deltamethod: Delta method functions

In bbolker/emdbook: Support Functions and Data for "Ecological Models and Data"

Delta method functions

Description

Delta-method implementations for Jensen's inequality and prediction uncertainty

Usage

deltamethod(fun, z, var = "x", params = NULL, max.order = 2)
deltavar(fun,meanval=NULL,vars,Sigma,verbose=FALSE)

Arguments

fun	Function of one (deltamethod) or more arguments, expressed in raw form (e.g. a*x/(b+x))
z	numeric vector of values
var	variable name
vars	list of variable names: needed if params does not have names, or if some of the values specified in params should be treated as constant
params	list or numeric vector of parameter values to substitute
meanval	possibly named vector of mean values of parameters
Sigma	numeric vector of variances or variance-covariance matrix
max.order	maximum order of delta method to compute
verbose	print details?

Details

deltamethod() is for computing delta-method approximations of the mean of a function of data; deltavar() is for estimating variances of a function based on the mean values and variance-covariance matrix of the parameters. If Sigma is a vector rather than a matrix, the parameters are assumed to be independently estimated.

Value

For deltavar(), a vector of predicted variances; for deltamethod() a vector containing the observed value of the function average, the function applied to the average, and a series of delta-method approximations

Author(s)

Ben Bolker

References

Lyons (1991), "A practical guide to data analysis for physical science students", Cambridge University Press

Examples

deltamethod(a*x/(b+x),runif(50),params=list(a=1,b=1),max.order=9)
deltavar(scale*gamma(1+1/shape),meanval=c(scale=0.8,shape=12),
   Sigma=matrix(c(0.015,0.125,0.125,8.97),nrow=2))
## more complex deltavar example
xvec = seq(-4,4,length=101)
x1 = xvec
x2 = xvec
v = matrix(0.2,nrow=3,ncol=3)
diag(v) = 1
m = c(b0=1,b1=1.5,b2=1)
v3  = deltavar(1/(1+exp(-(b0+b1*x1+b2*x2))),meanval=m,Sigma=v)
plot(xvec,v3)

bbolker/emdbook documentation built on July 4, 2023, 1:16 p.m.