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# Re: st: deriving the BIC when the vce(robust) option is used

 From mario fiorini To statalist@hsphsun2.harvard.edu Subject Re: st: deriving the BIC when the vce(robust) option is used Date Fri, 30 Nov 2012 10:16:03 +1100

```thanks Maarten.
Still I am not sure I get it 100%. In Stata the BIC is computed
according to BIC = -2*ln(likelihood) + ln(N)*k
and Stata uses
- e(ll) for the likelihood
- e(V) for k
- e(N) for N

Now, e(ll) is the same irrespectively of whether I use vce(robust) or
not. The same is true for e(N). The only difference is e(V).
I still don't understand why Stata reports a different e(V) and most
importantly, a different e(df_m) depending on whether vce(robust) is
used.

In my example I mentioned the problem of having a variable that is
nonzero for only 1 observation in the estimation sample. Note that, if
this does not happen, e(V), e(df_m) and the BIC are the same
irrespectively of whether I use vce(robust) or not. So while I take
your argument, I think it is unclear why the dummy case impacts the
reported e(df_m) and the BIC.
In any case, Stata output should explain what you just mentioned about
the pseudo-likelihood. I don't think that's so obvious.
thanks for taking the time to reply,

Mario

On 30 November 2012 01:27, Maarten Buis <maartenlbuis@gmail.com> wrote:
> On Wed, Nov 28, 2012 at 11:10 PM, mario fiorini wrote:
>> using Stata 11.2, I was trying to derive the Bayesian Information
>> Criterion (BIC) after a regression with the vce(robust) option, and
>> noted that the BIC is computed uisng the rank of e(V).
>
> Your main problem is not determining the number coefficients used but
> recovering the likelihood. As soon as you specified the -vce(robust)-
> option you no longer got the likelihood but the pseudo-likelihood.
> Information criteria work with distributions while quasi-likelihood
> deliberately avoids those, as a consequence the two are not
> compatible. So you need to choose between robust standard errors or an
> information criterion; you can't have both.
>
> Hope this helps,
> Maarten
>
> ---------------------------------
> Maarten L. Buis
> WZB
> Reichpietschufer 50
> 10785 Berlin
> Germany
>
> http://www.maartenbuis.nl
> ---------------------------------
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```