How many cases are required for each variable in order to build a linear regression model and/or a Multivariate Regression Splines Model?
Also,
- Is it a rule of thumb, or does there exist a statistical justification?
- Any bibliographical references?
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$\begingroup$ You may wish to check out this similar question on CV: stats.stackexchange.com/questions/10079/… $\endgroup$– gung - Reinstate MonicaCommented Nov 28, 2011 at 1:53
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$\begingroup$ I added a tag for splines, in case anyone wants to list rules of thumb for them. $\endgroup$– gung - Reinstate MonicaCommented Nov 30, 2011 at 18:57
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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.
answered Nov 30, 2011 at 18:55
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$\begingroup$ +1 The second paragraph is great advice. In principle, all you need is one more observation than you have parameters (including the constant). That extra observation is needed to estimate the error variance and to obtain standard errors for the parameter estimates. Those SEs may be large, but whether that's a problem depends on the objectives of the analysis. $\endgroup$– whuber ♦Commented Nov 30, 2011 at 20:04