dear members,
Thanks Peter, Bert, Rolf and Terry. Regrets to reply
this late.
iF you say that balancedness is not required for lm, I think there is some
inconsistency. The coded vectors can still be correlated and unless lm handles
it with some trick, aov and lm are essentially the same. I even came to know
that aov calls lm internally! Moroevr, can you please give me a reference that
explains how exactly lm handles semipartial correlations (if at all it does). I
am just curious.
Moroever, If I drop some elements to make my data balanced, will the results
(from aov and lm) be reliable, i.e makes the correct inference about my sample?
THanking You,
AkshaY Kulkarni
________________________________
From: peter dalgaard <pdalgd at gmail.com>
Sent: Tuesday, January 18, 2022 6:13 PM
To: akshay kulkarni <akshay_e4 at hotmail.com>
Cc: R help Mailing list <r-help at r-project.org>
Subject: Re: [R] unbalanced design in multifactor anova....
In brief, aov() requires balancedness (or at least you _really_ need to know
what you are doing otherwise), lm() does not, but you need to be careful that
results, like in any multiple regression, depends on test order. For models with
random effects, things get tricky and you likely need to use the
"lme4" package.
- Peter D.
> On 18 Jan 2022, at 08:14 , akshay kulkarni <akshay_e4 at hotmail.com>
wrote:
>
> dear members,
> I have a question on anova as implemented in R.
>
> If there is an unbalanced design in multifactor anova, will aov or lm work
properly? I was reading a book on excel where the author points that in an
unbalanced design, the factors, as coded vectors, are correlated. He says that
variance will be allocated properly only when the coded vectors are
uncorrelated. But he also justifies that the function TREND() in Excel handles
this automatically using semipartial correlations.
>
> What about aov or lm in R, which are used to implement anova? Should we do
some thing extra for them to work properly in an unbalanced design? Or will the
coding system used by R to represent the factors or levels internally handles
the correlation?
>
> THanking you,
> Yours sincerely,
> AKSHAY M KULKARNI
>
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>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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