deltamethod {emdbook}R Documentation

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
params list or named 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, 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)

[Package emdbook version 1.1.1.1 Index]