compositional data: percent values sum up to 1

again, under another subject:
sorry, maybe an all too trivial question. But we have power data from J
frequency spectra and to have the same range for the data of all our
subjects, we just transformed them into % values, pseudo-code:

power[i,j]=power[i,j]/sum(power[i,1:J])

of course, now we have a perfect linear relationship in our x design-matrix,
since all power-values for each subject sum up to 1.

How shall we solve this problem: just eliminate one column of x, or
introduce a restriction which says exactly that our power data sum up to
1 for each subject?

Thanks a lot

Christoph

What are you trying to do?  What I would do with this depends on many 
factors.

spencer graves

Christoph Lehmann wrote:

again, under another subject:
sorry, maybe an all too trivial question. But we have power data from J
frequency spectra and to have the same range for the data of all our
subjects, we just transformed them into % values, pseudo-code:

power[i,j]=power[i,j]/sum(power[i,1:J])

of course, now we have a perfect linear relationship in our x design-matrix,
since all power-values for each subject sum up to 1.

How shall we solve this problem: just eliminate one column of x, or
introduce a restriction which says exactly that our power data sum up to
1 for each subject?

Thanks a lot

Christoph

I want to do a logistic regression analysis, and to compare with, a
discriminant analysis. The mentioned power maps are my exogenous data,
the dependent variable (not mentioned so far) is a diagnosis
(ill/healthy)

thanks for the interest and the help

Christoph

On Sun, 2003-06-01 at 21:01, Spencer Graves wrote:

What are you trying to do?  What I would do with this depends on many 
factors.

spencer graves

Christoph Lehmann wrote:

again, under another subject:
sorry, maybe an all too trivial question. But we have power data from J
frequency spectra and to have the same range for the data of all our
subjects, we just transformed them into % values, pseudo-code:

power[i,j]=power[i,j]/sum(power[i,1:J])

of course, now we have a perfect linear relationship in our x design-matrix,
since all power-values for each subject sum up to 1.

How shall we solve this problem: just eliminate one column of x, or
introduce a restriction which says exactly that our power data sum up to
1 for each subject?

Thanks a lot

Christoph

"glm" will do multinomial logistic regression.  However, if J is large, 

I doubt if that will do what you want.  If it were my problem, I might 
feel a need to read the code for "glm" and modify it to do what I want. 
  Perhaps someone else can suggest something better.

hth.  spencer graves

Christoph Lehmann wrote:

I want to do a logistic regression analysis, and to compare with, a
discriminant analysis. The mentioned power maps are my exogenous data,
the dependent variable (not mentioned so far) is a diagnosis
(ill/healthy)

thanks for the interest and the help

Christoph

On Sun, 2003-06-01 at 21:01, Spencer Graves wrote:

What are you trying to do?  What I would do with this depends on many 
factors.

spencer graves

Christoph Lehmann wrote:

again, under another subject:
sorry, maybe an all too trivial question. But we have power data from J
frequency spectra and to have the same range for the data of all our
subjects, we just transformed them into % values, pseudo-code:

power[i,j]=power[i,j]/sum(power[i,1:J])

of course, now we have a perfect linear relationship in our x design-matrix,
since all power-values for each subject sum up to 1.

How shall we solve this problem: just eliminate one column of x, or
introduce a restriction which says exactly that our power data sum up to
1 for each subject?

Thanks a lot

Christoph