scoring: Maximum-Likelihood Estimation

In geonet: Intensity Estimation on Geometric Networks with Penalized Splines

Maximum-Likelihood Estimation

Description

Scoring algorithm for maximum-likelihood estimation of a penalized Poisson model while treating the smoothing parameters as fixed. Since the model matrix Z when fitting a point process model on a geometric network is very large with usually several millions of entries, scoring builds an sparse representations of matrices in R.

Usage

scoring(theta, rho, data, Z, K, ind, eps_theta = 1e-05)

score(theta, rho, data, Z, K, ind)

fisher(theta, rho, data, Z, K, ind)

Arguments

theta	An initial vector of model coefficients.
rho	The current vector of smoothing parameters. For each smooth term, including the baseline intensity of the network, one smoothing parameter must be supplied.
data	A data frame containing the data.
Z	The (sparse) model matrix where the number of column must correspond to the length of the vector of model coefficients theta.
K	A (sparse) square penalty matrix of with the same dimension as theta.
ind	A list which contains the indices belonging to each smooth term and the linear terms.
eps_theta	The termination condition. If the relative change of the norm of the model parameters is less than eps_theta, the scoring algorithm terminates and returns the current vector of model parameters.

Details

scoring performs the scoring algorithm for maximum-likelihood estimation according to Fahrmeir et al. (2013). This algorithm is based on the score-function and the Fisher-information of the log-likelihood. score returns the score-function (the gradient of the log-likelihood) and fisher returns the Fisher-information (negative Hessian of the log-likelihood).

Value

The maximum likelihood estimate for fixed smoothing parameters.

References

Fahrmeir, L., Kneib, T., Lang, S. and Marx, B. (2013). Regression. Springer.

geonet documentation built on July 11, 2022, 9:08 a.m.