The structure of my data is causing me some trouble because I'd prefer to aggregate it but I'm not sure of the implications.
It's from an experiment comparing dwell time. The subjects were randomly assigned to one of two habitats. The habitats are identical except for an area that has been modified with characteristics that mimic (possibly) preferred habitats.
There are numerous subjects but we measure how much time each spends in the modified area each day.
There is evidence that differing amounts of sunlight affect habitat utilization and since we can't control the weather, we record whether each day is cloudy or sunny. We have gathered data on twenty-one consecutive days.
I would like to estimate the habitat effect on the difference in dwell times using a simple linear model such as:
$$ E(y \mid \mathbf{x}) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1 x_2 $$
where $x_1$ is the habitat indicator, $x_2$ is the sunny/cloudy indicator, and we consider the possibility that the habitat difference can be modulated by the weather by estimating the habitat and weather interaction: $x_1x_2$.
Obviously this completely ignores the sequential and grouped nature of the data since we measure each subject multiple times.
In order to assume independence of the error term, I think I would need something like
$$ E(y \mid \mathbf{x}) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1 x_2 + \beta_4 x_3 + \beta_5 x_5 $$
where $x_1$ and $x_2$ are as above, but $x_3$ is a subject-level fixed effect, and $x_5$ is something like a subject-level AR(1) term to account for within subject autocorrelation.
So my question is this: what is the hazard in aggregating the data so that each subject's outcome is the sum of time spent in the modified area on sunny days and cloudy days? If I simply add up each subject's time, I can estimate my first model without worrying about the autocorrelation or the individual fixed effects, right?
