Update crossover
- include SUR
- Update vignette
A crossover design is a design in which the research exploits multiple observations on individuals across different outcomes and different treatments in order to improve power. The design assumes that (a) that different outcomes are correlated for individuals and (b) different outcomes are affected by different treatments. For example, suppose that a researcher wants to know the effect of watching public service announcements (PSAs) about recycling on environmental attitudes, on the one hand, and the effect of watching PSAs about washing hands on attitudes toward personal hygiene, on the other. For a crossover design one makes use of an assumption (a) that environmental attitudes and attitudes towards hygiene are correlated and (b) the recycling announcement does not affect hygiene attitudes and the washing hands announcement does not affect attitudes towards the environment. If (a) holds there can be efficiency gains from using a SUR estimator and if (b) holds these gains do not introduce risk of bias. See REFERENCE for further motivation.