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I am trying to fully understand where the conditional part of the term conditional logistic regression comes from. In particular, I can't seem to find a source in the literature that emphasizes that you are conditioning on some sort of sufficient statistic for the stratum parameters. Additionally, I can't seem to find a source that explains the intuition behind conditioning on such statistics.

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I think Conditional Logistic Regression part of Categorical Data Analysis by Alan Agresti will be helpful in this situation.

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