I am trying to develop the design for an observational study, but I am struggling with the number of observations that would allow us to estimate our model and generalize its results. As a dependent variable, we have a score of a psychological structure (varies between 1-100), and we have two families of predictors:
- Measurements of other psychological factors.
- Socio-economic controls.
We will probably be going to explore different specifications for the dependent variable (enter it as it is, enter it as a dummy variable for whether a person is placed among the highest 25 percentile of the distribution, etc.).
A popular thumb rule for deciding the required number of observations is the one-in-ten rule (or one of its variations), but it seems to better fit a classification problem, and even worse, oversimplistic. I came across this article, that presents a more scientific method, but it refers mainly to linear models with priors for the sizes of the expected coefficients.
Our main goal in this part of our research is to find which variables have the strongest predictive powers for $y$. We will have about ~50 predictors, and for most of them, we don't have any prior (there is no other article that correlated these measurements).
Is there any method to simulate the number of required observations under observational study, that does not require priors on the coefficients?