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.
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)
The maximum likelihood estimate for fixed smoothing parameters.
An initial vector of model coefficients.
The current vector of smoothing parameters. For each smooth term, including the baseline intensity of the network, one smoothing parameter must be supplied.
A data frame containing the data.
The (sparse) model matrix where the number of column must
correspond to the length of the vector of model coefficients theta.
A (sparse) square penalty matrix of with the same dimension as
theta.
A list which contains the indices belonging to each smooth term and the linear terms.
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.
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).
Fahrmeir, L., Kneib, T., Lang, S. and Marx, B. (2013). Regression. Springer.