Efficient Monte Carlo methods for conditional logistic regression

Exact inference for the logistic regression model is based on generating th e permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the rem aining (nuisance) parameters. Despite the availability of fast numerical al gorithms for the exact computations, there are numerous instances where a d ata set is too large to be analyzed by the exact methods, yet too sparse or unbalanced for the maximum likelihood approach to be reliable. What is nee ded is a Monte Carlo alternative to the exact conditional approach which ca n bridge the gap between the exact and asymptotic methods of inference. The problem is technically hard because conventional Monte Carlo methods lead to massive rejection of samples that do not satisfy the linear integer cons traints of the conditional distribution. We propose a network sampling appr oach to the Monte Carlo problem that eliminates rejection entirely. Its adv antages over alternative saddlepoint and Markov Chain Monte Carlo approache s are also discussed.