Goodness of Fit with Zero Degrees of Freedom

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3 total messages Started by Chuck Haas Thu, 08 Oct 1992 14:49

#457

Author: Chuck Haas
Date: Thu, 08 Oct 1992 14:49

23 lines
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Suppose I have a set of categorical data.
						trait present				trait absent				group  totals
group	a	a1												a0											at
group b		b1												b0											bt
... etc.

The group totals should be regarded as fixed.  I fit a model to this
data.  If the model has k parameters and there are m groups, then I know
that I could do a goodness of fit test (e.g., Fisher chi-square or
likelihood ratio) and compare to the chi-square distribution with m-k
degrees of freedom.

Suppose, however, that I fit a model with k=m parameters.  How do I then
test goodness of fit.  In other words, how much slippage should be
allowed before I reject the null hypothesis of model adequacy
(conditional on the parameters)?

Charles N. Haas
Professor, Environmental Engineering
Drexel University, Philadelphia PA 19104
======================================
CHaas@COE.Drexel.Edu

Re: Goodness of Fit with Zero Degrees of Freedom

#459

Author: Darrell Roy Hougen
Date: Thu, 08 Oct 1992 19:11

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chaas@coe.drexel.edu (Chuck Haas) writes:


*>Suppose I have a set of categorical data.
...
*> If the model has k parameters and there are m groups, then I know
*>that I could do a goodness of fit test (e.g., Fisher chi-square or
*>likelihood ratio) and compare to the chi-square distribution with m-k
*>degrees of freedom.

I'm not sure I understand your problem, but shouldn't the number of
degrees of freedom be equal to the number of data rather than the
number of categories?

Darrell

Re: Goodness of Fit with Zero Degrees of Freedom

#461

Author: USENET News System
Date: Thu, 08 Oct 1992 22:37

18 lines
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In article <1b2156INNnnf@roundup.crhc.uiuc.edu>, hougen@vision.csl.uiuc.edu (Darrell Roy Hougen) writes:
> 
> chaas@coe.drexel.edu (Chuck Haas) writes:
> 
> 
> *>Suppose I have a set of categorical data.
> ...
> *> If the model has k parameters and there are m groups, then I know
> *>that I could do a goodness of fit test (e.g., Fisher chi-square or
> *>likelihood ratio) and compare to the chi-square distribution with m-k
> *>degrees of freedom.
> 
> I'm not sure I understand your problem, but shouldn't the number of
> degrees of freedom be equal to the number of data rather than the
> number of categories?
> 
No, however the parameters should be estimated from the _grouped_
data. See Conover "Non-parametric Statistics" (or some-such title)

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