Re: st: Adjustment to likehood value due to dependence of data observations

[Stas Kolenikov <skolenik@gmail.com>]

Abdul,

if your data are not i.i.d., then the likelihood coming out of GLM is
plain wrong, and should not be used as an input to the information
criteria calculations. There is no magic "correction", like divide
some term by an effective number of observations, or add some penalty,
or anything -- it just does not work that way. In more accurate
computations of the so-called extended BIC, you will see that
different parameters will contain different amount of information
(which makes sense: the time-invariant parameters have fewer degrees
of freedom associated with them, while time-varying parameters are
easier to estimate). This cannot be fixed in any obvious way, other
than calculating the more appropriate information criteria.

I guess -robust- option would make a lot of sense here. The general
theory of GEE states that the sandwich estimator should be OK provided
that the mean structure is specified correctly. (The answer to the
question of "why fixing the standard errors for a wrong model" is
exactly this fact of separability of the mean and variance components
in GEE models. This will not be true for other models, such as
classical multilevel models or covariance-based SEMs.) I would
strongly second Maarten's suggestion to play with -corr- option of
-xtgee- and entertain several lags of AR and stationary structures (if
your data allows for this); I would settle with the method that gives
you the largest (the most conservative) standard errors. Writing a
do-file with several options, -estimates save-ing the results and
-estimates tab-bing them afterwards may likely give you the results
faster than waiting for the perfect advice to emerge from statalist
(which may never happen, in the end).

On Thu, Sep 22, 2011 at 9:10 AM, Abdul Q Memon <a.memon@ucl.ac.uk> wrote:
> Dear All
>
> I would really appreciate your reply on this.
>
> I have run several models using glm (possion and negative binomial)
> command in STATA. Based on the log-likelihood and BIC values I have
> selected the most appropriate models (with smallest BIC values). After
> this I have run GEE with AR1 structure for only the preferred model to
> account for serial correlation in data. I have these two questions.
>
> 1. Since my model seclection is based on (log-likelihood and BIC values)
> and in this case data is not independent (time series and panel data), is
> there a way in stata to adjust the likelihood after running glm command if
> the data is not independent.
>
> 2. After running gee command still there is some trend in residuals. Do i
> need to run robust command to adjust standard errors after gee?? my
> understanding is robust command is for corrections to standard error after
> OLS.
>
> Many thanks
>
> Memon
>
>
>
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-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
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