Hi,
This is the unique reponse that I have received for my questions concerning my problem
of logistic regeression. I want to thank Blaise F. E. for his suggestions:
******************The querry***********
I want to conduct a practical logistic regression
procedure using SAS or SPSS, and I want to know first
the assumptions that my data have to verify :
Let say that I have Y=0 and 1.
And X1,X2,X3,X4 continuos variables.
1/Can I use all my variables in the method ,
X1,X2,X3,X4, without the assumptions of Gaussian
(normal) distribution?
2/ What happen if some of my explanatory variables are
correlated?
if corr(X1,X2) > 0.5, can I choose either X1 or X2 or
I can use both variables. And the model will choose
the appropriate one (the signficant one)
3/ What is the important of the Intercept.
4/In SAS what levels must I use for the method, alpha
=0,05 or 0,1 for entry and Stay options will be OK?
5/If my model is fitted, can I obtain the probability
confidence interval of the probability of event (Y=1)
of a new observation or individual.
6/ There exists any interesting graphical
presentations to show the relation between the
appropriate variables and the probability.
****************Blaise suggestions*********
I suggest you get hold of a copy of Alan Agresti's book Introducton to
Categorical Data Analysis. It will answer all your questions.
1. If you do a Bayesian analysis in WinBUGS you can set the
distributions of X1-X4 to be pretty much anything you like and the correct answers will
be obtained by Gibbs sampling. However, SAS and SPSS do not support
Bayesian analysis.
If you are doing a non-Bayesian analysis it may be possible to find
transformations that makes the predictors approximately normal.
If not, use of standard maximum likelihood or least squares methods may
yield biased results. If your sample size is large the bias may be
small. Apart from bias, you certainly won't be able to use any standard errors
or confidence intervals they produce. That means no hypothesis tests are
valid,either.
2. Same as in conventional linear models: the results are wrong! Try
using principal components analysis to get uncorrelated predictors. Dropping
one variable may work OK. Leaving both in is a bad idea.
3. It represents a baseline probability (on a logit scale) that
individual cases depart from, according to the values of the predictors.
4. It sounds like you are using a stepwise regression. I would say it a
bad technique and I would recommend that you avoid it.
5. Yes. Simply evaluate the right hand side of the model equation, set
it equal to log(p/(1-p) and solve for p.
6. I think so, but look in the Agresti book.
Thank you again Blaise
***************************************
Adel
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