[Ifeffit] CORRELATION MATRIX IN IFEFFIT

[Matt Newville]

Hi Renato,

On 3/23/06, Renato Canha Ambrosio <rcanha at ccet.ufrn.br> wrote:
>
> Hi folks
>
>
> I'm need to explore more the correlation matrix R(ij)given by ifeffit since
> my fit several variables are ajusted (the number is far bellow the number of
> independent data points).
> In my MACRO, the command correl (@all, @all, print) permit to obtain the
> correlation matrix.
> So I have some questions about the calculation of correlations (rij):
> 1) Is  the correlations(rij) calculated in ifeffit the sample linear
> correlation which measures the linear dependence between two vectos (in this
> sense, I'm thinking the term vector as a nx1 matrix in which n corresponds
> to the sample size - perhaps the number of fit iteractions)? If so, can I
> use a conventional hypothesis test like t (t = rij*sqrt[(n-1)/(1-rij**rij)]
> and how many degress of fredon can I consider to fint the t score on the
> table of t student distribution?

Not exactly....  The correlation matrix here is the inverse of the
covariance matrix from the least-squares fit.   That's not quite the
same as measuring the correlation between two statistically sampled
variables that might have some relation (for example, a person's
height and their weight).

The correlations reported tell you how one variable (say, N) would
respond if another variable (say, R) were moved from it's best-fit
(minimal chi-square) value.   I think it doesn't make a lot of sense
to try to apply t-tests to these numbers, but I might be thinking
about the issues too simplistically.

> 2) As I need to explore more the correlation matriz I would like to know if
> someone uses principal component analysis on Rij or some other chemometric
> approach.

I think this is a different meaning of correlation.   We're not saying
that all pairs of values for the variables (N,R) are equally valid --
one pair (or rather, a finite range of values) give a better match to
the observed data.   The correlations here (along with the reported
uncertainties) tell us about the shape and extent of that finite range
of values.

If I'm not understanding your questions, please let me know,

--Matt