It's also extendable, so I can add linear modulators for time, for example,

across trials and this is really useful for assessing habituation or fatigue or

practice effects or performance related changes across time.

We can also add other basis functions to capture some non-linear effects

across time.

For example, we could add a quadratic regressor, quadratic function to my

linear one or we could add an exponential modulator as well.

And that might be particularly useful, because many times reaction time and

other kinds of time dependent effects can often vary exponentially with time.

So the power log practice deposits a very similar relationship

to an exponential decrees across time with increasing practice.

Finally, the implementation of this is all done by adding

regressors to the GLM design matrix.

So, it really fits nicely into the linear modeling framework.

Here are some cautions.

A standard approach is to modulate only the amplitude of this brief event,

stick function or an epoch.

So this is okay for many purposes but there's no guarantee that is this is

the most accurate or best model, there are some alternatives.

One, for example is if you're studying reaction time.

It's also possible to modulate the duration of an epoch with some

tricky manipulations all in the GLM framework.

As with other regressors, if you have multiple basis functions,

including basis sets for your event or quadratic or other non-linear modulators,

it may not be straightforward to do a t-test that captures that parametric

modulation effect altogether, so we have to be careful about that.

Linear modulators are really convenient, if you want to access a t-test and

do a t-test at the group level.

If you enter multiple modulators, be careful.

In some software, like in SPM software, which is very popular,

modulators are entered after the first one are orthogonalized

with respect to earlier ones.

So they're only allowed to explain variance that's not captured by the first

modulator and this not a standard multiple regression in which the effects compete to

explain variance.

It's actually a higher hierarchical regression in the sense that they're

entered stepwise and the first modulators is entered first and allowed to explain as

much variance as it can and then the the subserver modulators are entered.

So if you don't like this property,

you can change that by modifying the code if you desire.

And finally, let's look at the image of a design matrix

with really a complicated set of regressors and modulators.

What this all means?

It puts the pieces together.

So now we've got two trial types, A and B.

But now we've broken those two trial types into 18 regressors and

we've also added some nuisance covariates, maybe related to head motion.

So the first nine regressors model trial type A and

the second nine regressors model trial type B.

And now if you just look at the trial type A regressors,

the first three columns model the average response to trial type A,

but it does it with three basis functions.

So this is the three parameter basis that we talked about before with economical,

the derivative and the dispersion derivative.

Those together can capture the average response of trial type A with some

flexibility in the shape.

The next three capture the linear modulation by time,

the affect of time on the average or

trial number and you can see that there.

And that's true, we have to create a risk for each of the three basic functions and

then the third three capture the linear modulation by performance.

For example, reaction time.

Again, with one modulator per basis function.

So that's a little bit about unpacking how it might actually look in your design

matrix.

That's the end of this section.

Thank you.