hessian_from_formula: Automatic differentiation of formulae

In glmmrBase: Generalised Linear Mixed Models in R

Automatic differentiation of formulae

Description

Exposes the automatic differentiator. Allows for calculation of Jacobian and Hessian matrices of formulae in terms of specified parameters. Formula specification is as a string. Data items are automatically multiplied by a parameter unless enclosed in parentheses.

Usage

hessian_from_formula(form_, data_, colnames_, parameters_)

Arguments

form_	String. Formula to differentiate specified in terms of data items and parameters. Any string not identifying a function or a data item names in 'colnames' is assumed to be a parameter.
data_	Matrix. A matrix including the data. Rows represent observations. The number of columns should match the number of items in 'colnames_'
colnames_	Vector of strings. The names of the columns of 'data_', used to match data named in the formula.
parameters_	Vector of doubles. The values of the parameters at which to calculate the derivatives. The parameters should be in the same order they appear in the formula.

Value

A list including the jacobian and hessian matrices.

Examples

# obtain the Jacobian and Hessian of the log-binomial model log-likelihood. 
# The model is of data from an intervention and control group
# with n1 and n0 participants, respectively, with y1 and y0 the number of events in each group. 
# The mean is exp(alpha) in the control 
# group and exp(alpha + beta) in the intervention group, so that beta is the log relative risk.
hessian_from_formula(
  form_ = "(y1)*(a+b)+((n1)-(y1))*log((1-exp(a+b)))+(y0)*a+((n0)-(y0))*log((1-exp(a)))",
  data_ = matrix(c(10,100,20,100), nrow = 1),
  colnames_ = c("y1","n1","y0","n0"),
  parameters_ = c(log(0.1),log(0.5)))

glmmrBase documentation built on April 3, 2025, 10:44 p.m.