st: Re: One regression or many. was: Re:

[Steve Samuels <sjsamuels@gmail.com>]

David Ashcraft:

I'm going to answer the best I can, considering that I find the question a bit vague.

You must have multiple observations per manager Likewise, if you are going to do a separate regression for each manager, the benchmarks must vary between decisions.

To answer your question--the two approaches will not, in general, give the same results. 

Good references are  at the end of the manual entry for -xtmixed-. For the separate regression approach, see an example Applied Longitudinal Data AnalysisModeling Change and Event Occurrence Judith D. Singer & John B. Willett Oxford, Press, 2003.

I don't think a single simple regression will work because of observations for each manager are correlated. My choice would be a mixed model with random manager intercepts and, perhaps slopes, with belief and other predictors as fixed effects with possible interactions. . As decisions must take place over calendar time, you would control for that and, perhaps, add an auto-correlation error term. -xtmixed- can accommodate clustering of managers, by location, for example.  You can loosen the dependence on the Gaussian assumption by bootstrapping.

The separate regression approach is attractive because it is easy to show. But if other predictors are relevant it becomes complicated.  If there are different amounts of information per manager, weighting would be necessary, but this in turn leads back to a mixed model.



On Nov 30, 2011, at 10:04 PM, David Ashcraft wrote:

Steve,

Can you please explain a little further. Let me rephrase the question initially asked. Whether coefficients obtained after running regression on all managers (full dataset) are same as the average coefficients obtained from running regressions on individual mangers. I don't know a paper that has done analysis on this pattern, and would like to know, if there exist any analysis like that. My idea is, both method should reflect the similar results.    

David


----- Original Message -----
From: Steve Samuels <sjsamuels@gmail.com>
To: statalist@hsphsun2.harvard.edu
Cc: 
Sent: Thursday, December 1, 2011 1:39:29 AM
Subject: Re: st: Re:



Yuval, 

I don't have access to your article, but I have an observation: The predictions (real and counterfactual) that are averaged are not independent, because they are all functions of the estimated regression coefficients. I don't think a t-test accommodate the non-independence. In Stata, I would use -margins- or -lincom- after -margins-.

Steve



On Nov 26, 2011, at 9:09 AM, Yuval Arbel wrote:

David,

You can simply use Difference in Difference (DD) analysis:

Run a regression on the group of managers who take the first (second)
approach. Then predict what would have happened to the performance of
each manager in the case that he/she takes the other approach and use
the -ttest- to see whether the difference is significant.

Note to define dummy variables in any case that variables are ordinal,
i.e., the numerical values have no quantitative meaning

I use this approach quite often. You can look at the second part of my
following paper published in RSUE:

Arbel, Yuval; Ben Shahar,Danny; Gabriel, Stuart  and Yossef Tobol:
"The Local Cost of Terror: Effects of the Second Palestinian Intifada
on Jerusalem House Prices".Regional Science and Urban Economics (2010)
40:  415-426

On Sat, Nov 26, 2011 at 12:11 PM, David Ashcraft
<ashcraftd@rocketmail.com> wrote:
> Hi Statalist,
> 
> This is more like an econometric than a Stata question. I am little lost on the following scenario:
> 
> The situation is: I want to measure the performance of managers, who has a specific approach against those who do not. I have several individual managers in each category. One way is to regress the performance of these managers against their benchmark for the whole data using
> -regress manager benchmark, by(belief)
> The second option is to run individual regression on each manager and get the coefficients of individual regressions and run a ttest alpha, by(belief) .
> 
> 
> Now the question is, how different is the result from the ttest of alpha from that of the alpha of the regression equation.
> Any help will be really appreciated.
> 
> If anyone can suggest an academic paper on similar scenarios, that would be a great help.
> 
> 
> David
> 
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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street, Haifa, Israel
e-mail: yuval.arbel@gmail.com

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