R: Transform derivatives wrt mu to derivatives wrt linear...

gamlss.etamu {mgcv} | R Documentation

## Transform derivatives wrt mu to derivatives wrt linear predictor

### Description

Mainly intended for internal use in specifying location scale models. Let `g(mu) = lp`, where `lp` is the linear predictor, and `g` is the link function. Assume that we have calculated the derivatives of the log-likelihood wrt `mu`. This function uses the chain rule to calculate the derivatives of the log-likelihood wrt `lp`. See `trind.generator` for array packing conventions.

### Usage

    gamlss.etamu(l1, l2, l3 = NULL, l4 = NULL, ig1, g2, g3 = NULL,
      g4 = NULL, i2, i3 = NULL, i4 = NULL, deriv = 0)

### Arguments

`l1` | array of 1st order derivatives of log-likelihood wrt mu.
`l2` | array of 2nd order derivatives of log-likelihood wrt mu.
`l3` | array of 3rd order derivatives of log-likelihood wrt mu.
`l4` | array of 4th order derivatives of log-likelihood wrt mu.
`ig1` | reciprocal of the first derivative of the link function wrt the linear predictor.
`g2` | array containing the 2nd order derivative of the link function wrt the linear predictor.
`g3` | array containing the 3rd order derivative of the link function wrt the linear predictor.
`g4` | array containing the 4th order derivative of the link function wrt the linear predictor.
`i2` | two-dimensional index array, such that `l2[,i2[i,j]]` contains the partial w.r.t. params indexed by i,j with no restriction on the index values (except that they are in 1,...,ncol(l1)).
`i3` | third-dimensional index array, such that `l3[,i3[i,j,k]]` contains the partial w.r.t. params indexed by i,j,k.
`i4` | third-dimensional index array, such that `l4[,i4[i,j,k,l]]` contains the partial w.r.t. params indexed by i,j,k,l.
`deriv` | if `deriv==0` only first and second order derivatives will be calculated. If `deriv==1` the function goes up to 3rd order, and if `deriv==2` it provides also 4th order derivatives.

### Value

A list where the arrays `l1`, `l2`, `l3`, `l4` contain the derivatives (up to order four) of the log-likelihood wrt the linear predictor.

### Author(s)

Simon N. Wood <simon.wood@r-project.org>.

### See Also

`trind.generator`

[Package mgcv version 1.8-17 Index]