asypow (version 2012.04-1)

info.reparam: Reparameterize Expected Information Matrix

Description

Calculates the expected information matrix after reparameterization of a model using the method of propagation of error.

Usage

info.reparam(theta, info.mat, dg)

Arguments

theta

Matrix of parameters of the linear part of the model. Each row represents a group. This is under the original parameterization.

info.mat

The information matrix under the original parameterization.

dg

A function that computes the partial derivatives of g, the transformation function. Let g.i be the function which transforms the vector of old parameters, theta, into the i'th element of the new parameters. The function dg should take

Value

• Returns the expected information matrix under the new parameterization.

concept

information

References

Bishop, Y.M., Fienberg, S.E., and Holland, P.W. (1975) Discrete Multivariate analysis: Theory and Practice MIT Press, Cambridge, Mass. Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics Chapman and Hall, London. Tong, Y.L. (1990). The Multivariate Normal Distribution Springer-Verlag, New York.

Examples

# A logistic model posits that the probability of response
# is a logtistic function of a + b*x.
# Consider the value of x that produces 50\%
# response, x = -a/b. Since -a/b is not one of the parameters
# of the model, we must reparameterize to
# roe[1] = -a/b
# roe[2] = b
dg <- function(theta) {
# theta is a vector of length 2 containing c(a,b)
# dg <- [d{roe[1]}/d{a} d{roe[1]}/d{b}
#        d{roe[2]}/d{a} d{roe[2]}/d{b}]
  a <- theta[1]
  b <- theta[2]
  return(matrix(c(-1/b,a/b^2,0,1), nrow=2, ncol=2, byrow=TRUE))
}
# Let a = -0.9 and b = .7
theta <- c(-.9, .7)
# assign a set of covariate values
covar <- c(0.3, .9, 1.3, 2.5)
# Use info.binomial.design to calculate the information
# matrix under the original parameterization
info.orig <- info.binomial.design(model="linear", link="logistic", 
                                  theta=theta, xpoints=covar)
# Get the information matrix of the reparameterized model
info.new <- info.reparam(theta, info.orig, dg)
print(info.new)