[BioC] linear models and intercepts with LIMMA

[Ramsi Haddad]

Dear Jim,

	Thanks for your explanation.  My confusion is over the fact that both
regression and ANOVA are called by the same function.  
I guess I don't need the intercept as Gordon suggested for the factor
co-variates, but I thought I needed an intercept for a continuous
co-variate.  
	My original message indicated that the intercept can be calculated by
loosing one of the samples when using group (factor) data.  If I use
only a continuous covariate, like age, I can get an intercept and still
keep the age co-variate.  The trouble arises when I add a factor (like
group) and a continuous co-variate (like age).  In this case, I can get
an intercept, but I loose a factor.  

	I am not intending to do anything with the intercept.  For this reason,
I am taking Gordon's advice and not calculating an intercept.

Thanks all.

Ramsi

	
> Ramsi Haddad wrote:
> > Dear List,
> > 
> > 	I have been working with LIMMA and I'm a bit confused by the linear
> > models.  I have a group with 4 factors.  I want to remove covariates
> > from the main effects before I look at contrasts.  Before I do this, I
> > was trying out the different combinations of ~ .  When I say
> > lmFit(~group), this is supposed to calculate an intercept.  This works. 
> > The problem is that my groupCTL disappears.  If I say lmFit(~ -1 +
> > group), I gather that the intercept is constrained to (0,0) and that
> > lmFit(~ 0 + group) does not calculate an intercept.
> > 	My problem is that I want lmFit to give me an intercept and not take
> > away my groupCTL!  Below is the code showing what I mean.  Everything
> > works, its just that I want my contrast matrix to include
> > groupPE-groupCTL, but I can't do this when the intercept is calculated. 
> 
> You are misunderstanding the models you are fitting. In the first place, 
> with ANOVA there is no assumption of a linear relationship between the 
> factor levels, so removing the intercept term doesn't constrain the 
> intercept to (0, 0). In this case, the intercept term indicates what 
> sort of model you want to fit, either a cell means or factor effects model.
> 
> Without an intercept you are fitting a cell means model in which you are 
> estimating the mean expression for each factor level (e.g., the model is 
> y_ij = u_i + e_ij). In this case, doing the contrasts is quite 
> straightforward.
> 
> If you add an intercept term, you are fitting a factor effects model in 
> which all of the other factors are specified in relation to some mean 
> value. In this case, all the other factors are specified in relation to 
> the mean of the groupCTL (e.g., the model is y_ij = u. + t_i + e_ij). 
> Here u. is the mean of the groupCTL samples, and the t_i are the amounts 
> that each of the other group means differ from the groupCTL mean. 
> Therefore, the contrasts are specified by the t_i values themselves if 
> you are comparing to groupCTL, and are specified by e.g., groupPE - 
> groupTIL for the other contrasts.
> 
> HTH,
> 
> Jim
> 
> 
> > 
> > Any assistance in clarifying this matter would be appreciated.  Thanks
> > 
> > Ramsi
> > 
> > 
> > 
> >>table(group)
> > 
> > group
> > CTL  PE TIL TNL 
> >  17  22  12  10 
> > 
> > 
> >>design.e <- model.matrix(~group)
> > 
> > 
> >>colnames(design.e)
> > 
> > [1] "(Intercept)" "groupPE"     "groupTIL"    "groupTNL"   
> > 
> > 
> >>design.e <- model.matrix(~-1 + group)
> > 
> > 
> >>colnames(design.e)
> > 
> > [1] "groupCTL" "groupPE"  "groupTIL" "groupTNL"
> > 
> > 
> >>design.e <- model.matrix(~0 + group)
> > 
> > 
> >>colnames(design.e)
> > 
> > [1] "groupCTL" "groupPE"  "groupTIL" "groupTNL"
> > 
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