Posted by
Art Kendall on
Nov 30, 2011; 2:18pm
URL: http://spssx-discussion.165.s1.nabble.com/Correlation-matrix-is-not-positive-definite-tp4999980p5035687.html
The £uorescence spectra have been
normalised by reducing
the area under each spectrum to a value of 1according
to Bertrand and Scotter [11].
This results in compositional data (similar to making the
data ipsative) so the R matrix is not positive definite for this
reason alone. However, this is a step in doing a Q matrix or dual
scaling (aka correspondence analysis).
Did you do this? Do you have access to that article?
The words standardize and normalize have many different meanings and
are frequently used interchangeably even within disciplines. Please
click <help> ; type "Proximities" in the edit box; scroll down
to and click <standardize> under related topics. Are one of
these what is done in your field? If not what is done?
Answer 2: Growth time is varied in minutes, but not of equal intervals.
Then it is a repeated factor with unequal intervals, You may be able
to use the actual intervals in a model if you have them. B is a
least ordinal.
In that article given that cases are plotted against the PCs it is
possible that the authors did Q factor analysis (using a PC kind of
factor analysis).
In that instance the matrix is transposed and variables become cases
and cases become variables.
It may also be possible that they just input the correlation matrix.
If I recall correctly when a correlation matrix is used as input N
is not specified.
Even so, there would be 2 reasons for the matrix to be not positive
definite. One is because the data within a case sum to a constant
If I am reading things correctly you have
You have 3 Independent variables:
A type of bacterium between cases 4 levels a nominal level variable
B growth time repeated within cases 7 levels an ordinal level
variable with unequal intervals of (un)known size.
C wavelength repeated within cases a ratio level variable at 171
equal
intervals
and one dependent variable intensity a ratio level variable.
That is 4788 cells with 1 measurement of intensity in each.
The degrees of freedom are enhanced by the repeated nature of your
data.
With 1 measurement per cell the ABC interaction cannot be
distinguished form error (i.e., it must be pooled with error).
If your goal is to find points along the spectrum at which the the
types of bacteria can be discriminated then your focus would be on
the AC interaction.
AB, and BC could then be pooled with error.
When there is an up spike or down spike in the spectrum does it
occur at one measurement value on C or does it occur on a few?
Do you expect that different bacteria will have different sets of
spikes? Or do you expect something else?
Is it at all practical to generate another set of 4788 cells? Is
this a tedious or highly automated process?
There are still some exploratory possibilities. I do not intend to
frustrate you. Suggestions can be more focused when the list has a
little better handle on the what the situation is. Perhaps list
members more experienced in specifying MIXED or GLM models could
make suggestions.
Art Kendall
Social Research Consultants
On 11/29/2011 10:16 PM, viswa21 wrote:
Hi Art,
Question 1:
Is this correct? You have 3 Independent variables:
A type of bacterium between cases 4 levels a nominal level variable
B growth time repeated within cases 7 levels a ??? level variable
C wavelength repeated within cases a ratio level variable at 171 equal
intervals
and one dependent variable intensity a ratio level variable.
That is 4788 cells with 1 measurement of intensity in each.
Answer 1: yes, it is correct.
Question 2: Is factor B repeats of a single parameter? i.e., are the levels
ordered? At equal intervals? 7 distinct settings of different parameters,
i.e., a nominal level variable?
Answer 2: Growth time is varied in minutes, but not of equal intervals.
Answer seems like nominal level variable.
Our research field do not use Q factor analysis.
http://spssx-discussion.1045642.n5.nabble.com/file/n5034443/Leblanc_Monitoring_the_identity_of_bacteria_using_their_intrinsic_fluorescence.pdf
Leblanc_Monitoring_the_identity_of_bacteria_using_their_intrinsic_fluorescence.pdf
Please take a look at the PDF file attached.
Thanks for your help.
--
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Art Kendall
Social Research Consultants