Struct Log 

pub struct Log {}

The log link $g(\mu) = \log(\mu)$ avoids linear predictors that give negative expectations.

Trait Implementations

impl Link<Exponential<Log>> for Log

fn func<F: Float>(y: F) -> F

Maps the expectation value of the response variable to the linear predictor. In general this is determined by a composition of the inverse natural parameter transformation and the canonical link function.

fn func_inv<F: Float>(lin_pred: F) -> F

Maps the linear predictor to the expectation value of the response.

impl Transform for Log

fn nat_param<F: Float>(lin_pred: Array1<F>) -> Array1<F>

The natural parameter of the response distribution as a function of the linear predictor: $\eta(\omega) = g_0(g^{-1}(\omega))$ where $g_0$ is the canonical link. For canonical links this is the identity.

fn d_nat_param<F: Float>(lin_pred: &Array1<F>) -> Array1<F>

The derivative $\eta'(\omega)$ of the transformation to the natural parameter. If it is zero in a region that the IRLS is in, the algorithm may have difficulty converging. It is given in terms of the link and variance functions as $\eta'(\omega_i) = \frac{1}{g'(\mu_i) V(\mu_i)}$.

fn adjust_errors<F: Float>(errors: Array1<F>, lin_pred: &Array1<F>) -> Array1<F>

Adjust the error/residual terms of the likelihood function based on the first derivative of the transformation. The linear predictor must be un-transformed, i.e. it must be X*beta without the transformation applied.

fn adjust_variance<F: Float>( variance: Array1<F>, lin_pred: &Array1<F>, ) -> Array1<F>

Adjust the variance terms of the likelihood function based on the first and second derivatives of the transformation. The linear predictor must be un-transformed, i.e. it must be X*beta without the transformation applied.

fn adjust_errors_variance<F: Float>( errors: Array1<F>, variance: Array1<F>, lin_pred: &Array1<F>, ) -> (Array1<F>, Array1<F>)

Adjust the error and variance terms of the likelihood function based on the first and second derivatives of the transformation. The adjustment is performed simultaneously. The linear predictor must be un-transformed, i.e. it must be X*beta without the transformation applied.