[R] meaning of error message about collinearity

[Liaw, Andy]

You are using a method that needs to estimate the covariance matrix of all
the variables.  If you have 80 variables, there are (80+1)*80/2 = 3240
variances and covariances to estimate.  How many data points do you think
you need to do that?

Some people assume the covariance matrix is diagonal (i.e., assuming all the
variables are uncorrelated).  Even then you still have 80 variances to
estimate.  Besides, I don't think lda() does that.

If you really have to discrinimate 40 data points with 80 variables, use
methods that do not rely on the estimation of covariance matrix.

Andy

> -----Original Message-----
> From: Adaikalavan Ramasamy [mailto:ramasamy at stats.ox.ac.uk]
> Sent: Friday, July 12, 2002 4:08 PM
> To: r-help at r-project.org; allstat at jiscmail.ac.uk
> Subject: [R] meaning of error message about collinearity
> 
> 
> Just a quick question. I am trying to fit an LDA model with a 
> restricted
> subsample. My X is a numerical matrix and Y is vector of 
> factor response.
> 
> fit _  lda( Y[1:50]  ~ X[1:50, ]  )
> 
> gives the following error message: variables are collinear in:
> lda.default(x, grouping, ...)
> 
> I am guessing this is the problem of rank deficiency as I 
> have about 80
> variable. [since the lda works with subsample of size 80 and above]
> 
> Q1: Is my interpretation of the error message correct ?
> Q2: I am using the fit to prediction purposes etc. Is this 
> likely to be
> affected. ie  how serious is this problem ?
> Q3: Is there a good website about sound statistical 
> theory/practical of
> overcoming problem of rank deficiency if this is indeed the 
> source of the
> error.
> 
> Many thanks, Adai.
> 
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