How many cases are required for each variable in order to build a linear regression model and/or a Multivariate Regression Splines Model?
- Is it a rule of thumb, or does there exist a statistical justification?
- Any bibliographical references?
I've often heard of 10 cases per variable as a rule of thumb. It is not clear if this is to mean that you start at 10 cases with 1 covariate, or 20 cases (since you also loose a degree of freedom due to the intercept). I scanned the indexes to a few of my old stats books, and didn't find any reference to a place where this was discussed (although it could be in there somewhere, just not indexed in a way that I could find it). I also don't know of any references in the statical literature or any statistical justification for such a rule of thumb.
Moreover, I don't see how there could be and I think such rules of thumb are worthless. The minimum number of cases is contingent on many things, e.g., cost of collecting data, and your goal (minimum for a test of significance?, minimum to achieve a specified level of precision in your parameter estimates?, minimum for the prediction of future cases with some level of accuracy? etc). Since no single number (such as 10 / covariate) could be optimal for all goals, at all costs of gathering more data and with all levels of resources available for doing so, I argue that there cannot be a statistical justification.
I don't know of any rules of thumb regarding splines, but I believe that the same arguments imply any such would be just as worthless.