emdbook (version 1.3.13)

deltamethod: 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)

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

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?

Author

Ben Bolker

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.

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)