>> NOT_USED <not_used@COMCAST.NET> 10/25/05 7:11 PM >>>
I don't understand why some of the answers to this question imply that
OLS is invalid if the dependent variable is skewed or not continuous.
OLS is based on the distribution of errors for the correct linear
model, so everything is relative to the independent variables. Can't say
much until we
know about these variables.
If the DV is not continuous (or close to it) OLS is the wrong model. A
7 point variable is not enough
First, the residuals cannot be continuous, and therefore cannot be
Second, the predicted values can be outside the range of the the DV
(less than 1 or more than 7) which makes no sense.
there are other reasons too, but that's enough
Also-- just because most of the survey answers are 5 6 or 7 does not
make the variable skewed-- could still be symmetric around 6 or even 5.5
Actually, no, it couldn't.
First of all, in your original post you said
75% give scores of 6 or 7
If all 75% were 6
Then the median is really not determinable, but it's at least 6.
The mean can't possibly be 6, because there are none above 6
What if all 75% were 7? then the median is 7 and the mean can't be 7
What if 37% were 6 and 38% were 7?
Then the median is 6.5, and the mean can't be 6.5
If the median isn't = to the mean, the distribution is skewed.
And if Y is skewed so will the residuals be. (I recall seeing a proof in
Faraway's book on linear models, but I don't recall the details). I
tested it out, though, with a DV as you describe and a nearly perfect
linear model (one IV that was the DV plus some random noise) and the
residuals are, sure enough, skewed.
OLS is simply NOT THE RIGHT APPROACH.
The right approach is, as David and I (and I think others) have told
you, to do ordinal or multinomial logistic, preferably using
SURVEYLOGISTIC if you have the information, or using LOGISTIC if you do
Peter L. Flom, PhD
Assistant Director, Statistics and Data Analysis Core
Center for Drug Use and HIV Research
National Development and Research Institutes
71 W. 23rd St
New York, NY 10010
(212) 845-4485 (voice)
(917) 438-0894 (fax)