info.mvlogistic: Expected Information Matrix for a Multivariate Logistic Model

Description

Calculates the expected information matrix for a multivariate logistic model where the parameter $p$, probability of an event, depends on the covariates, $x = c(x[1], x[2], \dots, x[n])$, through a logistic, $p = exp(u)/(1+exp(u))$, model. The variable $u$ is a linear combination of the covariates via a set of coefficients, $coef = c(coef[1], coef[2], \dots, coef[n])$, $u = Sum (coef[i] * x[i]) i = 1, \dots ,n$.

The usual use of this routine is for tabulated data in which case the x's will all be 0 or 1 valued indicator variables.

Usage

info.mvlogistic(coef, design, rss=1)

Arguments

coef

Vector of length p (number of covariates) giving coefficients of variables.

design

Matrix of dimension $(n X p)$ each row of which gives values of covariates at one of the n design points.

Note: Most models will include a constant term and the column of design corresponding to this term will be identically 1.

rss

The relative sample size at each design point. The default is the same sample size at each design point. If changed from the default, rss should be a vector of length n.

Value

The information matrix for one observation for this design.

References

Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics Chapman and Hall, London.

Examples

Run this code

# Find the information matrix for a multivariate
# logistic design with variables x, y and z
#    Define coefficient matrix so that 
#    u = 1 + .5*x + .7*y + .9*z
coef <- c(1, .5, .7, .9)
#    Define the design matrix so that there are 10 design points
intercept <- rep(1, 10)
x <- rnorm(10)
y <- rnorm(10)
z <- rnorm(10)
design <- cbind(intercept, x, y, z)
#    Use info.mvlogistic to find the information matrix for
#    this design
info.xyz <- info.mvlogistic(coef, design)
print(info.xyz)