Log transformations: dummy variables

[stats123123123]

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[Rich Ulrich]

(1) If anyone in the world is ever going to see your results,
they should naturally ask why you chose your "dummy" values
so badly that you felt the need to take the log. Answer: No.

(2) The important reason for taking a log is to correct the
scaling -- If you think that equal proportionate changes are
what is important in the predicted - or predictor - there is
a good chance you should take the log.

Heteroscedasticity can *alert*  you to the possibility of bad
scaling. If the scaling isn't bad, maybe the source or scope
of data which is the problem...  and that's something you
have to interpret *around*.  Maybe, break the sample into
parts?  Or, write your conclusions with extra caution,
warning about the trouble with the model.

--
Rich Ulrich

________________________________

> Date: Sun, 13 Mar 2011 23:19:37 +0100
> From: [hidden email]
> Subject: Log transformations: dummy variables
> To: [hidden email]
>
> Hi all,
>
> I have to perform a regression analysis and when performing the
> analysis with the normal data I get a scatterplot which could indicate
> heteroscedasticity.
> So I decided to transform the data by logging everything, however I
> have quite a gew dummy variables. My questions are:
> 1. Do I also log dummies (after adding 1)?
> 2. Do I have to log all the continous variables or can I only log the
> dependent variable?
> 3. How do I interpret the results?
>
> Any help would be greatly appreciated.

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[Art Kendall-2]

What is heteroscedastic? The raw data? The residuals?

What is the substantive nature of your variables?  Are there reasons to expect heteroscedasticity?

Art Kendall
Social Research Consultants?

On 3/13/2011 6:19 PM, Garnik Kazarjan wrote:

Hi all,
 
I have to perform a regression analysis and when performing the analysis with the normal data I get a scatterplot which could indicate heteroscedasticity.
So I decided to transform the data by logging everything, however I have quite a gew dummy variables. My questions are:
1. Do I also log dummies (after adding 1)?
2. Do I have to log all the continous variables or can I only log the dependent variable?
3. How do I interpret the results?
 
Any help would be greatly appreciated.

[Jon K Peck]

On 3/13/2011 6:19 PM, Garnik Kazarjan wrote:
Hi all,

I have to perform a regression analysis and when performing the analysis with the normal data I get a scatterplot which could indicate heteroscedasticity.
So I decided to transform the data by logging everything, however I have quite a gew dummy variables. My questions are:
1. Do I also log dummies (after adding 1)?
2. Do I have to log all the continous variables or can I only log the dependent variable?
3. How do I interpret the results?

Any help would be greatly appreciated.



There are a number of problems with this question.

First, the easy one.  It makes no difference what the two values are for a dummy variable.  There is nothing magic about zero one, that is just a convenience.

Second, having heteroscedastic residuals is not generally a major problem.  It does not introduce bias, although it affects the coefficient se's and results in some loss of efficiency.

Third, there are techniques for accounting for it without changing the form of the model.  WLS in Statistics can do this.

Fourth, the functional form of the model should not be dictated by heterscedasticity.  It should come from your theoretical formulation.  A common question is whether you need to convert to a per capital basic or divide by a cost index or such.  Log forms (both sides) give constant-elasticity-of-substitution modells that can be appropriate.

HTH,
Jon Peck