28 Feb
2010
28 Feb
'10
10:45 p.m.
I just wanted to make sure that I have the test outcomes interpreted correctly for the
likelihood ratio test. . .
If you get something really small using the 1-pchisq(r, df = 1) calculation, what you are
testing the null = "the restrictions are valid". Which means, the estimates
from the "short" regression is not different from the "long" one, or
the extra covariates DON'T change things.
Is this analogous to the f-test, where you are using the f-dist to test if the extra
coefficients DO matter (so a small p-value there would suggest that you should keep the
extra coefficients in?
EXL
28 Feb
28 Feb
10:52 p.m.
oops, I think I got that direction backward. the null is that the restricted version is
valid for BOTH test, and the alt hypothesis is that the unrestricted version is valid.
Sorry about the confusion . . these are perhaps more similar than I initially thought . .
.
EXL
On 2/28/10 10:45 PM, "Eric Lin" <elin at hbs.edu> wrote:
I just wanted to make sure that I have the test outcomes interpreted correctly for the
likelihood ratio test. . .
If you get something really small using the 1-pchisq(r, df = 1) calculation, what you are
testing the null = "the restrictions are valid". Which means, the estimates
from the "short" regression is not different from the "long" one, or
the extra covariates DON'T change things.
Is this analogous to the f-test, where you are using the f-dist to test if the extra
coefficients DO matter (so a small p-value there would suggest that you should keep the
extra coefficients in?
EXL
1 Mar
1 Mar
8:08 a.m.
The F test and the likelihood ratio test are indeed very close to one
another and serve basically the same purpose. But whereas the F test
works for linear models, the likelihood ratio test works for all
maximum likelihood models (including linear models).
Gary
---
http://gking.harvard.edu
On Sun, Feb 28, 2010 at 10:52 PM, Lin, Eric <elin at hbs.edu> wrote:
oops, I think I got that direction backward. ?the null
is that the
restricted version is valid for BOTH test, and the alt hypothesis is that
the unrestricted version is valid.
Sorry about the confusion . . ?these are perhaps more similar than I
initially thought . . .
EXL
On 2/28/10 10:45 PM, "Eric Lin" <elin at hbs.edu> wrote:
I just wanted to make sure that I have the test outcomes interpreted
correctly for the likelihood ratio test. . .
If you get something really small using the 1-pchisq(r, df = 1)
?calculation, what you are testing the null = ?the restrictions are valid?.
?Which means, the estimates from the ?short? regression is not different
from the ?long? one, or the extra covariates DON?T change things.
Is this analogous to the f-test, where you are using the f-dist to test if
the extra coefficients DO matter (so a small p-value there would suggest
that you should keep the extra coefficients in?
EXL
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10:53 a.m.
New subject: PS4: Intercept term for regressions / MLE
Hi everyone,
Maybe I'm overthinking it, but should there be an intercept term in the regressions
for mu in Parts 1-3, and for sigma in Part 3?
It seems like there should not be any intercept terms because coefficients for intercept
terms would be uninterpretable since there's no "reference" group.
Comments?
Best regards,
Joseph
Joseph Poj Gavinlertvatana
Doctoral student, Marketing
Harvard Business School
203 Wyss Hall, Soldiers Field, Boston, MA 02163
Ph 617.230.5907
Fx 617.496.4397
Txt/Vm 617.910.0563
Em pgavinlertvatana at hbs.edu
1:05 p.m.
New subject: PS4: Intercept term for regressions / MLE
Hi Joseph,
The short answer is that, yes, there should be an intercept term for
both parameters. Gary's book actually has a discussion of this on
pages 63-66. He notes that when you have more than two parameters you
are estimating, you can't drop parameters of less substance (e.g., the
intercept) from the likelihood (p. 63). This applies not only to mu,
but also to sigma^2 -- see the discussion on this point at the bottom
of page 65 and at the top of page 66 (for example, equation 4.10 --
where the intercept is included).
I think you're right in the sense that these coefficients don't have a
meaningful interpretation, but you do want to include them in for
purposes of deriving the maximum likelihood estimates. You also
wouldn't want to model your covariates with a linear functional form
that has a constrained intercept of zero, which is what I think the
approach you're suggesting does.
hope that helps --
Maya
On Mon, Mar 1, 2010 at 10:53 AM, Gavinlertvatana, Poj
<pgavinlertvatana at hbs.edu> wrote:
Hi everyone,
Maybe I?m overthinking it, but should there be an intercept term in the
regressions for mu in Parts 1-3, and for sigma in Part 3?
It seems like there should not be any intercept terms because coefficients
for intercept terms would be uninterpretable since there?s no ?reference?
group.
Comments?
Best regards,
Joseph
Joseph Poj Gavinlertvatana
Doctoral student, Marketing
Harvard Business School
203 Wyss Hall, Soldiers Field, Boston, MA 02163
Ph?? 617.230.5907
Fx?? 617.496.4397
Txt/Vm 617.910.0563
Em pgavinlertvatana at hbs.edu
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