# info.mvloglin: Expected Information Matrix for a Multivariate Log-Linear... In asypow: Calculate Power Utilizing Asymptotic Likelihood Ratio Methods

## Description

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

 `1` ``` info.mvloglin(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.

`info.mvlogistic`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# Find the information matrix for a multivariate # log-linear design with variables x, y and z # Define coefficient matrix so that # u = .1 + .2*x + .3*y + .3*z coef <- c(.1, .2, .3, .4) # Define the design matrix so that there are 10 design points intercept <- rep(1, 10) x <- seq(.1, .2, length=10) y <- seq(.25, .3, length=10) z <- seq(.2, .3, length=10) design <- cbind(intercept, x, y, z) # Use info.mvloglin to find the information matrix for # this design info.xyz <- info.mvloglin(coef, design) print(info.xyz) ```

### Example output

```          intercept          x          y          z
intercept 4.7237667 0.34641982 0.43039106 0.29130408
x         0.3464198 0.02659991 0.03196129 0.02196045
y         0.4303911 0.03196129 0.03934650 0.02674042
z         0.2913041 0.02196045 0.02674042 0.01826283
```

asypow documentation built on May 2, 2019, 2:37 a.m.