Summary. Discrete data, particularly count and contingency table data, are typically analyzed using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analyzed using third order procedures, with major improvements in accuracy and with intrinsic separation of information concerning parameter components. This paper extends these higher order results to discrete data, yielding a methodology that is widely applicable and accurate to second order. The extension can be described in terms of an approximating exponential model expressed in terms of a score variable. The development is outlined and the flexibility of the approach illustrated by examples. 1
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