Categorical Data Analysis Using The SAS® System, 2nd Edition

Appendix B: Theory for Exact Conditional Inference

Section 10.5 provides a brief overview of the methodological ideas behind conditional asymptotic inference. For the model

you partition the s + t vector β into components β₀, an s × 1 vector of stratum-specific intercepts, and β₁, a t × 1 vector of parameters of interest. For this discussion, consider β₀ to include the stratum-specific intercepts and/or any other nuisance parameters, that is, parameters that correspond to explanatory variables beyond the ones of interest. Consider β₁ to be a vector of parameters of interest. Partition X into a corresponding X₀ and X₁.

The sufficient statistics ...