1. ## comparing models

This might be a "101" question but hey, The Ecologist" encouraged me to ask questions , lots and lots of stupid questions.

So when I have two competing models and I use
Code:
``anova(m1,m2)``
to test whether a reduction of the residual sum of squares is statistically significant or not, I understand that it is based on a chi-squared test, but I read that it only makes sense if the models are nested.

Why does it only makes sense if the models are nested?

2. ## The Following User Says Thank You to bugman For This Useful Post:

gianmarco (08-21-2015)

3. ## Re: comparing models

hi,
just a quick idea, before coffee: in anova the F test uses the ratio of the variance of the effect and the residuals. So, to compare the two models one needs a common basis for the residual noise. If the two models were completely independent that would not work.

does this make sense?

regards

4. ## The Following User Says Thank You to rogojel For This Useful Post:

bugman (08-21-2015)

5. ## Re: comparing models

So in this context the term nested is not referring to nested models as in random effects nested in fixed effects, we are saying the models must be subsets of the models we are testing?

As in:

m1 <- aov(y~x1+x2+x3+error)

vs

m2<-aov(y~x1+x2+error)?

Am I on the right track?

6. ## Re: comparing models

Yes, I think so.

regards

7. ## Re: comparing models

Nested models can be several things in the world of statistics. However, with regards to model comparison, then this refers to the larger model containing all the terms of the smaller model (as you represented in your equations).

8. ## Re: comparing models

Thanks evelyn13,

yes, looks like I was getting the terminology confused. Actually I was aware that it only makes sense to be comparing full and reduced models, it was the use of the word nested that threw me.

9. ## Re: comparing models

Hi,
this seems to be sort of accepted:

E.g. in this book they use the term "nested model" as you use it.

http://www.amazon.de/gp/product/0387...h_gw_p14_d0_i1

10. ## Re: comparing models

Just stumbled on this thread wjhile looking for another, they typically have to be nested so you have a degree of freedom to look up in the Chi sq dist. So if one model had 3 terms and the other 2, you woulud be on the Chi sq dist with 1 degree of freedom.

And as mentioned they are nest within each other (saturated and reduced) .

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