Phillip and Ben,

Thanks a bunch. I now understand why sequential and marginal results are not
the same, although I have to read up a little on the "contrast" that Ben
mentioned.

Thanks for the clarification.

On Thu, Jan 20, 2011 at 12:51 PM, Phillip Chapman <
pchapman@stat.colostate.edu> wrote:

> Basil,
>
> I think that the issue is how lme (and R generally) parameterizes factorial
> models.  The "marginal" anova fits each effect after the others.  That does
> not produce what SAS calls type III sums of squares unless the model has no
> interactions or you use the "sum to zero" parameterization.
>
> Consider a tiny example:
>
> A  B
> 1  1
> 1  2
> 2  1
> 2  2
>
> The default R design matrix will be:
>
> int    A     B    A:B
>  1    0      0     0
>  1    0      1     0
>  1    1      0     0
>  1    1      1     1
>
> Fitting columns sequentially gives the usual A, B and A:B sums of squares.
> Fitting these "marginally", the B column will be added last, thus the anova
> will compare the full model to the model with only the int, A and A:B
> columns.  With only those three columns the model is constrained so that the
> first row A=1,B=1 has the same mean as the second row A=1,B=2, so the
> equality of those two means is the hypothesis tested.  That is not the same
> hypothesis as the type III B hypothesis.  The type III B null hypothesis is
> that the average of the means for rows 1 and 3 equals the average of the
> means for rows 2 and 4 (e.g. B low vs B high).
>
> If you use the contr.sum option, then the design matrix will be:
>
> int    A     B    A:B
>  1    -1    -1     1
>  1    -1     1    -1
>  1    1     -1   -1
>  1    1      1     1
>
> These columns are orthogonal, so the order of fit does not matter and
> sequential SS's equal marginal SS's
>
> Phil Chapman
>
>
> On 1/20/2011 10:51 AM, Ben Bolker wrote:
>
>> On 11-01-20 12:24 PM, Iannone, Basil wrote:
>>
>>> Dear R users,
>>>
>>> I am having a problem with interpreting "anova" results of a linear mixed
>>> effects model.
>>>
>>> The data I am analyzing is from study that was set up as a randomized
>>> block design with two factors at two levels. The model is:
>>>
>>>        m1<- lme(Y~A*B, random = ~1|Block)
>>>
>>> The design is completely balanced and no data are missing. When I run a
>>> sequential anova I get a p-value = 0.02 for factor B. When I run a
>>> marginal anova (specified by "type = "marginal""), I get a p-value = 0.29
>>> for factor B. The model summary ("summary (m1)" ) agrees with the
>>> marginal
>>> test and shows a p-value = 0.29 for factor B. Further when I graph values
>>> of Y against levels of B, I see no difference.
>>>
>>> I thought that sequential and marginal anovas should produce the same
>>> results when the design is balanced. Can someone please explain to me why
>>> the results of the "anova(m1)" differ from the results of "anova(m1, type
>>> = "marginal")" and "summary(m1)."
>>>
>>> Thanks for your help,
>>>
>>    Haven't spent a lot of time thinking this through, but I'm guessing
>> that the problem is with the interaction term.
>>    Can you give a reproducible example (to save me the trouble of making
>> one up)?
>>
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>>
>
>


-- 
Basil Iannone
University of Illinois at Chicago
Department of Biological Sciences (MC 066)
845 W. Taylor St.
Chicago, IL  60607-7060
Email: bianno2@uic.edu
Phone: 312-355-3231
Fax: 312-413-2435
http://www2.uic.edu/~bianno2

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