Dear Tiffany,
Quoting Tiffany Huang <[log in to unmask]>:
> Dear SPMers,
>
> In my experiment, I have two stimuli presented before subjects making a
> response, stimulus A and B. Stimulus A always appears before stimulus B by a
> variable period, say a couple seconds. Because I am interested in the
> difference between the two stimuli, I entered a column of event time for
> stimulus A and and another for stimulus B in the same design matrix. Before
> defining a contrast, I calculated the correlation coefficient between the
> two regressors (stimulus A and B). It was highly correlated (r~=.6 and
> p<.000). Here are my questions:
>
> 1. Is this design still making sense for the contrast that I am interested
> in (i.e., A-B) given such a high correlation between the two regressors?
It does not make sense to use p-values when two vectors are
deterministic (as in your design). However, it still makes sense to
talk of regressors being "correlated" (as correlation is
computationally simply a normalized inner product). The magnitude of
this correlation is important to the efficiency of estimation of the
coefficients.
>
> 2. To determine whether two regressros are dependent or independent, do I
> just use the p value or is there any common values in the coefficient that I
> should look for?
The term "independent" is a concept that applies to random variables,
and again makes no sense to apply when discussing a deterministic
vector.
>
> 3.In general, how do dependent regressors affect the model and results?
> Should I get rid of dependent regressors even though SPM was able to
> estimate the beta?
The degree of correlation between regressors determines the variance
matrix of the estimated coefficients. Contrary to folk wisdom, there
is no general need to avoid design matrices that have correlated
columns. What is ultimately relevant in a hypothesis testing framework
is power, which depends on these variances (and hence the correlations
among regressors) and the assumed effect size.
As an aside, I would be concerned about the assumption that the
hemodynamic system will have identical input-output relationships for
two closely spaced stimuli. Others might have some helpful information
about using non-linear modeling of the hemodynamic response in an
attempt to account for such hemodynamic refractory-period effects.
Eric
>
> Any help on any of these questions would help. Thanks in advance.
>
> Tiffany
>
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