Possible alternative models for analysis
In the previous section, we described the random slopes model (Eqs. (One possible alternative is to use a model that has the same mean structure as in (1) but an unstructured covariance matrix:We refer to this as the “linear trajectories, free covariance” model. Since this is a marginal model, rather than one that is conditional on participant, there are now no random effects for intercept and slope. Instead, an unstructured covariance matrix is used to allow correlation between measurements taken on the same person. An unstructured covariance matrix allows these correlations to take any value, as opposed to restricting to the specific functional form implied by the random slopes model.A less restrictive model allows the mean trajectory in the control group to vary freely, while still requiring the treatment effect to be proportional to time:Another, even less restrictive, model allows the trajectories in each group to vary freely over time, but still constrains the expected value of the outcome at baseline to be the same in the two groups:Unlike the treatment effects in (1), (6) and (7), which all assume the treatment effect takes the form 