Xiaohui Chen wrote:
Frank E Harrell Jr 写道:
Xiaohui Chen wrote:
step or stepAIC functions do the job. You can opt to use BIC by
changing the mulplication of penalty.
I think AIC and BIC are not only limited to compare two pre-defined
models, they can be used as model search criteria. You could
enumerate the information criteria for all possible models if the
size of full model is relatively small. But this is not generally
scaled to practical high-dimensional applications. Hence, it is often
only possible to find a 'best' model of a local optimum, e.g.
measured by AIC/BIC.
Sure you can use them that way, and they may perform better than other
measures, but the resulting model will be highly biased (regression
coefficients biased away from zero). AIC and BIC were not designed to
be used in this fashion originally. Optimizing AIC or BIC will not
produce well-calibrated models as does penalizing a large model.
Sure, I agree with this point. AIC is used to correct the bias from the
estimations which minimize the KL distance of true model, provided the
assumed model family contains the true model. BIC is designed for
approximating the model marginal likelihood. Those are all
post-selection estimating methods. For simutaneous variable selection
and estimation, there are better penalizations like L1 penalty, which is
much better than AIC/BIC in terms of consistency.
The main point is to use some kind of penalization. Lots of people are
using AIC/BIC to select models using ordinary unpenalized least squares
or maximum likelihood, and that doesn't work well.
On the other way around, I wouldn't like to say the over-penalization
of BIC. Instead, I think AIC is usually underpenalizing larger models
in terms of the positive probability of incoperating irrevalent
variables in linear models.
If you put some constraints on the process (e.g., if using AIC to find
the optimum penalty in penalized maximum likelihood estimation), AIC
works very well and BIC results if far too much shrinkage
(underfitting). If using a dangerous process such as stepwise
variable selection, the more conservative BIC may be better in some
sense, worse in others. The main problem with stepwise variable
selection is the use of significance levels for entry below 1.0 and
especially below 0.1.
What's the point to use AIC on penalized MLE? I think generally you can
view the penalty as the prior regularization and using certain
optimization algorithm to find the MAP estimate.
Simulations show that AIC can choose the optimum L2 penalty in PMLE
using the effective degrees of freedom of each model. Optimizing BIC
choose far too much shrinkage.
Frank
Frank
X
Frank E Harrell Jr 写道:
Smita Pakhale wrote:
Hi Maria,
But why do you want to use forwards or backwards
methods? These all are 'backward' methods of modeling.
Try using AIC or BIC. BIC is much better than AIC.
And, you do not have to believe me or any one else on
this.
How does that help? BIC gives too much penalization in certain
contexts; both AIC and BIC were designed to compare two
pre-specified models. They were not designed to fix problems of
stepwise variable selection.
Frank
Just make a small data set with a few variables with
known relationship amongst them. With this simulated
data set, use all your modeling methods: backwards,
forwards, AIC, BIC etc and then see which one gives
you a answer closest to the truth. The beauty of using
a simulated dataset is that, you 'know' the truth, as
you are the 'creater' of it!
smita
--- Charilaos Skiadas <[EMAIL PROTECTED]> wrote:
A google search for "logistic regression with
stepwise forward in r" returns the following post:
https://stat.ethz.ch/pipermail/r-help/2003-December/043645.html
Haris Skiadas
Department of Mathematics and Computer Science
Hanover College
On May 28, 2008, at 7:01 AM, Maria wrote:
Hello,
I am just about to install R and was wondering
about a few things.
I have only worked in Matlab because I wanted to
do a logistic
regression. However Matlab does not do logistic
regression with
stepwiseforward method. Therefore I thought about
testing R. So my
question is
can I do logistic regression with stepwise forward
in R?
Thanks /M
______________________________________________
--
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
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