 or more specifying the knots in a non-adaptive way.
`N`	a `numeric`. The number of basis function evaluations used in the support. Default value 200.
`Delta`	a `numeric`. Basis functions are evaluated at `Delta`-grid values in the support. If missing, `Delta` is set to the length of the support divided by `N`. If specified, overrides the use of `N`.
`lambda`	a `numeric`. The parameter that controls the amount of penalization.
`coefficients`	an optional specification of the initial parameters used for the numerical optimization.
`fit`	a `logical`. Specifies if the model is to be fitted. Default is `TRUE`.
`varMethod`	a `character`. Specifies the method used for estimation of the variance matrix of the parameter estimators. Currently the default value, `'Fisher'`, and `'none'` are implemented. Using `'Fisher'` a sandwich estimator based on the Fisher information is used, whereas `'none'` means that the variance matrix is not estimated.
`...`	additional parameters that are passed on to `ppmFit`.

ppSmooth preprocesses the formula and extracts the smooth terms before a PointProcessModel is created by a call to pointProcessModel. Terms of the form s(.) in the formula are treated as special terms. They are replaced by an automatic basis expansion in terms of B-splines, and the corresponding parameters are penalized using the standard integral of the square of the second derivative to ensure smoothness.

Though the basis expansion is in terms of B-splines, there is an internal reparametrization in terms of orthogonal basis components, which results in the smoothness penalty being the ordinary Euclidean norm times lambda.

The knots argument determines how many knots are used. The locations of the knots are determined by the quantiles for the distribution of interdistances between points from the response and points from the terms in the formula. Each term uses its own set of knots.

All the B-spline basis functions have support within the support interval and are 0 on the boundary. A constant and linear a function are added to the set of B-spline basis functions, whose coefficients are not penalized by default.

The sandwich estimator depends on the amount of penalization. If the fit is oversmoothed, and thus biased, the resulting confidence intervals on the filter functions are most likely misleading.

The function ppSmooth returns an object of class PointProcessSmooth, which is an extension of PointProcessModel.

The method does not yet support automatic data adaptive selection of lambda. An information quantity (which in this case is TIC) can be extracted using getInformation. This quantity can be minimized over at grid for selection of lambda.

Niels Richard Hansen Niels.R.Hansen@math.ku.dk.

PointProcessModel, pointProcessModel, ppKernel.

ppstat documentation built on May 2, 2019, 5:26 p.m.