ppKernel: Generalized linear point process modeling using reproducing...

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

View source: R/PointProcessKernel.R

Description

The function ppKernel fits a generalized linear point process model based on expansions of smooth terms in a reproducing kernel Hilbert space.

Usage

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ppKernel(formula, data, family, support = 1, N = 200, Delta, lambda, 
coefficients, modelMatrix = TRUE, fit = modelMatrix, varMethod = 'Fisher', 
kernel = sobolevKernel, specThres = 1e-8, ...)

Arguments

formula

an object of class formula. A symbolic description of the model to be fitted. Kernel 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.

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 parameters.

modelMatrix

a logical. Specifies if the model and kernel matrices are to be computed. Default is TRUE.

fit

a logical. Specifies if the model is to be fitted. Default value is that the model is only fitted if the model matrix is computed. If the formula does not have a response variable the model is not fitted - disregarding the value of fit.

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.

kernel

a function. The reproducing kernel. Default value is the sobolevKernel, which is the reproducing kernel for the (2, 2) Sobolev space. Any vectorized function that computes a positive definite matrix on a grid (and take one additional parameter, see details) is allowed.

specThres

a numeric. Determines the incompleteness of the factorization of the Gram matrix. A value of 0 means using the complete factorization. An incomplete factorization is obtained for positive values. Default value is 1e-8.

...

additional parameters that are passed on to ppmFit.

Details

ppKernel preprocesses the formula, and all terms of the form k(.) are treated specially as kernel terms when a PointProcessKernel is created. Other terms are treated as in a direct call of pointProcessModel. The kernel terms are penalized by the norm in the reproducing kernel Hilbert space given by the kernel.

Using the default kernel, the sobolevKernel, the resulting fit is almost identical to that obtained by ppSmooth. The gaussianKernel is available as an alternative. All kernels are called with an additional argument t = support[2], which for the two kernels mentioned rescales the support to [0,1]. Hence a kernel should allow for such an argument even if it is ignored.

The kernel enters only through a Gram matrix computation on an N by N grid, which is then factorized. The current factorization is via the spectral decomposition, and for computational efficiency an incomplete factorization is used. The specThres argument is the threshold for the smallest eigenvalue used relative to the largest eigenvalue.

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 ppKernel generally requires less memory than ppSmooth but gradient computations and thus the estimation can be slower.

Value

An object of class PointProcessKernel, which is an extension of the PointProcessModel class.

Note

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.

The current implementation is entirely in R. Certain precomputations in ppSmooth are implemented much more efficiently in compiled code. In future versions the corresponding precomputations for ppKernel will be transferred to compiled code.

Author(s)

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

See Also

PointProcessKernel, pointProcessModel, ppSmooth.


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