Again, when in doubt, go back to the fundamental principles. Degrees of
freedom measures number of ways two populations can be different. In
Hogg/Klugman, they test two distribution functions while cumming is
testing whether a set of groups from a population is from a distribution
function(L0). How many ways can a set of groups of data be different
from a distribution function? Obvious, a lot more ways. The process
variance within the population will make the sample different even if
they are from the same distribution function. Therefore, your test
statistic needs to be higher. Thus, makes it harder to reject when you
have more degrees of freedom.
As far as why the degree of freedom in cumming is (number of groups -
number parameters), I am not sure either. It does make some sense.
There is an overlap between the parameters and the groups of data(one
data is defined by parameters and the other one is defined by number of
groups). Thus, you need to subtract them out. However, gut feeling
tells me that I should further subtract 1 from the resulting degree of
freedom. This is because everything has to add up to 100 %. Thus, if
you have N groups of data, you really need to know only N-1 of them.
Consider the following analogy: If you have only one way to go home,
and I am guessing which way you will take to go home. How many choices
or freedom can I guess? I think you have no choice but go that only
one way. Thus, zero degrees of freedom for me to guess wrong. Now, if
you have N ways to go home afterwork, then I will have N-1 degrees of
freedom to guess wrong. Thus, N-1 degrees of freedom.
Why didn't cumming subtract 1 out is unclear to me. I suspect he
probably doesn't have a complete set of data. In other words, he
probably performed his test on a certain section of the data. Thus,
everything does not add up to 100%. Of course, I did not research any
further to prove this. It's just a speculation.
Also, cumming's argument for accepting Logistic model for female
mortality is very weak. Neither Logistic nor Gompertz fits well for the
female population. He accept the Logistic model by rejecting the
Gompertz. I am not convinced. Just because Female mortality is not
defined by Gompertz, there no reason they have to be defined by
Logistic.
---Yin
Consider the following analogy
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From: michael.j.miller.cufc@statefarm.com
To: studygroup9@lists.casact.org
Subject: Likelihood Ratio Test
Date: Thursday, October 22, 1998 12:03PM
Sorry to bother everyone as we're trying to cram everything in, but I
was
wondering if anyone had a quick and easy answer to why Cummins (Ch. 4)
says
the degrees of freedom for the likelihood ratio test is the number of
groups minus the number of parameters and Hogg/Klugman say the degrees
of
freedom is just the number of parameters. Exam question 1990/15 uses
Hogg/Klugman and 1991/23 uses Cummins. I'm not clear on when to use
what.
Thanks.