- having a dependent variable $Y$ that is a proportion (i.e., the proportion of observations made at the given time point that satisfy a condition, where each time point involves 50 to 250 observations)
- $Y$ is measured at a series of time time points $X$, where $X = 1, 2, 3, ...$, typically to around 400.
- At initial time points, $Y$ typically equals zero or close to zero
- After an extended period of time $Y$ typically equals one or close to one
- At some point in between a transition occurs where values of $Y$ increase
- Throughout there is considerable time point to time point variability and given that Y is a proportion, the distribution of errors is not normal. Note also that the values of zero and one are common.
Properties of the data vary across studies, such as:
- the initial value of $Y$
- the time point when the value of $Y$ starts to increase
- the duration of transition from values mainly around 0 to mainly around 1
- What would be a good modelling approach to such data?
- How could the onset of the transition from values close to zero to values close to one be detected, especially given the non-normal errors?