R help - Nov 2016 - Helmert contrasts and weighted means

Hi all!

Suppose that we have got a response y and an unbalanced treatment x with three
levels or groups.
The treatment is unbalanced by design. Indeed, the first group has 3
replications and the other two have two replications each.
 
For instance, in R the data might look like this:

y = c(66.18, 66.69, 50.31, 51.99, 52.07, 52.87, 54.03)
group = as.factor(c(rep("a", 3), rep("b", 2),
rep("c",2)))

The group means are:
    a       b       c 
61.06   52.03   53.45 

and the overall mean is 56.31.

Using Helmert contrasts in lm I get the following
> my.mod = lm(y~group, contrasts = list(group = "contr.helmert"))
> summary(my.mod)
Call:
lm(formula = y ~ group, contrasts = list(group = "contr.helmert"))

Residuals:
     1      2      3      4      5      6      7 
  5.12   5.63 -10.75  -0.04   0.04  -0.58   0.58 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   55.513      2.540  21.858 2.59e-05 ***
group1        -4.515      3.012  -1.499    0.208    
group2        -1.032      1.851  -0.557    0.607    
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Residual standard error: 6.598 on 4 degrees of freedom
Multiple R-squared:  0.4093,	Adjusted R-squared:  0.114 
F-statistic: 1.386 on 2 and 4 DF,  p-value: 0.3489

Here comes the questions. Is it possible to modify Helmert contrasts in order to
use weighted means instead of means of means?

Thanks

Erlis

> On 10 Nov 2016, at 16:30 , erlis ruli <erlis.ruli at gmail.com>
wrote:
> 
> Here comes the questions. Is it possible to modify Helmert contrasts in
order to use weighted means instead of means of means?
I think not. Not in general. I suppose you can set up a contrast matrix that
would make the intercept equal to the overall mean, but the definition would
depend on the group sizes. Contrast matrices are by design something that
specifies a mapping FROM parameter space TO observation space and shouldn't
depend on which observations you have or don't have.

Put differently, you would have to modify the entire design matrix if you
removed a few rows.

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

Thanks for the reply.
> I suppose you can set up a contrast matrix that would make the intercept
equal to the overall mean, but the definition would depend on the group sizes.
Any suggestion on how to set up one?

Erlis