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)Vignette
See vignette("chandwich-vignette", package = "chandwich") for an overview of the package.