Re: Re: st: about residuals and coefficients

[Yuval Arbel <yuval.arbel@gmail.com>]

For those of you who wish to read the insights of Kahneman, I attach a
link to his Auto-Bibliography description published in the Noble Prize
website.
What I'm referring to is particularly the section regarding his military service


http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2002/kahneman-bio.html

On Thu, Sep 5, 2013 at 10:54 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
> David,
>
> I see as part of our job to educate our students (and the general
> public) - how to interpret correctly statistical information (with
> some caution). There are many common mistaken beliefs in the general
> public regarding statistical information, which leads to wrong
> conclusions.
>
> A famous example that comes to my mind (from a book written by the
> mathematician Haim Shapira) - is a statement made in the O.J. Simpson
> trial ("among all persons who hit their wives, only a fraction
> actually murdered them" - where the correct question should be -
> "among all the murdered women, what is the percentage of cases where
> the murderer was the hitting husband?")
>
> I treat statistical inference in the same way Winston ChurcilI treats
> Democracy (it is a bad system - but the best among all the existing
> alternatives). In my opinion - one should view regression analysis as
> a very rough approximation. Recall, that regression analysis "works"
> under very very long series of assumptions, where collinearity is only
> one problem. We did not start talking about functional form and model
> specification, simultaneity etc.
>
> Yet, from all the alternatives, when I make comparisons across groups
> - I'd rather make them by using projection of regression analysis,
> rather than simple descriptive statistics comparison.
>
> An interesting discussion in this context - is given by the noble
> prize winner Daniel Kahneman. He concludes - that projected values
> produced from a regression analysis - is better than intuitive
> prediction (according to the principle - "the prediction should be
> weaker than the information it is relied on")
>
> On Thu, Sep 5, 2013 at 8:48 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
>> Yuval,
>>
>> Part of your comment illustrates the practice that I am criticizing.
>> In general, regression analysis, desirable or actual, estimates the
>> effect of each predictor after adjusting for (not "controlling for")
>> the contributions of the other predictors.  One does not have equal
>> conditions or ceteris paribus unless the collection of the data was
>> designed to produce such structure.
>>
>> For sophisticated users of regression analysis, the distinction
>> between "adjusting for" and "controlling for" may be largely semantic.
>>  For less-sophisticated users or consumers of the results, language
>> such as "controlling for" gives the misleading impression that
>> something is being held constant.  For observational data, that is
>> usually an overstatement.
>>
>> Many patterns of correlation among predictors are not substantial
>> enough to qualify as "collinearity."
>>
>> I am not familiar with the example of repair expenditures on a Toyota
>> car, but the negative coefficient on one of the predictors is
>> implausible only if one tries to interpret it in the same way as the
>> coefficient in the corresponding simple regression.  In the model that
>> uses both mileage and age as predictors, the coefficient of age
>> summarizes the change in repair expenditures per unit increase in age
>> after adjusting for simultaneous linear change in mileage.  For a
>> more-detailed understanding, one would have to look at the structure
>> of the data (e.g., cross-sectional or longitudinal, the particular
>> cars involved).  If the two-predictor model is not an appreciably
>> better fit than the one-predictor models, it would be appropriate to
>> remove one of the predictors.
>>
>> David Hoaglin
>>
>> On Thu, Sep 5, 2013 at 5:00 PM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>> David,
>>>
>>> I believe there are two levels in the regression analysis: 1) what is
>>> desirable; 2) what is possible to achieve.
>>>
>>> In terms of desirability, the objective of the regression analysis is
>>> to isolate the effect of each covariate after controlling other
>>> factors (what we call "under equal conditions" or "ceteris paribus")
>>>
>>> In terms of actual possibility - the degree of success depends (among
>>> other things) on the degree of collinearity.
>>>
>>> High and low collinearity are dealt with in each and every Econometric
>>> textbook that I am familiar with.
>>>
>>> Moreover, the example of repair expenditures on Toyota car as a linear
>>> function of mileage and age of the car is very well known: it yield
>>> negative coefficient on one of the explanatory variable (implying the
>>> implausible outcome that as the age of the car goes up, the repair
>>> expenditures goes down. This problem is resolved when one of these
>>> variables are omitted.
>>>
>>> In term of correct practice - if you get implausible outcome - the
>>> first thing you should eliminate - is high collinearity.
>>>
>>> At least the textbooks I know reflect this insight.
>>>
>>> P.S. There is a possible methodology to remedy collinearity called ORR
>>> - and I believe it also exists in Stata. Economists don't like this
>>> methodology very much - because you enter a bias into the model, in
>>> order to decrease collinearity
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
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>
>
>
> --
> Dr. Yuval Arbel
> School of Business
> Carmel Academic Center
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1: yuval.arbel@carmel.ac.il
> e-mail2: yuval.arbel@gmail.com
> You can access my latest paper on SSRN at:  http://ssrn.com/abstract=2263398
> You can access previous papers on SSRN at: http://ssrn.com/author=1313670



-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com
You can access my latest paper on SSRN at:  http://ssrn.com/abstract=2263398
You can access previous papers on SSRN at: http://ssrn.com/author=1313670
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/