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Science Forum Index » Statistics - Math Forum » comparison of non-nested models...
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| DanielBaier... |
 Posted: Tue Jul 22, 2008 1:02 am |
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Hi All,
I have a response variable y and 30 known predictors x_1, ... x_30. I
would like to know, whether the variables x_1, ..., x_10 have a higher
explanatory value for y than x_11, ..., x_30. I developed a simple
linear regression model based on x_1, ..., x_10 and another one based
on x_11, ..., x_30 and compared their RSS. However, that seems to be
unfair, because the second model has more variables. In addition, I
want to know, whether the first model is _significantly_ better than
the second one.
I found a lot of methods for variable selection and tests for reduced
models vs full models in standard text books, but I am still helpless
my problem above. I am grateful for any advices or references.
Best wishes,
Daniel |
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| Bruce Weaver... |
| Posted: Tue Jul 22, 2008 2:23 am |
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Guest
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On Jul 22, 7:02 am, DanielBaier <daniba... at (no spam) yahoo.com> wrote:
Quote: Hi All,
I have a response variable y and 30 known predictors x_1, ... x_30. I
would like to know, whether the variables x_1, ..., x_10 have a higher
explanatory value for y than x_11, ..., x_30. I developed a simple
linear regression model based on x_1, ..., x_10 and another one based
on x_11, ..., x_30 and compared their RSS. However, that seems to be
unfair, because the second model has more variables. In addition, I
want to know, whether the first model is _significantly_ better than
the second one.
I found a lot of methods for variable selection and tests for reduced
models vs full models in standard text books, but I am still helpless
my problem above. I am grateful for any advices or references.
Best wishes,
Daniel
Some authors suggest using Akaike's Information Criterion (AIC) or one
of its competitors for comparing non-nested models. E.g., see section
F in the GraphPad regression book (link below).
http://www.graphpad.com/manuals/prism4/RegressionBook.pdf
--
Bruce Weaver
bweaver at (no spam) lakeheadu.ca
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM." |
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| Ray Koopman... |
| Posted: Tue Jul 22, 2008 11:11 am |
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On Jul 22, 4:02 am, DanielBaier <daniba... at (no spam) yahoo.com> wrote:
Quote: Hi All,
I have a response variable y and 30 known predictors x_1, ... x_30. I
would like to know, whether the variables x_1, ..., x_10 have a higher
explanatory value for y than x_11, ..., x_30. I developed a simple
linear regression model based on x_1, ..., x_10 and another one based
on x_11, ..., x_30 and compared their RSS. However, that seems to be
unfair, because the second model has more variables. In addition, I
want to know, whether the first model is _significantly_ better than
the second one.
I found a lot of methods for variable selection and tests for reduced
models vs full models in standard text books, but I am still helpless
my problem above. I am grateful for any advices or references.
Best wishes,
Daniel
Kevin A. Clarke. A Simple Distribution-Free Test for Nonnested
Hypotheses. Political Analysis 15:3 (Summer 2007).
http://www.rochester.edu/college/psc/clarke/SDFT.pdf
http://www.rochester.edu/college/psc/clarke/SDFTsupplement.pdf |
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| RichUlrich... |
| Posted: Tue Jul 22, 2008 3:15 pm |
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On Tue, 22 Jul 2008 05:23:46 -0700 (PDT), Bruce Weaver
<bweaver at (no spam) lakeheadu.ca> wrote:
Quote: On Jul 22, 7:02 am, DanielBaier <daniba... at (no spam) yahoo.com> wrote:
Hi All,
I have a response variable y and 30 known predictors x_1, ... x_30. I
would like to know, whether the variables x_1, ..., x_10 have a higher
explanatory value for y than x_11, ..., x_30. I developed a simple
linear regression model based on x_1, ..., x_10 and another one based
on x_11, ..., x_30 and compared their RSS. However, that seems to be
unfair, because the second model has more variables. In addition, I
want to know, whether the first model is _significantly_ better than
the second one.
I found a lot of methods for variable selection and tests for reduced
models vs full models in standard text books, but I am still helpless
my problem above. I am grateful for any advices or references.
Best wishes,
Daniel
Some authors suggest using Akaike's Information Criterion (AIC) or one
of its competitors for comparing non-nested models. E.g., see section
F in the GraphPad regression book (link below).
http://www.graphpad.com/manuals/prism4/RegressionBook.pdf
AIC and BIC are the usual recommendations. I am curious
about what other people think of AIC and BIC.
The piece that Bruce cites has some comments that strike
me as a bit odd. There is a paragraph on terminology to
avoid when discussion AIC, such as "rejecting" or
"accepting" hypotheses or trying to report as a P value.
I've felt that way, but for different reasons than theirs.
To me, AIC and BIC seem to have inferior status, like they are
not real tests but they are the best we have available,
and they are *almost* as good as real tests. These authors
seem to take a hostile attitude towards hypothesis testing.
Reading between the lines, I conclude that these authors deem the
AIC perspective of "information science" to be the better approach.
They do state that terms like P-value "carry too much baggage, so
should only be used in the context of statistical hypothesis testing"
(p. 147).
- Back to the original problem.
Given set A of predictors and set B of differnt predictors, I
am always curious about their effective *overlap* -- the
variables are not overlapping, but the effective prediction
might be, or might not be. That is (since they are in the same
sample), How much will A add to B? B, to A? Are either of these
statistically significant, by the usual tests for increase? Both?
--
Rich Ulrich |
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| C Hanck... |
| Posted: Tue Jul 22, 2008 9:33 pm |
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