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# Re: st: A reference for "how many independent variables one regression can have?"

 From Richard Williams To statalist@hsphsun2.harvard.edu, Subject Re: st: A reference for "how many independent variables one regression can have?" Date Fri, 13 Dec 2013 12:10:11 -0500

```A few comments:

```
* Long and Freese lay out some sample size suggestions for Maximum Likelihood Methods (e.g. logit) on p. 77 of
```
http://www.stata.com/bookstore/regression-models-categorical-dependent-variables/

```
I summarize their recommendations on pp. 3-4 of http://www3.nd.edu/~rwilliam/xsoc73994/L02.pdf .
```
* This paper claims that 10 may be more than you need:

http://aje.oxfordjournals.org/content/165/6/710.full.pdf

```
* I would say 10 cases per parameter rather than 10 cases per observation. With something like an mlogit model, you might estimate, say, 3 parameters for every independent variable.
```
```
* Like Richard Goldstein suggests, you may need a minimum number of cases. Long and Freese say you need at least 100 cases for a ML analysis. On the other hand, for something like a T test and the regression model equivalents of it, you can get by with some absurdly small number of cases if assumptions of normality are met. (Interesting tidbit: Counter to common practice, Long and Freese say you need to use more stringent p values when N is small, since the small sample properties of ML significance tests are not known).
```
```
* As a practical matter, I suspect you usually need much more than 10 cases per parameter if you want to get statistically significant results.
```
At 10:50 AM 12/13/2013, Ariel Linden wrote:
```
```Hi All,

I came across a statement in a book I am using to teach a class on
evaluation that says "a common rule of thumb is that 1 independent variable
can be added for every 10 observations." (it goes on to say that this
depends on multicollinearity and desired level of precision). The book does
not provide a reference for this statement.

Does someone know of a reference for this ratio, or perhaps a different
ratio?

Thanks!

Ariel

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