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# RE: st: Comparing coefficients across sub-samples

 From "Jacobs, David" To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: Comparing coefficients across sub-samples Date Wed, 1 Aug 2012 18:21:14 +0000

```I'm a bit doubtful about Beta weights.  They have largely gone out of style since the 1970s or so at least in sociology and political science, because they standardize on the basis of standard deviations. It follows that one cannot compare Beta weights between models if the runs are conducted on samples with different variable standard deviations.

Why not instead just compare the size of the unstandardized coefficients?  Often since regression coefficients (including those reported by Stata's fixed-effect routines) are in units of the dependent variable, one can say how much change a one unit change in an explanatory variable produces in a dependent variable.  Suppose, for example, your dependent variable is in dollar amounts. Then the (unstandardized) coefficient on an explanatory variable is equal to the change in dollars a one unit change in an explanatory variable would produce.

Or if your dependent variable is not so easily interpreted and if you can't get Stata to produce elasticities, other options probably are available.  Again if you log both the dependent variable and an explanatory variable, the coefficient on that explanatory variable will be an elasticity equal to the percentage change in a dependent variable attributable to a one percent change in the logged explanatory variable.  If logged variables won't be appropriate for many possible reasons (such as zero values in the variables), any decent introductory econometrics book will show you how to compute elasticities at the mean by multiplying a regression coefficient by the ratio of the mean of the dependent and the explanatory variables.  The fact you are estimating with fixed-effects rather than OLS does not matter.

Dave Jacobs

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fitzgerald, James
Sent: Wednesday, August 01, 2012 10:22 AM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Comparing coefficients across sub-samples

Hi Dave,

I tried using margins, eyex to calculate elasticities but I got the following error message:

"Could not calculate numerical derivatives - - discontinuous region with missing values encountered".

Have you any suggestions as to why I am receiving this error? Stata says this is the generic form of r(459), but does not go into any specifics as to what is actually causing the error to occur.

Also, suest and sureg do not support xtreg.

Best Regards

James

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jacobs, David
Sent: 01 August 2012 14:11
To: 'statalist@hsphsun2.harvard.edu'
Subject: RE: st: Comparing coefficients across sub-samples

If you want to compare coefficient size, try using elasticities either by logging the explanatory and dependent variable or by using the Stata command for this.

If you want to test for differences in coefficient size and the dependent variables are correlated, use the two equation estimator called -sureg-.  If -sureg- won't work, consider the Stata test called -suest-.

Dave Jacobs

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Fitzgerald, James
Sent: Wednesday, August 01, 2012 6:06 AM
To: <statalist@hsphsun2.harvard.edu>
Subject: Re: st: Comparing coefficients across sub-samples

Thanks for the suggestion, but unfortunately xtreg does not allow the beta option.

Regards

James

> Dear James,
>
> You can put the option "beta" after the "regress" command to obtain the standardized beta coefficients:
>
> regress y x , beta
>
> Best,
>
> --- 2012年8月1日 星期三，Fitzgerald, James <J.Fitzgerald2@ucc.ie> ?道?
>
>> 寄件人: Fitzgerald, James <J.Fitzgerald2@ucc.ie>
>> 主?: RE: st: Comparing coefficients across sub-samples
>> 收件人: "Lisa Marie Yarnell" <lisayarnell@yahoo.com>,
>> "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
>> 日期: 2012年8月1日,星期三,下午3:04
>> Hi Lisa
>>
>> Thank you very much for your response!
>>
>> I am looking for both the methodology and the command, if it exists.
>>
>> Does Stata have a command for generating "standardised"
>> betas, or do I just transform my variables by hand and re-run my
>> regressions?
>>
>> Thanks again
>>
>> James
>>
>> ________________________________________
>> From: Lisa Marie Yarnell [lisayarnell@yahoo.com]
>> Sent: 01 August 2012 04:29
>> To: statalist@hsphsun2.harvard.edu;
>> Fitzgerald, James
>> Subject: Re: st: Comparing coefficients across sub-samples
>>
>> Hi James,
>>
>> Typically the effect of a predictor in two different groups can be
>> compared with the unstandardized beta. You can do a statistical test
>> of the difference in the betas using the z-score formula below.  I
>> usually just calculate the difference between unstandardized betas
>> from two different models by hand, though Stata might have a command
>> to do this for you.  Is that what you are looking for: the Stata
>> command?
>>
>>             (b1 ? b2)
>>
>>      b1 and b2 are the unstandardized regression weights that you
>> want
>> z = --------------------
>>
>>           to test the difference
>> between
>>       √(seb12 + seb22)
>>              seb1
>> and seb2are the standard errors of these unstandardized
>>       ↑
>>
>>
>>           regression weights, found
>> next to the weights themselves
>> This is a square root sign!
>>               in your
>> SPSS output.  Remember to square them.
>> Take the square root of the
>> entire value in parentheses.
>>
>> In terms of comparing the *magnitude* of the effect in the two
>> different subsamples, it is more correct to do this qualitatively by
>> comparing the *standardized* beta for the variable of interest
>> against effect size rules of thumb for small/medium/large (which
>> sometimes differ by discipline, such as social
>> sciences/education/engineering).  Just report the standardized beta
>> as the effect size in each group; it would be a qualitative statement
>> about the effect in each group.
>>
>> Here are rules that I have:
>> Standardized regression coefficients:
>> * Keith’s (2006) rules for effects on school learning: .05 = too
>> small to be considered meaningful, .above .05 = small but meaningful
>> effect, .10 = moderate effect, .25 = large effect.
>> * Cohen’s (1988) rules of thumb: .10 = small, .30 = medium, >  (or
>> equal to) .50 = large
>>
>> Lisa
>>
>>
>>
>>
>> ----- Original Message -----
>> From: "Fitzgerald, James" <J.Fitzgerald2@ucc.ie>
>> To: "statalist@hsphsun2.harvard.edu"
>> <statalist@hsphsun2.harvard.edu>
>> Cc:
>> Sent: Tuesday, July 31, 2012 4:14 PM
>> Subject: st: Comparing coefficients across sub-samples
>>
>> Hi Statalisters
>>
>> I am running the same model on two sub-samples as follows:
>>
>> xtreg ltdbv lnta tang itang prof mtb if nolowlntalowtang==1, fe
>> cluster(firm)
>>
>> xtreg ltdbv lnta tang itang prof mtb if nolowlntalowtang==0, fe
>> cluster(firm)
>>
>> I want to compare the explanatory power of lnta across the two
>> sub-samples i.e. in which sub-sample does lnta explain significantly
>> more of the variation in ltdbv?
>>
>> Can anyone give me some advice on how to achieve this?
>>
>>
>> James
>> *
>> *  For searches and help try:
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>> *  http://www.ats.ucla.edu/stat/stata/
>>
>> *
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>>
>
> *
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```