R help - Jul 2015 - How to specified contrasts in anova (lm)

Dear list,

I have the following anova that I want to fit in R:

y_{ijk} = \mu + \alpha_i + \beta_{j(i)} + \epsilon_{ijk}

This is an application in biology, in which we are measuring a certain
(continuous) characteristic of a group of cells.
Hence y_{ijk} corresponds to the measurement on cell k of type i in batch j.

Batch is nested in type, meaning that we have multiple batches for each
cell type and each batch contains only cells of a given type. To complicate
things, the design is unbalanced.

I can "manually" fit the model, with the following constraints:
\sum_{i=1}^m \alpha_i = 0
and
\sum_{j=1}^{n_i} \beta_{j(i)} = 0.

This gives me m  + 1 constraints, where m is the number of types.

A minimal (toy) example in R is:

a <- as.factor(c(rep(1, 4), rep(2, 6)))
b <- as.factor(rep(1:5, each=2))
y <- rnorm(10)

fit <- lm(y ~ a + b)

This call to lm will fit the wrong model, using two constraints (with the
"contr.sum" specification), \sum_{i=1}^m \alpha_i = 0 and
\sum_{j=1}^{n}
\beta_{j} = 0, and resulting in a singular design matrix.
Is there a way to specify the right constraints in lm?

Thanks in advance for any help,
davide

-- 
Davide Risso, PhD
Post Doctoral Scholar
Division of Biostatistics
School of Public Health
University of California, Berkeley
344 Li Ka Shing Center, #3370
Berkeley, CA 94720-3370
E-mail: davide.risso at berkeley.edu

	[[alternative HTML version deleted]]

Note that the toy example you provided is garbage. It has nothing to
do with contrasts (i.e. constraints) -- the DESIGN is singular: The
(2) - (1) difference for factor A  is exactly the same as the (3,4,5)
average - (1,2)average for B. I suspect you need to use a mixed
effects model treating batch as random, not fixed, but that is just a
guess as I do not know in detail what you have done.

So unless you have misstated or I have misunderstood, this indicates
that your statistical understanding is wanting and you should consult
a local statistical expert (of which there must be many) instead of
proceeding on your own. This is **NOT** about R and is off topic here.

Also, if you do wish to post here on R questions in future, please
follow the posting guide and post in plain text, not HTML.

Cheers,
Bert
Bert Gunter

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
   -- Clifford Stoll


On Wed, Jul 1, 2015 at 12:30 PM, Davide Risso <davide.risso at
berkeley.edu> wrote:
> Dear list,
>
> I have the following anova that I want to fit in R:
>
> y_{ijk} = \mu + \alpha_i + \beta_{j(i)} + \epsilon_{ijk}
>
> This is an application in biology, in which we are measuring a certain
> (continuous) characteristic of a group of cells.
> Hence y_{ijk} corresponds to the measurement on cell k of type i in batch
j.
>
> Batch is nested in type, meaning that we have multiple batches for each
> cell type and each batch contains only cells of a given type. To complicate
> things, the design is unbalanced.
>
> I can "manually" fit the model, with the following constraints:
> \sum_{i=1}^m \alpha_i = 0
> and
> \sum_{j=1}^{n_i} \beta_{j(i)} = 0.
>
> This gives me m  + 1 constraints, where m is the number of types.
>
> A minimal (toy) example in R is:
>
> a <- as.factor(c(rep(1, 4), rep(2, 6)))
> b <- as.factor(rep(1:5, each=2))
> y <- rnorm(10)
>
> fit <- lm(y ~ a + b)
>
> This call to lm will fit the wrong model, using two constraints (with the
> "contr.sum" specification), \sum_{i=1}^m \alpha_i = 0 and
\sum_{j=1}^{n}
> \beta_{j} = 0, and resulting in a singular design matrix.
> Is there a way to specify the right constraints in lm?
>
> Thanks in advance for any help,
> davide
>
> --
> Davide Risso, PhD
> Post Doctoral Scholar
> Division of Biostatistics
> School of Public Health
> University of California, Berkeley
> 344 Li Ka Shing Center, #3370
> Berkeley, CA 94720-3370
> E-mail: davide.risso at berkeley.edu
>
>         [[alternative HTML version deleted]]
>
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> and provide commented, minimal, self-contained, reproducible code.

Hi Bert,

I apologize for the HTML. I will pay more attention in the future.

I know that the lm() command of my toy example fits the wrong model
with a singular design, maybe I shouldn't have included it.

I believe that the model with the additional constraint(s) is not
garbage. But I don't know how to specify the additional constraints in
lm() (hence, I believe it's an R question).

I also know that I can fit a mixed effect model, but this was not the
point of my previous email.

Best,
davide