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Re: st: non-normal residuals

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: non-normal residuals Date Tue, 12 Feb 2013 15:51:07 +0000

```Some of this is textbook stuff but a standard if not universal line is
that linearity is the most important assumption of the linear model.

I'd like to repeat my advice that residual vs fitted plots are the
best general guide to whether the pattern of residuals is
satisfactory.

The

On Tue, Feb 12, 2013 at 3:32 PM, Xixi Lin <winnielxx@gmail.com> wrote:
> Thanks Maarten,
>
> If the non-normal residual is not a big problem for linear regression,
> what about heterokedasticity? I tried to test whether my linear
> regression makes sense by testing the assumptions, and the results
> showed that residuals are not normal and residual variances are not
> constant. I thought robust standard errors were correcting for
> heterokedasticity, and it would not change the coefficients? Since the
> coefficients do not change for the regression, what is the point of
> using robust standard errors if my goal is to get the coefficients?
>
> I used ladder/gladder commands because I thought if I can transform
> the variables to normal, then the residuals might be normal as
> well.----It turned out to be not working, because most of the
> independent variables do not have a fit transformation to normal.
>
> In order to make my regression more valid, what else shall I do? Shall
> I try to add and test for more independent variables?
>
> Thanks a lot for your patience and help.
>
> Best,
> Xixi Lin
>
> On Tue, Feb 12, 2013 at 7:17 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
>> Non-Gaussianity(*) of the residuals is on its own almost never a real
>> problem. Linear regression(**) is well known to be remarkably robust
>> in that sense. What you need to take care of is whether or not your
>> effects are linear, as strong deviations from Gaussianity can be a
>> sign that that might be a problem. But as long as your effects are
>> reasonably linear, you either do nothing about non-Gaussianity or you
>> specify -vce(robust)- or you specify -vce(bootstrap)-. I'd be worried
>> if the method matters.
>>
>> Notice that -ladder- or -gladder- do not look at residuals but at the
>> marginal distribution, so those commands cannot solve your problem.
>>
>> -- Maarten
>>
>> (*) Gaussian distribution is another name for the "normal"
>> distribution without the normative connotation.
>>
>> (**) OLS is the name of the algorithm used for estimating the
>> parameters of a linear regression model. So the name of the model you
>> want to estimate is "linear regression model" not "OLS".
>>
>> On Mon, Feb 11, 2013 at 11:22 PM, Xixi Lin <winnielxx@gmail.com> wrote:
>>> Hi All,
>>>
>>> I have a cross-sectional multiple regression, I wanna use OLS, and
>>> tested for its assumptions. It turned out that the residuals are not
>>> normal. And I tried to transform Y and X to other forms, however, it
>>> does not help to solve the non-normality problem. I use the following
>>> code to find the best fit for transformation.
>>>
>>>
>>> Is there any other way that I can fix the non-normality problem? Thanks.
>>>
>>> Best,
>>> Xixi Lin
>>> *
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>>
>>
>>
>> --
>> ---------------------------------
>> Maarten L. Buis
>> WZB
>> Reichpietschufer 50
>> 10785 Berlin
>> Germany
>>
>> http://www.maartenbuis.nl
>> ---------------------------------
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```