Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 218 / 1 / c

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- Solution c

Solution

Add a sex-by-treatment interaction term:

logit (p_{i}) = β_{0} + β_{S} M_{i} + β_{T} T_{i} + β_{ST} M_{i} T_{i} .

In R the formula becomes prop ~ sex * treatment. There are four parameters for four cell probabilities, so this model is saturated and, provided the cell proportions lie strictly between zero and one, fits each observed proportion exactly. It therefore recovers all the stated order relations.

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