# scoring: Maximum-Likelihood Estimation In geonet: Intensity Estimation on Geometric Networks with Penalized Splines

 scoring R Documentation

## 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.