8 May
2003
8 May
'03
8:28 p.m.
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I need to simulate some predicted values and must estimate a variance =
covariance matrix from five imputed data sets. Does anybody know the =
formula for estimating the five matrices?
Traci
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<DIV><FONT face=3DArial size=3D2>I need to simulate some predicted =
values and must=20
estimate a variance covariance matrix from five imputed data=20
sets. Does anybody know the formula for estimating the =
five=20
matrices?</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial
size=3D2>Traci</FONT></DIV></BODY></HTML>
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8 May
8 May
8:35 p.m.
All multiple imputation questions have the same answer. :-).
just do what you would have done if you had 1 data set. just do it five
times.
how about someone write a function for the class to take m data sets, do
something (user specified), take simluations, combine them and return the
sims. then we could forget about the difference between datasets that are
multply imputed and datasets that are fully observed.
Gary
On Thu, 8 May 2003, Traci Burch wrote:
I need to simulate some predicted values and must
estimate a variance
covariance matrix from five imputed data sets. Does anybody know the
formula for estimating the five matrices?
Traci
8:39 p.m.
oh duh! so like simulate predicted values from each one and then take the
average of those predictions. Okay, gotcha. I was thinking, compute five
VCov matrices, average those, then make predictions. That is easier.
Traci
----- Original Message -----
From: "Gary King" <king(a)harvard.edu>
To: "Traci Burch" <tburch(a)fas.harvard.edu>
Cc: <gov2001-l(a)fas.harvard.edu>
Sent: Thursday, May 08, 2003 8:35 PM
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
All multiple imputation questions have the same answer. :-).
just do what you would have done if you had 1 data set. just do it five
times.
how about someone write a function for the class to take m data sets, do
something (user specified), take simluations, combine them and return the
sims. then we could forget about the difference between datasets that are
multply imputed and datasets that are fully observed.
Gary
On Thu, 8 May 2003, Traci Burch wrote:
I need to simulate some predicted values and must
estimate a variance
covariance matrix from five imputed data sets. Does anybody know the
formula for estimating the five matrices?
Traci
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
8:41 p.m.
right. always go to the quantity of interest for each data set. compute
sims, then combine. its totally unnatural, I agree, but once you get the
hang of it its easy like everything else...
Gary
On Thu, 8 May 2003, Traci Burch wrote:
oh duh! so like simulate predicted values from each
one and then take the
average of those predictions. Okay, gotcha. I was thinking, compute five
VCov matrices, average those, then make predictions. That is easier.
Traci
----- Original Message -----
From: "Gary King" <king(a)harvard.edu>
To: "Traci Burch" <tburch(a)fas.harvard.edu>
Cc: <gov2001-l(a)fas.harvard.edu>
Sent: Thursday, May 08, 2003 8:35 PM
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
All multiple imputation questions have the same answer. :-).
just do what you would have done if you had 1 data set. just do it five
times.
how about someone write a function for the class to take m data sets, do
something (user specified), take simluations, combine them and return the
sims. then we could forget about the difference between datasets that are
multply imputed and datasets that are fully observed.
Gary
On Thu, 8 May 2003, Traci Burch wrote:
I need to simulate some predicted values and must
estimate a variance
covariance matrix from five imputed data sets. Does anybody know the
formula for estimating the five matrices?
Traci
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
8:48 p.m.
New subject: [gov2001-l] stat significance & control variables
How does one make sense of a key causal variable that does not appear
significant in model 1, but becomes very significant in model 2 after a
causally unrelated control variable is added which is correlated with
both outcome and key causal variables? I mean even if we shouldn't
include that control variable, what does the change in significance for
the key causal variable signal - if anything?
Cheers,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Thursday, May 08, 2003 8:41 PM
To: Traci Burch
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
right. always go to the quantity of interest for each data set. compute
sims, then combine. its totally unnatural, I agree, but once you get
the
hang of it its easy like everything else...
Gary
On Thu, 8 May 2003, Traci Burch wrote:
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
oh duh! so like simulate predicted values from each
one and then take
the
average of those predictions. Okay, gotcha. I was
thinking, compute
five
VCov matrices, average those, then make predictions.
That is easier.
Traci
----- Original Message -----
From: "Gary King" <king(a)harvard.edu>
To: "Traci Burch" <tburch(a)fas.harvard.edu>
Cc: <gov2001-l(a)fas.harvard.edu>
Sent: Thursday, May 08, 2003 8:35 PM
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
>
> All multiple imputation questions have the same answer. :-).
>
> just do what you would have done if you had 1 data set. just do it
five
> times.
>
> how about someone write a function for the class to take m data
sets, do
> something (user specified), take simluations,
combine them and
return the
> sims. then we could forget about the difference
between datasets
that are
> multply imputed and datasets that are fully
observed.
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > I need to simulate some predicted values and must estimate a
variance
> > covariance matrix from five imputed data
sets. Does anybody know
the
formula for estimating the five matrices?
Traci
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
8:55 p.m.
New subject: [gov2001-l] stat significance & control variables
if you have a linear model, then controlling for a variable that is
uncorrleated with your key causal variable will have no effect on
anything. (in nonlinear models, it will be close to this situation).
since it changes things, it must be correlated. if its causally prior and
and also has an effect on the dep var, then it should be included. so
drop model 1!
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
How does one make sense of a key causal variable that
does not appear
significant in model 1, but becomes very significant in model 2 after a
causally unrelated control variable is added which is correlated with
both outcome and key causal variables? I mean even if we shouldn't
include that control variable, what does the change in significance for
the key causal variable signal - if anything?
Cheers,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Thursday, May 08, 2003 8:41 PM
To: Traci Burch
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
right. always go to the quantity of interest for each data set. compute
sims, then combine. its totally unnatural, I agree, but once you get
the
hang of it its easy like everything else...
Gary
On Thu, 8 May 2003, Traci Burch wrote:
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
oh duh! so like simulate predicted values from
each one and then take
the
average of those predictions. Okay, gotcha. I
was thinking, compute
five
VCov matrices, average those, then make
predictions. That is easier.
Traci
----- Original Message -----
From: "Gary King" <king(a)harvard.edu>
To: "Traci Burch" <tburch(a)fas.harvard.edu>
Cc: <gov2001-l(a)fas.harvard.edu>
Sent: Thursday, May 08, 2003 8:35 PM
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
>
> All multiple imputation questions have the same answer. :-).
>
> just do what you would have done if you had 1 data set. just do it
five
> times.
>
> how about someone write a function for the class to take m data
sets, do
> something (user specified), take
simluations, combine them and
return the
> sims. then we could forget about the
difference between datasets
that are
> multply imputed and datasets that are fully
observed.
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > I need to simulate some predicted values and must estimate a
variance
> > covariance matrix from five imputed
data sets. Does anybody know
the
formula for estimating the five matrices?
Traci
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
9:05 p.m.
New subject: [gov2001-l] stat significance & control variables
A hypothetical case out of curiosity:
If democracy is regressed on income, and the latter is insignificant in
model 1, but once we control for weather becomes significant (cold
weather is correlated - but *causally* unrelated - with democracy)..
what does it mean? I doubt that including weather as control would be
legitimate, even if it were a theoretically less absurd variable.
? :) ?
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Thursday, May 08, 2003 8:56 PM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] stat significance & control variables
if you have a linear model, then controlling for a variable that is
uncorrleated with your key causal variable will have no effect on
anything. (in nonlinear models, it will be close to this situation).
since it changes things, it must be correlated. if its causally prior
and
and also has an effect on the dep var, then it should be included. so
drop model 1!
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
How does one make sense of a key causal variable that
does not appear
significant in model 1, but becomes very significant in model 2 after
a
causally unrelated control variable is added which is
correlated with
both outcome and key causal variables? I mean even if we shouldn't
include that control variable, what does the change in significance
for
the key causal variable signal - if anything?
Cheers,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Thursday, May 08, 2003 8:41 PM
To: Traci Burch
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
right. always go to the quantity of interest for each data set.
compute
sims, then combine. its totally unnatural, I agree,
but once you get
the
hang of it its easy like everything else...
Gary
On Thu, 8 May 2003, Traci Burch wrote:
> oh duh! so like simulate predicted values from each one and then
take
the
> average of those predictions. Okay, gotcha. I was thinking,
compute
five
> VCov matrices, average those, then make predictions. That is
easier.
>
> Traci
> ----- Original Message -----
> From: "Gary King" <king(a)harvard.edu>
> To: "Traci Burch" <tburch(a)fas.harvard.edu>
> Cc: <gov2001-l(a)fas.harvard.edu>
> Sent: Thursday, May 08, 2003 8:35 PM
> Subject: Re: [gov2001-l] Amelia and variance covariance matrix
>
>
> >
> > All multiple imputation questions have the same answer. :-).
> >
> > just do what you would have done if you had 1 data set. just do
it
five
know
> times.
>
> how about someone write a function for the class to take m data
sets, do
> something (user specified), take
simluations, combine them and
return the
> sims. then we could forget about the
difference between datasets
that are
> multply imputed and datasets that are fully
observed.
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > I need to simulate some predicted values and must estimate a
variance
> > > covariance matrix from five imputed data sets. Does anybody the
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
formula for estimating the five matrices?
Traci
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
9:13 p.m.
New subject: [gov2001-l] stat significance & control variables
first of all, who cares about 'significance'? (answer: not you, not me,
not anyone who can compute quantities of interest!). so let's assume that
you meant to write instead 'important' or some such.
now presumably you picked 'weather' to mean 'a variable that has no effect
on any of the variables in your study'. well, it could by chance be
related. but even a chance correlation for a control variable (a var that
is causally prior to your key causal variable) can cause a problem. so
control for it. now there is a cost to controlling for a ton of these
variables since for each one you need to estimate an extra parameter and
so you reduce the bias but you can increase the variance. so there may be
a tradeoff.
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
A hypothetical case out of curiosity:
If democracy is regressed on income, and the latter is insignificant in
model 1, but once we control for weather becomes significant (cold
weather is correlated - but *causally* unrelated - with democracy)..
what does it mean? I doubt that including weather as control would be
legitimate, even if it were a theoretically less absurd variable.
? :) ?
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Thursday, May 08, 2003 8:56 PM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] stat significance & control variables
if you have a linear model, then controlling for a variable that is
uncorrleated with your key causal variable will have no effect on
anything. (in nonlinear models, it will be close to this situation).
since it changes things, it must be correlated. if its causally prior
and
and also has an effect on the dep var, then it should be included. so
drop model 1!
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
How does one make sense of a key causal variable
that does not appear
significant in model 1, but becomes very significant in model 2 after
a
causally unrelated control variable is added
which is correlated with
both outcome and key causal variables? I mean even if we shouldn't
include that control variable, what does the change in significance
for
the key causal variable signal - if anything?
Cheers,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Thursday, May 08, 2003 8:41 PM
To: Traci Burch
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
right. always go to the quantity of interest for each data set.
compute
sims, then combine. its totally unnatural, I
agree, but once you get
the
hang of it its easy like everything else...
Gary
On Thu, 8 May 2003, Traci Burch wrote:
> oh duh! so like simulate predicted values from each one and then
take
the
> average of those predictions. Okay, gotcha. I was thinking,
compute
five
> VCov matrices, average those, then make predictions. That is
easier.
>
> Traci
> ----- Original Message -----
> From: "Gary King" <king(a)harvard.edu>
> To: "Traci Burch" <tburch(a)fas.harvard.edu>
> Cc: <gov2001-l(a)fas.harvard.edu>
> Sent: Thursday, May 08, 2003 8:35 PM
> Subject: Re: [gov2001-l] Amelia and variance covariance matrix
>
>
> >
> > All multiple imputation questions have the same answer. :-).
> >
> > just do what you would have done if you had 1 data set. just do
it
five
know
> times.
>
> how about someone write a function for the class to take m data
sets, do
> something (user specified), take
simluations, combine them and
return the
> sims. then we could forget about the
difference between datasets
that are
> multply imputed and datasets that are fully
observed.
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > I need to simulate some predicted values and must estimate a
variance
> > > covariance matrix from five imputed data sets. Does anybody the
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
>
formula for estimating the five matrices?
>
> Traci
>
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
9 May
9 May
5:15 p.m.
New subject: [gov2001-l] stat significance & control variables
As far as significance of coefficients is concerned - I thought it's a
good approximation of the narrowness of confidence intervals for
quantities of interest: even if we only report the latter in the paper,
I thought we can use coefficients' significance as a proxy when checking
models.. Can there be a case when coefficients are insignificant, but
the confidence intervals for q-o-interest are narrow and substantively
different from null?
Stan
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Thursday, May 08, 2003 9:13 PM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
first of all, who cares about 'significance'? (answer: not you, not me,
not anyone who can compute quantities of interest!). so let's assume
that
you meant to write instead 'important' or some such.
now presumably you picked 'weather' to mean 'a variable that has no
effect
on any of the variables in your study'. well, it could by chance be
related. but even a chance correlation for a control variable (a var
that
is causally prior to your key causal variable) can cause a problem. so
control for it. now there is a cost to controlling for a ton of these
variables since for each one you need to estimate an extra parameter and
so you reduce the bias but you can increase the variance. so there may
be
a tradeoff.
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
get
A hypothetical case out of curiosity:
If democracy is regressed on income, and the latter is insignificant
in
model 1, but once we control for weather becomes
significant (cold
weather is correlated - but *causally* unrelated - with democracy)..
what does it mean? I doubt that including weather as control would be
legitimate, even if it were a theoretically less absurd variable.
? :) ?
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Thursday, May 08, 2003 8:56 PM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] stat significance & control variables
if you have a linear model, then controlling for a variable that is
uncorrleated with your key causal variable will have no effect on
anything. (in nonlinear models, it will be close to this situation).
since it changes things, it must be correlated. if
its causally prior
and
and also has an effect on the dep var, then it should be included. so
drop model 1!
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
> How does one make sense of a key causal variable that does not
appear
> significant in model 1, but becomes very
significant in model 2
after
a
> causally unrelated control variable is added which is correlated
with
both outcome
and key causal variables? I mean even if we shouldn't
include that control variable, what does the change in significance
for
the key causal variable signal - if anything?
Cheers,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Thursday, May 08, 2003 8:41 PM
To: Traci Burch
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] Amelia and variance covariance matrix
right. always go to the quantity of interest for each data set.
compute
> sims, then combine. its totally unnatural, I agree, but once you the
hang of it its easy like everything else...
Gary
On Thu, 8 May 2003, Traci Burch wrote:
> oh duh! so like simulate predicted values from each one and then
take
the
> average of those predictions. Okay, gotcha. I was thinking,
compute
five
> VCov matrices, average those, then make predictions. That is
easier.
>
> Traci
> ----- Original Message -----
> From: "Gary King" <king(a)harvard.edu>
> To: "Traci Burch" <tburch(a)fas.harvard.edu>
> Cc: <gov2001-l(a)fas.harvard.edu>
> Sent: Thursday, May 08, 2003 8:35 PM
> Subject: Re: [gov2001-l] Amelia and variance covariance matrix
>
>
> >
> > All multiple imputation questions have the same answer. :-).
> >
> > just do what you would have done if you had 1 data set. just do
it
five
know
> times.
>
> how about someone write a function for the class to take m data
sets, do
> something (user specified), take
simluations, combine them and
return the
> sims. then we could forget about the
difference between datasets
that are
> multply imputed and datasets that are fully
observed.
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > I need to simulate some predicted values and must estimate a
variance
> > > covariance matrix from five imputed data sets. Does anybody the
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
>
formula for estimating the five matrices?
>
> Traci
>
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
6:09 p.m.
New subject: [gov2001-l] stat significance & control variables
The reason why we care about the quantities of interest rather than the
significance of coefficients is important. If there is the most important
thing you want to take home from this course, this might be it.
Suppose that we find that in a logistic regression predicting war, the
coefficient for the variable that measures democracy is significant at
0.05 level. This is not surprising because we know democracy is somehow
related to war. In fact, we know that in the real world nothing is ever
completely independent: if we have a large enough data set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of interest. If
we predict that democracy decreases the probability of going to war by
0.000000000001 percentage point (though this is signifinicant with 100
stars), we may not really care. But, if we predict the difference to be 10
percentage point with only one star, this may have a more important
implication.
models.. Can there be a case when coefficients are
insignificant, but
the confidence intervals for q-o-interest are narrow and substantively
different from null?
Sure. Anything can happen if the quantity of interest is a non-linear
function of coefficients: remember that g(E(x)) is not generally equal to
E(g(X)). In fact, the null hypothesis w.r.t a coefficient is often
different from the null hypothesis w.r.t a qunatity of interest, so we
can't even compare the two.
Kosuke
6:32 p.m.
New subject: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but then
every variable you throw in your analysis will be signficantly different
from zero, pretty much no matter what it is (since the CIs will be tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example. sometimes it may
correspond with things of interest and somethings not. but why figur out
when it would happen? better to just compute the quantity of interest in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
The reason why we care about the quantities of
interest rather than the
significance of coefficients is important. If there is the most important
thing you want to take home from this course, this might be it.
Suppose that we find that in a logistic regression predicting war, the
coefficient for the variable that measures democracy is significant at
0.05 level. This is not surprising because we know democracy is somehow
related to war. In fact, we know that in the real world nothing is ever
completely independent: if we have a large enough data set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of interest. If
we predict that democracy decreases the probability of going to war by
0.000000000001 percentage point (though this is signifinicant with 100
stars), we may not really care. But, if we predict the difference to be 10
percentage point with only one star, this may have a more important
implication.
models.. Can there be a case when coefficients
are insignificant, but
the confidence intervals for q-o-interest are narrow and substantively
different from null?
Sure. Anything can happen if the quantity of interest is a non-linear
function of coefficients: remember that g(E(x)) is not generally equal to
E(g(X)). In fact, the null hypothesis w.r.t a coefficient is often
different from the null hypothesis w.r.t a qunatity of interest, so we
can't even compare the two.
Kosuke
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
7:08 p.m.
New subject: [gov2001-l] stat significance & control variables
On the other hand, should we estimate quantities of interest of
insignificant variables?
Is it reasonable to assert that we should check for significance before
simulating the quantity of interest?
Thanks.
Beau Kilmer
Pre-doctoral Candidate
John F. Kennedy School of Government
PhD Mailboxes
79 JFK Street
Cambridge, MA 02138
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu]
Sent: Friday, May 09, 2003 5:33 PM
To: kimai(a)fas.harvard.edu
Cc: smarkus(a)fas.harvard.edu; gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but then
every variable you throw in your analysis will be signficantly different
from zero, pretty much no matter what it is (since the CIs will be
tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example. sometimes it may
correspond with things of interest and somethings not. but why figur
out
when it would happen? better to just compute the quantity of interest
in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
to
The reason why we care about the quantities of
interest rather than
the
significance of coefficients is important. If there is
the most
important
thing you want to take home from this course, this
might be it.
Suppose that we find that in a logistic regression predicting war, the
coefficient for the variable that measures democracy is significant at
0.05 level. This is not surprising because we know democracy is
somehow
related to war. In fact, we know that in the real
world nothing is
ever
completely independent: if we have a large enough data
set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of
interest. If
we predict that democracy decreases the probability of
going to war by
0.000000000001 percentage point (though this is signifinicant with 100
stars), we may not really care. But, if we predict the difference to
be 10
percentage point with only one star, this may have a
more important
implication.
> models.. Can there be a case when coefficients are insignificant,
but
> the confidence intervals for q-o-interest are
narrow and
substantively
different from
null?
Sure. Anything can happen if the quantity of interest is a non-linear
function of coefficients: remember that g(E(x)) is not generally equal E(g(X)). In fact, the null hypothesis w.r.t a
coefficient is often
different from the null hypothesis w.r.t a qunatity of interest, so we
can't even compare the two.
Kosuke
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
7:22 p.m.
New subject: [gov2001-l] stat significance & control variables
Why not always estiamte the quantities of interest? The estimation of
quantities of interest is the goal of any research anyway. Certainly, you
shouldn't change your quantities of interest because a coefficient is not
significant. Your quantities of interest should be motivated by a
substantive question.
Kosuke
On Fri, 9 May 2003, Beau Kilmer wrote:
On the other hand, should we estimate quantities of
interest of
insignificant variables?
Is it reasonable to assert that we should check for significance before
simulating the quantity of interest?
Thanks.
Beau Kilmer
Pre-doctoral Candidate
John F. Kennedy School of Government
PhD Mailboxes
79 JFK Street
Cambridge, MA 02138
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu]
Sent: Friday, May 09, 2003 5:33 PM
To: kimai(a)fas.harvard.edu
Cc: smarkus(a)fas.harvard.edu; gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but then
every variable you throw in your analysis will be signficantly different
from zero, pretty much no matter what it is (since the CIs will be
tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example. sometimes it may
correspond with things of interest and somethings not. but why figur
out
when it would happen? better to just compute the quantity of interest
in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
to
The reason why we care about the quantities of
interest rather than
the
significance of coefficients is important. If
there is the most
important
thing you want to take home from this course,
this might be it.
Suppose that we find that in a logistic regression predicting war, the
coefficient for the variable that measures democracy is significant at
0.05 level. This is not surprising because we know democracy is
somehow
related to war. In fact, we know that in the real
world nothing is
ever
completely independent: if we have a large enough
data set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of
interest. If
we predict that democracy decreases the
probability of going to war by
0.000000000001 percentage point (though this is signifinicant with 100
stars), we may not really care. But, if we predict the difference to
be 10
percentage point with only one star, this may
have a more important
implication.
> models.. Can there be a case when coefficients are insignificant,
but
> the confidence intervals for q-o-interest
are narrow and
substantively
different
from null?
Sure. Anything can happen if the quantity of interest is a non-linear
function of coefficients: remember that g(E(x)) is not generally equal E(g(X)). In fact, the null hypothesis w.r.t a
coefficient is often
different from the null hypothesis w.r.t a qunatity of interest, so we
can't even compare the two.
Kosuke
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
7:28 p.m.
New subject: [gov2001-l] stat significance & control variables
by definition a QoI is of interest. so estimate it. assess and represent
the degree to which your estimate is uncertain. what more could you
possibly want?
here's an answer to your question: suppose we're interested in the
expected number of years of live you will lose if you take a "big pox"
vaccine. suppose that there is no sig diff between that number and 0.
great you say, sign me up. who cares whether its not sig I say. here's
why: 4% of the time if you take this vaccine you die a slow horrible
death (and the expected number of years of live lost is around 80). are
you going to tell me that 4% is less than 5% and so you still don't care?
now do it in reverse: suppose you compute the qoi and present the full
posterior distribution of the qoi, the number of years of lives lost.
This contains all relevant information about your question. there is no
other information you could be interested in about this quantity. so no
reason to compute significance. although of course you could ask the
probability of losing any years of life (the area under the curve to the
right of 0), but whether that is beyond some threshold isn't particularly
of interest.
Gary
On Fri, 9 May 2003, Beau Kilmer wrote:
On the other hand, should we estimate quantities of
interest of
insignificant variables?
Is it reasonable to assert that we should check for significance before
simulating the quantity of interest?
Thanks.
Beau Kilmer
Pre-doctoral Candidate
John F. Kennedy School of Government
PhD Mailboxes
79 JFK Street
Cambridge, MA 02138
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu]
Sent: Friday, May 09, 2003 5:33 PM
To: kimai(a)fas.harvard.edu
Cc: smarkus(a)fas.harvard.edu; gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but then
every variable you throw in your analysis will be signficantly different
from zero, pretty much no matter what it is (since the CIs will be
tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example. sometimes it may
correspond with things of interest and somethings not. but why figur
out
when it would happen? better to just compute the quantity of interest
in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
to
The reason why we care about the quantities of
interest rather than
the
significance of coefficients is important. If
there is the most
important
thing you want to take home from this course,
this might be it.
Suppose that we find that in a logistic regression predicting war, the
coefficient for the variable that measures democracy is significant at
0.05 level. This is not surprising because we know democracy is
somehow
related to war. In fact, we know that in the real
world nothing is
ever
completely independent: if we have a large enough
data set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of
interest. If
we predict that democracy decreases the
probability of going to war by
0.000000000001 percentage point (though this is signifinicant with 100
stars), we may not really care. But, if we predict the difference to
be 10
percentage point with only one star, this may
have a more important
implication.
> models.. Can there be a case when coefficients are insignificant,
but
> the confidence intervals for q-o-interest
are narrow and
substantively
different
from null?
Sure. Anything can happen if the quantity of interest is a non-linear
function of coefficients: remember that g(E(x)) is not generally equal E(g(X)). In fact, the null hypothesis w.r.t a
coefficient is often
different from the null hypothesis w.r.t a qunatity of interest, so we
can't even compare the two.
Kosuke
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
8:47 p.m.
New subject: [gov2001-l] 1.00000e+00
When R reports "1.00000e+00" what number is it?? (It cannot be above one
since it's probability..)
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Friday, May 09, 2003 7:29 PM
To: Beau Kilmer
Cc: gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
by definition a QoI is of interest. so estimate it. assess and
represent
the degree to which your estimate is uncertain. what more could you
possibly want?
here's an answer to your question: suppose we're interested in the
expected number of years of live you will lose if you take a "big pox"
vaccine. suppose that there is no sig diff between that number and 0.
great you say, sign me up. who cares whether its not sig I say. here's
why: 4% of the time if you take this vaccine you die a slow horrible
death (and the expected number of years of live lost is around 80). are
you going to tell me that 4% is less than 5% and so you still don't
care?
now do it in reverse: suppose you compute the qoi and present the full
posterior distribution of the qoi, the number of years of lives lost.
This contains all relevant information about your question. there is no
other information you could be interested in about this quantity. so no
reason to compute significance. although of course you could ask the
probability of losing any years of life (the area under the curve to the
right of 0), but whether that is beyond some threshold isn't
particularly
of interest.
Gary
On Fri, 9 May 2003, Beau Kilmer wrote:
by
non-linear
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
On the other hand, should we estimate quantities of
interest of
insignificant variables?
Is it reasonable to assert that we should check for significance
before
simulating the quantity of interest?
Thanks.
Beau Kilmer
Pre-doctoral Candidate
John F. Kennedy School of Government
PhD Mailboxes
79 JFK Street
Cambridge, MA 02138
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu]
Sent: Friday, May 09, 2003 5:33 PM
To: kimai(a)fas.harvard.edu
Cc: smarkus(a)fas.harvard.edu; gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but
then
every variable you throw in your analysis will be signficantly
different
from zero, pretty much no matter what it is (since the CIs will be
tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example.
sometimes it may
correspond with things of interest and somethings not. but why figur
out
when it would happen? better to just compute the quantity of interest
in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
the
The reason why we care about the quantities of
interest rather than
the
significance of coefficients is important. If
there is the most
important
> thing you want to take home from this course, this might be it.
>
> Suppose that we find that in a logistic regression predicting war, > coefficient for the variable that measures
democracy is significant
at
0.05 level.
This is not surprising because we know democracy is
somehow
related to war. In fact, we know that in the real
world nothing is
ever
completely independent: if we have a large enough
data set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of
interest. If
> we predict that democracy decreases the probability of going to war > 0.000000000001 percentage point (though this is
signifinicant with
100
stars), we may
not really care. But, if we predict the difference to
be 10
percentage point with only one star, this may
have a more important
implication.
> models.. Can there be a case when coefficients are insignificant,
but
> the confidence intervals for q-o-interest
are narrow and
substantively
> > different from null?
>
> Sure. Anything can happen if the quantity of interest is a > function of coefficients: remember that g(E(x))
is not generally
equal
to
> E(g(X)). In fact, the null hypothesis w.r.t a coefficient is often
> different from the null hypothesis w.r.t a qunatity of interest, so
we
can't
even compare the two.
Kosuke
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
8:54 p.m.
New subject: [gov2001-l] 1.00000e+00
It's 1.
Kosuke
On Fri, 9 May 2003, Stanislav Markus wrote:
When R reports "1.00000e+00" what number is
it?? (It cannot be above one
since it's probability..)
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary King
Sent: Friday, May 09, 2003 7:29 PM
To: Beau Kilmer
Cc: gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
by definition a QoI is of interest. so estimate it. assess and
represent
the degree to which your estimate is uncertain. what more could you
possibly want?
here's an answer to your question: suppose we're interested in the
expected number of years of live you will lose if you take a "big pox"
vaccine. suppose that there is no sig diff between that number and 0.
great you say, sign me up. who cares whether its not sig I say. here's
why: 4% of the time if you take this vaccine you die a slow horrible
death (and the expected number of years of live lost is around 80). are
you going to tell me that 4% is less than 5% and so you still don't
care?
now do it in reverse: suppose you compute the qoi and present the full
posterior distribution of the qoi, the number of years of lives lost.
This contains all relevant information about your question. there is no
other information you could be interested in about this quantity. so no
reason to compute significance. although of course you could ask the
probability of losing any years of life (the area under the curve to the
right of 0), but whether that is beyond some threshold isn't
particularly
of interest.
Gary
On Fri, 9 May 2003, Beau Kilmer wrote:
by
non-linear
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
On the other hand, should we estimate quantities
of interest of
insignificant variables?
Is it reasonable to assert that we should check for significance
before
simulating the quantity of interest?
Thanks.
Beau Kilmer
Pre-doctoral Candidate
John F. Kennedy School of Government
PhD Mailboxes
79 JFK Street
Cambridge, MA 02138
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu]
Sent: Friday, May 09, 2003 5:33 PM
To: kimai(a)fas.harvard.edu
Cc: smarkus(a)fas.harvard.edu; gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but
then
every variable you throw in your analysis will be signficantly
different
from zero, pretty much no matter what it is (since the CIs will be
tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example.
sometimes it may
correspond with things of interest and somethings not. but why figur
out
when it would happen? better to just compute the quantity of interest
in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
the
The reason why we care about the quantities of
interest rather than
the
significance of coefficients is important. If
there is the most
important
> thing you want to take home from this course, this might be it.
>
> Suppose that we find that in a logistic regression predicting war, > coefficient for the variable that measures
democracy is significant
at
0.05
level. This is not surprising because we know democracy is
somehow
related to war. In fact, we know that in the real
world nothing is
ever
completely independent: if we have a large enough
data set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of
interest. If
> we predict that democracy decreases the probability of going to war > 0.000000000001 percentage point (though this
is signifinicant with
100
stars),
we may not really care. But, if we predict the difference to
be 10
percentage point with only one star, this may
have a more important
implication.
> models.. Can there be a case when coefficients are insignificant,
but
> the confidence intervals for q-o-interest
are narrow and
substantively
> > different from null?
>
> Sure. Anything can happen if the quantity of interest is a > function of coefficients: remember that
g(E(x)) is not generally
equal
to
> E(g(X)). In fact, the null hypothesis w.r.t a coefficient is often
> different from the null hypothesis w.r.t a qunatity of interest, so
we
can't even compare the two.
Kosuke
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
9:21 p.m.
New subject: [gov2001-l] When a matrix is not positive definite
Dear all,
A quick technical question: we are running a negative binomial count
model, and are able to maximize its log likelihood and determine the parameters
without trouble. However, when we try to draw the coefficients from their multivariate
normal distribution, the computer complains that the Sigma we are
offering--the inverted negative hessian--is not positive definite. R has
no problem inverting the hessian; it is mvrnorm that is not satisfied. I
was curious, does anyone have suggestions as to what this might be, or how
to deal with it?
Many thanks.
Best,
Dan
PS We ran an almost idenitical model on a different dependent variable,
and it worked fine. This dependent variable doesn't differ much: there
are no NAs, and it is a non-negative integer that takes on values between
0 and 60. Same is true of the dependent variable involved in the trouble.
9:25 p.m.
New subject: [gov2001-l] When a matrix is not positive definite
PPS When we use "ginv" instead of "solve" to invert the Hessian
mvrnorm
is happy to generate coefficients--is there any reason why we shouldn't be
using the "ginv" function to compute the inverse of the negative Hessian?
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
Dear all,
A quick technical question: we are running a negative binomial count
model, and are able to maximize its log likelihood and determine the parameters
without trouble. However, when we try to draw the coefficients from their multivariate
normal distribution, the computer complains that the Sigma we are
offering--the inverted negative hessian--is not positive definite. R has
no problem inverting the hessian; it is mvrnorm that is not satisfied. I
was curious, does anyone have suggestions as to what this might be, or how
to deal with it?
Many thanks.
Best,
Dan
PS We ran an almost idenitical model on a different dependent variable,
and it worked fine. This dependent variable doesn't differ much: there
are no NAs, and it is a non-negative integer that takes on values between
0 and 60. Same is true of the dependent variable involved in the trouble.
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
9:48 p.m.
New subject: [gov2001-l] When a matrix is not positive definite
Here's a stop-gap answer:
I think that Kosuke told me that ginv is a shortcut for when
your Hessian isn't invertable and that you should really use
solve. Otherwise your numbers will be funky. Not positive
definite means...that it's not symmetric about the diagonal,
right? So ginv is taking a shortcut to give you numbers, but
you can't use the numbers because of the shortcut. I'm hungry.
I'm sure Kosuke will give you a more intelligible answer soon.
8)
Olivia.
----- Original Message -----
From: "Daniel Jacob Hopkins" <dhopkins(a)fas.harvard.edu>
To: "Kosuke Imai" <kimai(a)fas.harvard.edu>
Cc: "Stanislav Markus" <smarkus(a)fas.harvard.edu>du>;
<gov2001-l(a)fas.harvard.edu>
Sent: Friday, May 09, 2003 9:25 PM
Subject: Re: [gov2001-l] When a matrix is not positive definite
PPS When we use "ginv" instead of
"solve" to invert the
Hessian mvrnorm
is happy to generate coefficients--is there any reason
why we
shouldn't be
using the "ginv" function to compute the
inverse of the
negative Hessian?
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
> Dear all,
>
> A quick technical question: we are running a negative
binomial count
> model, and are able to maximize its log
likelihood and
determine the parameters
> without trouble. However, when we try to draw
the
coefficients from their multivariate
> normal distribution, the computer complains that
the Sigma
we are
> offering--the inverted negative hessian--is not
positive
definite. R has
> no problem inverting the hessian; it is mvrnorm
that is not
satisfied. I
> was curious, does anyone have suggestions as to
what this
might be, or how
> to deal with it?
>
> Many thanks.
>
> Best,
> Dan
>
> PS We ran an almost idenitical model on a different
dependent variable,
> and it worked fine. This dependent variable
doesn't differ
much: there
> are no NAs, and it is a non-negative integer that
takes on
values between
> 0 and 60. Same is true of the dependent variable
involved
in the trouble.
_______________________________________________
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11:31 p.m.
New subject: [gov2001-l] When a matrix is not positive definite
I had a problem similar to this, mvrnorm wouldn't let me draw from the
inverted hessian with the same messgae Dan got. My problem was that inverting
the hessian gave me a couple of negative numbers on the diagonal (i.e.
negative variances / standard errors - problem...). This is almost certainly
the reason you are getting a non-positive-semidefinited problem, and it comes
from the main diagonal. One way of cheating your way out of this would be to
get perform a regression using one of R's built in functions (i.e. use glm
instead of simulating the logit) and then use vcov to get the variance
covariance matrix. You could then use this and your simulated parameters in
mvrnorm. Of course this isn't really optimal because you'd ideally like to get
this variance matrix from simulation.
Ben
Quoting Olivia Lau <olau(a)fas.harvard.edu>du>:
Here's a stop-gap answer:
I think that Kosuke told me that ginv is a shortcut for when
your Hessian isn't invertable and that you should really use
solve. Otherwise your numbers will be funky. Not positive
definite means...that it's not symmetric about the diagonal,
right? So ginv is taking a shortcut to give you numbers, but
you can't use the numbers because of the shortcut. I'm hungry.
I'm sure Kosuke will give you a more intelligible answer soon.
8)
Olivia.
----- Original Message -----
From: "Daniel Jacob Hopkins" <dhopkins(a)fas.harvard.edu>
To: "Kosuke Imai" <kimai(a)fas.harvard.edu>
Cc: "Stanislav Markus" <smarkus(a)fas.harvard.edu>du>;
<gov2001-l(a)fas.harvard.edu>
Sent: Friday, May 09, 2003 9:25 PM
Subject: Re: [gov2001-l] When a matrix is not positive definite
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
PPS When we use "ginv" instead of
"solve" to invert the
Hessian mvrnorm
is happy to generate coefficients--is there any
reason why we
shouldn't be
using the "ginv" function to compute
the inverse of the
negative Hessian?
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
> Dear all,
>
> A quick technical question: we are running a negative
binomial count
> model, and are able to maximize its log
likelihood and
determine the parameters
> without trouble. However, when we try to
draw the
coefficients from their multivariate
> normal distribution, the computer complains
that the Sigma
we are
> offering--the inverted negative hessian--is
not positive
definite. R has
> no problem inverting the hessian; it is
mvrnorm that is not
satisfied. I
> was curious, does anyone have suggestions as
to what this
might be, or how
> to deal with it?
>
> Many thanks.
>
> Best,
> Dan
>
> PS We ran an almost idenitical model on a different
dependent variable,
> and it worked fine. This dependent variable
doesn't differ
much: there
> are no NAs, and it is a non-negative integer
that takes on
values between
> 0 and 60. Same is true of the dependent
variable involved
in the trouble.
_______________________________________________
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_______________________________________________
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11:52 p.m.
New subject: [gov2001-l] When a matrix is not positive definite
Also, make sure optim actually converged. The Hessian won't be positive
semi-definite if a local max is not found. And if the Hessian isn't
invertible, there might be a problem with your parameterization. For
example, identification problems will lead to a Hessian that's not full
rank.
-Ivan
10 May
10 May
12:17 a.m.
New subject: [gov2001-l] When a matrix is not positive definite
Olivia and Ivan are right. In most cases when Hessian is not invertible,
there is a problem with the model: e.g., the model is not identified. So,
check your model first.
Kosuke
On Fri, 9 May 2003, Olivia Lau wrote:
Here's a stop-gap answer:
I think that Kosuke told me that ginv is a shortcut for when
your Hessian isn't invertable and that you should really use
solve. Otherwise your numbers will be funky. Not positive
definite means...that it's not symmetric about the diagonal,
right? So ginv is taking a shortcut to give you numbers, but
you can't use the numbers because of the shortcut. I'm hungry.
I'm sure Kosuke will give you a more intelligible answer soon.
8)
Olivia.
----- Original Message -----
From: "Daniel Jacob Hopkins" <dhopkins(a)fas.harvard.edu>
To: "Kosuke Imai" <kimai(a)fas.harvard.edu>
Cc: "Stanislav Markus" <smarkus(a)fas.harvard.edu>du>;
<gov2001-l(a)fas.harvard.edu>
Sent: Friday, May 09, 2003 9:25 PM
Subject: Re: [gov2001-l] When a matrix is not positive definite
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
PPS When we use "ginv" instead of
"solve" to invert the
Hessian mvrnorm
is happy to generate coefficients--is there any
reason why we
shouldn't be
using the "ginv" function to compute
the inverse of the
negative Hessian?
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
> Dear all,
>
> A quick technical question: we are running a negative
binomial count
> model, and are able to maximize its log
likelihood and
determine the parameters
> without trouble. However, when we try to
draw the
coefficients from their multivariate
> normal distribution, the computer complains
that the Sigma
we are
> offering--the inverted negative hessian--is
not positive
definite. R has
> no problem inverting the hessian; it is
mvrnorm that is not
satisfied. I
> was curious, does anyone have suggestions as
to what this
might be, or how
> to deal with it?
>
> Many thanks.
>
> Best,
> Dan
>
> PS We ran an almost idenitical model on a different
dependent variable,
> and it worked fine. This dependent variable
doesn't differ
much: there
> are no NAs, and it is a non-negative integer
that takes on
values between
> 0 and 60. Same is true of the dependent
variable involved
in the trouble.
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
7:10 a.m.
New subject: [gov2001-l] When a matrix is not positive definite
or the code, which is probably even more likely to be wrong.
Gary
On Sat, 10 May 2003, Kosuke Imai wrote:
Olivia and Ivan are right. In most cases when Hessian
is not invertible,
there is a problem with the model: e.g., the model is not identified. So,
check your model first.
Kosuke
On Fri, 9 May 2003, Olivia Lau wrote:
Here's a stop-gap answer:
I think that Kosuke told me that ginv is a shortcut for when
your Hessian isn't invertable and that you should really use
solve. Otherwise your numbers will be funky. Not positive
definite means...that it's not symmetric about the diagonal,
right? So ginv is taking a shortcut to give you numbers, but
you can't use the numbers because of the shortcut. I'm hungry.
I'm sure Kosuke will give you a more intelligible answer soon.
8)
Olivia.
----- Original Message -----
From: "Daniel Jacob Hopkins" <dhopkins(a)fas.harvard.edu>
To: "Kosuke Imai" <kimai(a)fas.harvard.edu>
Cc: "Stanislav Markus" <smarkus(a)fas.harvard.edu>du>;
<gov2001-l(a)fas.harvard.edu>
Sent: Friday, May 09, 2003 9:25 PM
Subject: Re: [gov2001-l] When a matrix is not positive definite
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
PPS When we use "ginv" instead of
"solve" to invert the
Hessian mvrnorm
is happy to generate coefficients--is there any
reason why we
shouldn't be
using the "ginv" function to compute
the inverse of the
negative Hessian?
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
> Dear all,
>
> A quick technical question: we are running a negative
binomial count
> model, and are able to maximize its log
likelihood and
determine the parameters
> without trouble. However, when we try to
draw the
coefficients from their multivariate
> normal distribution, the computer complains
that the Sigma
we are
> offering--the inverted negative hessian--is
not positive
definite. R has
> no problem inverting the hessian; it is
mvrnorm that is not
satisfied. I
> was curious, does anyone have suggestions as
to what this
might be, or how
> to deal with it?
>
> Many thanks.
>
> Best,
> Dan
>
> PS We ran an almost idenitical model on a different
dependent variable,
> and it worked fine. This dependent variable
doesn't differ
much: there
> are no NAs, and it is a non-negative integer
that takes on
values between
> 0 and 60. Same is true of the dependent
variable involved
in the trouble.
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
9 May
9 May
11:55 p.m.
New subject: [gov2001-l] When a matrix is not positive definite
Sometimes, it's a small numerical problem. Try
(H+t(H))/2
This will make the matrix symmetric.
Kosuke
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
PPS When we use "ginv" instead of
"solve" to invert the Hessian mvrnorm
is happy to generate coefficients--is there any reason why we shouldn't be
using the "ginv" function to compute the inverse of the negative Hessian?
On Fri, 9 May 2003, Daniel Jacob Hopkins wrote:
Dear all,
A quick technical question: we are running a negative binomial count
model, and are able to maximize its log likelihood and determine the parameters
without trouble. However, when we try to draw the coefficients from their multivariate
normal distribution, the computer complains that the Sigma we are
offering--the inverted negative hessian--is not positive definite. R has
no problem inverting the hessian; it is mvrnorm that is not satisfied. I
was curious, does anyone have suggestions as to what this might be, or how
to deal with it?
Many thanks.
Best,
Dan
PS We ran an almost idenitical model on a different dependent variable,
and it worked fine. This dependent variable doesn't differ much: there
are no NAs, and it is a non-negative integer that takes on values between
0 and 60. Same is true of the dependent variable involved in the trouble.
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l(a)fas.harvard.edu
http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
7:14 p.m.
New subject: [gov2001-l] "undo" in R graphs
Is there some sort of 'undo' command for R plotting functions such as
text(), segments() etc...? If we write on graphs with text() using
locator() it would be nice to have an undo command...
Btw, I highly recommend locator() to anybody writing in graphs.
Thanks,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Friday, May 09, 2003 6:33 PM
To: Kosuke Imai
Cc: Stanislav Markus; gov2001-l(a)fas.harvard.edu
Subject: RE: [gov2001-l] stat significance & control variables
everyone pls read this message again. its an important point.
another way to think about it: suppose you were lucky enough to have
10,000,000 observations. more observations is obviously good. but then
every variable you throw in your analysis will be signficantly different
from zero, pretty much no matter what it is (since the CIs will be
tiny).
so significance tells you nothing at all about anything you might care
about as a political scientist in this example. sometimes it may
correspond with things of interest and somethings not. but why figur
out
when it would happen? better to just compute the quantity of interest
in
the first place.
Gawry
On Fri, 9 May 2003, Kosuke Imai wrote:
to
The reason why we care about the quantities of
interest rather than
the
significance of coefficients is important. If there is
the most
important
thing you want to take home from this course, this
might be it.
Suppose that we find that in a logistic regression predicting war, the
coefficient for the variable that measures democracy is significant at
0.05 level. This is not surprising because we know democracy is
somehow
related to war. In fact, we know that in the real
world nothing is
ever
completely independent: if we have a large enough data
set, the
coefficient for any variable will be significant.
The real question is how this translates into the quantity of
interest. If
we predict that democracy decreases the probability of
going to war by
0.000000000001 percentage point (though this is signifinicant with 100
stars), we may not really care. But, if we predict the difference to
be 10
percentage point with only one star, this may have a
more important
implication.
> models.. Can there be a case when coefficients are insignificant,
but
> the confidence intervals for q-o-interest are
narrow and
substantively
different from
null?
Sure. Anything can happen if the quantity of interest is a non-linear
function of coefficients: remember that g(E(x)) is not generally equal E(g(X)). In fact, the null hypothesis w.r.t a
coefficient is often
different from the null hypothesis w.r.t a qunatity of interest, so we
can't even compare the two.
Kosuke
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8 May
8 May
9:46 p.m.
New subject: [gov2001-l] stat significance & control variables
Stan,
Did you really pick the weather? If you did, here's one reason
why weather has significance:
We agree that free-markets lead to higher incomes and that
there's some link between free-markets and democracy. It's not
clear from the literature which way the link goes, but they're
correlated.
You also have to remember the geographical fact that most of the
world's industrialized countries are not in the tropics. (I can
only think of one exception -- Singapore.) This is the origin
of the "North" vs. "South" language to describe the debate
between developed vs. developing states respectively.
So if it's colder, the country is more likely to be a democratic
and developed state, and more likely to have higher income. The
causal link is indirect. If you're using some scale of
democracy, then this effect should be more apparent because the
stronger democracies are all developed states.
You might want to control for something other than the weather,
in that case. For example, geographic location? Europe, North
America, Asia, Africa, Latin America? You could even be fancy
and divide Asia up.
Olivia.
----- Original Message -----
From: "Stanislav Markus" <smarkus(a)fas.harvard.edu>
To: <gov2001-l(a)fas.harvard.edu>
Sent: Thursday, May 08, 2003 9:05 PM
Subject: RE: [gov2001-l] stat significance & control variables
A hypothetical case out of curiosity:
If democracy is regressed on income, and the latter is
insignificant in
model 1, but once we control for weather becomes
significant
(cold
weather is correlated - but *causally* unrelated -
with
democracy)..
what does it mean? I doubt that including weather as
control
would be
legitimate, even if it were a theoretically less
absurd
variable.
? :) ?
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Thursday, May 08, 2003 8:56 PM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] stat significance & control variables
if you have a linear model, then controlling for a variable
that is
uncorrleated with your key causal variable will have
no effect
on
anything. (in nonlinear models, it will be close to
this
situation).
since it changes things, it must be correlated. if
its
causally prior
and
and also has an effect on the dep var, then it should be
included. so
drop model 1!
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
> How does one make sense of a key causal variable that does
not appear
> significant in model 1, but becomes very
significant in
model 2 after
a
> causally unrelated control variable is added which is
correlated with
> both outcome and key causal variables? I mean
even if we
shouldn't
> include that control variable, what does the
change in
significance
for
> the key causal variable signal - if anything?
>
> Cheers,
> Stan
>
> ****************************
>
> Stanislav Markus
> Ph.D. Candidate
>
> Harvard University
> Department of Government
>
> e: smarkus(a)fas.harvard.edu
> t: 617.513.5407
>
>
>
> -----Original Message-----
> From: gov2001-l-admin(a)fas.harvard.edu
> [mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary
King
> Sent: Thursday, May 08, 2003 8:41 PM
> To: Traci Burch
> Cc: gov2001-l(a)fas.harvard.edu
> Subject: Re: [gov2001-l] Amelia and variance covariance
matrix
>
>
>
> right. always go to the quantity of interest for each data
set.
compute
> sims, then combine. its totally unnatural, I agree, but
once you get
> the
> hang of it its easy like everything else...
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > oh duh! so like simulate predicted values from each one
and then
take
> the
> > average of those predictions. Okay, gotcha. I was
thinking,
compute
> five
> > VCov matrices, average those, then make predictions. That
is
easier.
> >
> > Traci
> > ----- Original Message -----
> > From: "Gary King" <king(a)harvard.edu>
> > To: "Traci Burch" <tburch(a)fas.harvard.edu>
> > Cc: <gov2001-l(a)fas.harvard.edu>
> > Sent: Thursday, May 08, 2003 8:35 PM
> > Subject: Re: [gov2001-l] Amelia and variance covariance
matrix
> >
> >
> > >
> > > All multiple imputation questions have the same answer.
:-).
> > >
> > > just do what you would have done if you had 1 data set.
just do
it
> five
> > > times.
> > >
> > > how about someone write a function for the class to take
m data
> sets, do
> > > something (user specified), take simluations, combine
them and
> return the
> > > sims. then we could forget about the difference between
datasets
> that are
> > > multply imputed and datasets that are fully observed.
> > >
> > > Gary
> > >
> > > On Thu, 8 May 2003, Traci Burch wrote:
> > >
> > > > I need to simulate some predicted values and must
estimate a
> variance
> > > > covariance matrix from five imputed data sets. Does
anybody
know
the
_______________________________________________
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>
formula for estimating the five matrices?
>
> Traci
>
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10:47 p.m.
New subject: [gov2001-l] stat significance & control variables
This is a good point. We should always remeber that two variables which
appear to be uncorrelated can be related if you take into account for
other factors: i.e., the relationship can be indirect.
This is the famous Simpson's paradox. E(X*Y)=0 doesn't necessarily imply
E(X*Y|Z)=0 (although the latter implies the former by the law of iterated
expectations). More generally, X and Y can be pairwise independent when
they are dependent conditional on Z. very tricky!
Kosuke
On Thu, 8 May 2003, Olivia Lau wrote:
Stan,
Did you really pick the weather? If you did, here's one reason
why weather has significance:
We agree that free-markets lead to higher incomes and that
there's some link between free-markets and democracy. It's not
clear from the literature which way the link goes, but they're
correlated.
You also have to remember the geographical fact that most of the
world's industrialized countries are not in the tropics. (I can
only think of one exception -- Singapore.) This is the origin
of the "North" vs. "South" language to describe the debate
between developed vs. developing states respectively.
So if it's colder, the country is more likely to be a democratic
and developed state, and more likely to have higher income. The
causal link is indirect. If you're using some scale of
democracy, then this effect should be more apparent because the
stronger democracies are all developed states.
You might want to control for something other than the weather,
in that case. For example, geographic location? Europe, North
America, Asia, Africa, Latin America? You could even be fancy
and divide Asia up.
Olivia.
----- Original Message -----
From: "Stanislav Markus" <smarkus(a)fas.harvard.edu>
To: <gov2001-l(a)fas.harvard.edu>
Sent: Thursday, May 08, 2003 9:05 PM
Subject: RE: [gov2001-l] stat significance & control variables
A hypothetical case out of curiosity:
If democracy is regressed on income, and the latter is
insignificant in
model 1, but once we control for weather becomes
significant
(cold
weather is correlated - but *causally* unrelated
- with
democracy)..
what does it mean? I doubt that including weather
as control
would be
legitimate, even if it were a theoretically less
absurd
variable.
? :) ?
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: Gary King [mailto:king@harvard.edu]
Sent: Thursday, May 08, 2003 8:56 PM
To: Stanislav Markus
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] stat significance & control variables
if you have a linear model, then controlling for a variable
that is
uncorrleated with your key causal variable will
have no effect
on
anything. (in nonlinear models, it will be close
to this
situation).
since it changes things, it must be correlated.
if its
causally prior
and
and also has an effect on the dep var, then it should be
included. so
drop model 1!
Gary
On Thu, 8 May 2003, Stanislav Markus wrote:
> How does one make sense of a key causal variable that does
not appear
> significant in model 1, but becomes very
significant in
model 2 after
a
> causally unrelated control variable is added which is
correlated with
> both outcome and key causal variables? I
mean even if we
shouldn't
> include that control variable, what does the
change in
significance
for
> the key causal variable signal - if anything?
>
> Cheers,
> Stan
>
> ****************************
>
> Stanislav Markus
> Ph.D. Candidate
>
> Harvard University
> Department of Government
>
> e: smarkus(a)fas.harvard.edu
> t: 617.513.5407
>
>
>
> -----Original Message-----
> From: gov2001-l-admin(a)fas.harvard.edu
> [mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Gary
King
> Sent: Thursday, May 08, 2003 8:41 PM
> To: Traci Burch
> Cc: gov2001-l(a)fas.harvard.edu
> Subject: Re: [gov2001-l] Amelia and variance covariance
matrix
>
>
>
> right. always go to the quantity of interest for each data
set.
compute
> sims, then combine. its totally unnatural, I agree, but
once you get
> the
> hang of it its easy like everything else...
>
> Gary
>
> On Thu, 8 May 2003, Traci Burch wrote:
>
> > oh duh! so like simulate predicted values from each one
and then
take
> the
> > average of those predictions. Okay, gotcha. I was
thinking,
compute
> five
> > VCov matrices, average those, then make predictions. That
is
easier.
> >
> > Traci
> > ----- Original Message -----
> > From: "Gary King" <king(a)harvard.edu>
> > To: "Traci Burch" <tburch(a)fas.harvard.edu>
> > Cc: <gov2001-l(a)fas.harvard.edu>
> > Sent: Thursday, May 08, 2003 8:35 PM
> > Subject: Re: [gov2001-l] Amelia and variance covariance
matrix
> >
> >
> > >
> > > All multiple imputation questions have the same answer.
:-).
> > >
> > > just do what you would have done if you had 1 data set.
just do
it
> five
> > > times.
> > >
> > > how about someone write a function for the class to take
m data
> sets, do
> > > something (user specified), take simluations, combine
them and
> return the
> > > sims. then we could forget about the difference between
datasets
> that are
> > > multply imputed and datasets that are fully observed.
> > >
> > > Gary
> > >
> > > On Thu, 8 May 2003, Traci Burch wrote:
> > >
> > > > I need to simulate some predicted values and must
estimate a
> variance
> > > > covariance matrix from five imputed data sets. Does
anybody
know
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> > formula for estimating the five
matrices?
> >
> > Traci
> >
>
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26 comments
9 participants
participants (9)
-
ansell＠fas.harvard.edu -
Beau_Kilmer＠ksgphd.harvard.edu -
dhopkins＠fas.harvard.edu -
Gary King -
kdong＠fas.harvard.edu -
kimai＠fas.harvard.edu -
olau＠fas.harvard.edu -
smarkus＠fas.harvard.edu -
tburch＠fas.harvard.edu