Bimodal Residuals
Bob Sutter
regression model? The distribution is not skewed, just bimodal.
Thanks.
Rich Ulrich
wrote:
> What does a bimodal distribution of residuals indicate about a linear
> regression model? The distribution is not skewed, just bimodal.
>
Do you have a dichotomous variable as an important predictor?
Do you have unequal Ns and a dichotomous outcome?
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
Mike Kruger
> On 13 Nov 2002 17:37:45 -0800, bsut...@earthlink.net (Bob Sutter)
> wrote:
>
> > What does a bimodal distribution of residuals indicate about a linear
> > regression model? The distribution is not skewed, just bimodal.
> >
>
> Do you have a dichotomous variable as an important predictor?
> Do you have unequal Ns and a dichotomous outcome?
One way for residuals to be bimodal is when the values predicted can't
easily occur.
For example, if you had coded sex as 1=male, 2=female, your most
common prediction would be 1.5, so the most common residuals would be
-0.5 and +0.5. The residuals would total zero (by definition), but
there would be no actual residuals of zero.
There's also cases where you are missing a classification that should
be there in the model. Suppose, for example, the height of hobbits is
between 3 and 4 feet, and the height of men is between 5 and 6 feet.
With equal sized populations, a model that does not include a
dichotomy separating men and hobbits is going to end up with a lot of
4.5 feet predictions, but there will be no observations at that
height. This will give bimodal residuals -- of course in this case the
original data may be bimodal as well.
[and, continuing on because it's 4 a.m. but I can't sleep, something
this newsgroup ordinarily helps with] You could also have created what
we might term a folded dichotomy. Again, an example helps: Suppose
you have a sample of stores that sell food, which includes small food
shops, supermarkets, and giant superstores. Your dependent variable is
sales. For an independent variable, you classify stores into
"supermarkets" and "non-supermarkets". Unfortunately, the
non-supermarkets are both bigger and smaller than the supermarkets, so
you would expect the residuals from this group to be bimodal.
So, think about dichotomies.
In fact, think twice about dichotomies.
Bob Sutter
> wrote:
>
> > What does a bimodal distribution of residuals indicate about a linear
> > regression model? The distribution is not skewed, just bimodal.
> >
>
> Do you have a dichotomous variable as an important predictor?
> Do you have unequal Ns and a dichotomous outcome?
There are several dichotomous independent variables. The Ns are not
unequal and the outcome is continuous.
Thanks, Bob
Jay Weedon
wrote:
>Rich Ulrich <wpi...@pitt.edu> wrote in message news:<2l8atu0b0iqgl1i91...@4ax.com>...
>> On 13 Nov 2002 17:37:45 -0800, bsut...@earthlink.net (Bob Sutter)
>> wrote:
>>
>> > What does a bimodal distribution of residuals indicate about a linear
>> > regression model? The distribution is not skewed, just bimodal.
>> >
>>
>> Do you have a dichotomous variable as an important predictor?
>> Do you have unequal Ns and a dichotomous outcome?
>
>There are several dichotomous independent variables. The Ns are not
>unequal and the outcome is continuous.
I think that the hint you've been given is to see whether the negative
residuals belong predominantly to one level of a dichotomous variable
while the positive ones belong to the other level of the same
variable.
JW