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

 From "Ariel Linden" To Subject Re: Re: st: A reference for "how many independent variables one regression can have?" Date Sat, 14 Dec 2013 14:46:11 -0500

```I want to thank Richard Goldstein, Marta Garcia-Granero, and Richard
Williams for their very helpful responses to my posting!

Ariel

Date: Fri, 13 Dec 2013 12:10:11 -0500
From: Richard Williams <richardwilliams.ndu@gmail.com>
Subject: Re: st: A reference for "how many independent variables one
regression can have?"

* 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-varia
bles/

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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```