# chandwich

## Chandler-Bate
Sandwich Loglikelihood Adjustment

### What does chandwich do?

The `chandwich`

package performs adjustments of an
independence loglikelihood using a robust sandwich estimator of the
parameter covariance matrix, based on the methodology in Chandler and Bate
(2007). This can be used for cluster correlated data when interest
lies in the parameters of the marginal distributions or for performing
inferences that are robust to certain types of model misspecification.
Functions for profiling the adjusted loglikelihoods are also provided,
as are functions for calculating and plotting confidence intervals, for
single model parameters, and confidence regions, for pairs of model
parameters. Nested models can be compared using an adjusted likelihood
ratio test.

### A simple example

The main function in the chandwich package is
`adjust_loglik`

. It finds the maximum likelihood estimate
(MLE) of model parameters based on an independence loglikelihood in
which cluster dependence in the data is ignored. The independence
loglikelihood is adjusted in a way that ensures that the Hessian of the
adjusted loglikelihood coincides with a robust sandwich estimate of the
parameter covariance at the MLE. Three adjustments are available: one in
which the independence loglikelihood itself is scaled (vertical scaling)
and two others where the scaling is in the parameter vector (horizontal
scaling).

The `rats`

data contain information about an experiment in
which, for each of 71 groups of rats, the total number of rats in the
group and the numbers of rats who develop a tumor is recorded. We model
these data using a binomial distribution, treating each group of rats as
a separate cluster. The argument `binom_loglik`

to
`adjust_loglik`

is a function that returns a vector of the
loglikelihood contributions from each group of rats. In one-dimensional
examples like this the two adjustments using horizontal scaling are
identical, but this will not generally hold in more than one
dimension.

```
binom_loglik <- function(prob, data) {
if (prob < 0 || prob > 1) {
return(-Inf)
}
return(dbinom(data[, "y"], data[, "n"], prob, log = TRUE))
}
rat_res <- adjust_loglik(loglik = binom_loglik, data = rats)
plot(rat_res, type = 1:4, legend_pos = "bottom", lwd = 2, col = 1:4)
```

### Installation

To get the current released version from CRAN:

`install.packages("chandwich")`

### Vignette

See
`vignette("chandwich-vignette", package = "chandwich")`

for
an overview of the package.