# Parametric modulation, temporal basis functions in addition to correlated regressors Mkael

## Parametric modulation, temporal basis functions in addition to correlated regressors Mkael

Horg, Kimberly, Contributing Writer has reference to this Academic Journal, PHwiki organized this Journal Parametric modulation, temporal basis functions in addition to correlated regressors Mkael Symmonds Antoinette Nicolle Methods as long as Dummies 21st January 2008 Outline Parametric regressors: When are they useful Parametric regressors: What do they mean How to specify in SPM Linear in addition to non-linear effects Correlations between regressors in addition to orthogonalisation Parametric Design vs Factorial Design Factorial design: Experimental task has different factors that are independently manipulated. Each factor may take several levels. Events corresponding to each level of every factor are explicitly modelled by their own column in the design matrix. Assumes that each cell of the design matrix is homogeneous in addition to that stimuli differ only with regard to a single aspect across different levels of an experimental factor. Can test as long as categorical or parametric effects in addition to interactions by appropriate selection of contrasts to isolate one cognitive process at a time. ON / OFF, 2 LEVELS

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Parametric Design vs Factorial Design Factorial design: Experimental task has different factors that are independently manipulated. Each factor may take several levels. Events corresponding to each level of every factor are explicitly modelled by their own column in the design matrix. Assumes that each cell of the design matrix is homogeneous in addition to that stimuli differ only with regard to a single aspect across different levels of an experimental factor. Can test as long as categorical or parametric effects in addition to interactions by appropriate selection of contrasts to isolate one cognitive process at a time. 1,2,3,4,5  MANY LEVELS OR CONTINUOUS Parametric design: Every factor or variable has its own column in the design matrix  corresponding to one (independent) stimulus dimension of interest. Different levels of the factor, or the (continuous) variable are represented numerically within one column. Complex stimuli with a number of stimulus dimensions can be modelled by a set of parametric regressors tied to the presentation of each stimulus (e.g. faces can be described in terms of attractiveness, masculinity, symmetry, etc). This means that: 1. Statistical tests on the main effect of the condition (face presentation) will not be biased by variance within the condition due to systematic changes in the different stimulus dimensions increase in power 2. Can look at the contribution of each stimulus dimension independently 3. Can test predictions about the direction in addition to scaling of BOLD responses due to these different dimensions. Parametric Design vs Factorial Design Parametric Design vs Factorial Design Example: Very simple motor task – Subject presses a button then rests. Repeats this four times, with an increasing level of as long as ce. Hypothesis: We will see a linear increase in activation in motor cortex as the as long as ce increases Model: Factorial – regressor as long as each level of as long as ce of button press

Parametric Design vs Factorial Design Example: Very simple motor task – Subject presses a button then rests. Repeats this four times, with an increasing level of as long as ce. Hypothesis: We will see a linear increase in activation in motor cortex as the as long as ce increases Model: Factorial – regressor as long as each level of as long as ce of button press Time (scans) Contrast: 1 2 3 4 0 appropriate test to search as long as a linear increase Parametric Design vs Factorial Design Example: Very simple motor task – Subject presses a button then rests. Repeats this four times, with an increasing level of as long as ce. Hypothesis: We will see a linear increase in activation in motor cortex as the as long as ce increases Model: Factorial – regressor as long as each level of as long as ce of button press Time (scans) Contrast: -3 -1 1 3 0 No  need to mean-correct to look as long as differences between regressors that can be accounted as long as by a model of linearly increasing activation Parametric Design vs Factorial Design Example: Very simple motor task – Subject presses a button then rests. Repeats this four times, with an increasing level of as long as ce. Hypothesis: We will see a linear increase in activation in motor cortex as the as long as ce increases Model: Parametric – regressor as long as each level of as long as ce of button press Contrast: 1 0 0 Main effect of button pressing Time (scans)

Parametric Design vs Factorial Design Example: Very simple motor task – Subject presses a button then rests. Repeats this four times, with an increasing level of as long as ce. Hypothesis: We will see a linear increase in activation in motor cortex as the as long as ce increases Model: Parametric – regressor as long as each level of as long as ce of button press Contrast: 0 1 0 Linear effect of as long as ce Time (scans) Parametric Design vs Factorial Design Example: Very simple motor task – Subject presses a button then rests. Repeats this four times, with an increasing level of as long as ce. Hypothesis: We will see a linear increase in activation in motor cortex as the as long as ce increases Model: Can look at non-linear parametric effects by adding in a column Contrast: 0 0 1 0 Quadratic effect of as long as ce Time (scans) Parametric Design vs Factorial Design Factorial design: OK as long as simple design with limited number of levels of each factor. But need lots of regressors if many levels  hard to h in addition to le If your variables of interest vary over a continuous range, it is better to model this as a regressor with continuous values Parametric design: Good as long as designs with continuous variables where you want to per as long as m a multiple-regression type of analysis Correlated regressors can cause problems with interpretation. Not as straight as long as ward to look at interactions between factors

Specifying parametric regressors in SPM To look at higher-order effects Parametric vs Factorial Design  a real example Correlation of presentation rate of spoken words with neural activity R in addition to omly vary the rate of presentation of words between 10 in addition to 90 words per min Categorisation of different as long as ms of rate-dependent responses Buchel et al, Neuroimage 1998 Parametric vs Factorial Design  a real example Zeroth order  main effect of word presentation First order  linear effect of presentation rate Second order  quadratic effect of presentation rate Buchel et al, Neuroimage 1998 Demonstration of regionally specific word rate-dependent timecourses

Correlated Regressors Example of correlated regressors Experiment: Which areas of the brain are active in reward processing Subjects press a button to get a reward when they spot a red dot amongst green dots General Linear Model: Y = 1X1 + 2X2 + Y = BOLD response X1 = button press (movement) X2 = response to reward Example of correlated regressors Question: Which areas of the brain are active in reward processing The regressors are linearly dependent (temporally correlated – colinear), so variance attributable to an individual regressor (reward) may be confounded with another regressor (button press). As a result we dont know which part of the BOLD response is explained by movement in addition to which by response to getting a reward This may lead to misinterpretations of activations in certain brain areas E.g. primary motor cortex involved in reward processing We cant answer our question

How do I deal with it Avoid the problem by careful design of your experiment. Can use toolboxes Design Magic – Multicollinearity assessment as long as fMRI as long as SPM. URL: http://www.matthijs-vink.com/tools.html The only way you can avoid correlated regressors in a factorial design is to deliberately construct your experimental manipulations so that they are independent (orthogonal) How do I deal with it Avoid the problem by careful design of your experiment. Can use toolboxes Design Magic – Multicollinearity assessment as long as fMRI as long as SPM. URL: http://www.matthijs-vink.com/tools.html You can check as long as colinearity/orthogonality in SPM How do I deal with it Imagine you are trying to explain data point y in terms of vector x1 x1 y y = 1X1 1 = 1.5

How do I deal with it Adding in x2 changes the beta value of x1, as now x2 can explain some of the variance (a linear combination of x1 in addition to x2 perfectly explain y) x1 x2 y y = 1X1 + 2X2 1 = 1 2 = 1 You have changed your inference about x1 by adding in another correlated regressor How do I deal with it To look at how much of y is purely explained by x1, need to orthogonalise x2 x1 x2 x2 y y = 1X1 + 2X2 1 = 1.5 2 = 1 How do I deal with it SPM will automatically do serial orthogonalisation (note that this is only within each condition, so as long as each condition in addition to its associated parametric modulators) x1 x2 x2 y y = 1X1 + 2X2 1 = 1.5 2 = 1 We now have greater power to explain y in terms of x1 + x2 with no residual error  improves our conclusions about x1

How do I deal with it Parametric regressors are orthogonalised from left to right in the design matrix automatically by SPM Order in which you put parametric modulators is important!!! Put the most important modulators first (i.e. the ones whose meaning you dont want to change) Summary Use parametric modulators to investigate the effect of varying levels of a stimulus independently from the main effect of presenting the stimulus Can also look at non-linear effects Need to be aware of problems with inference due to correlated regressors Parametric modulators are serially orthogonalised in SPM Thanks to Rik Hensons slides: www.mrc-cbu.cam.ac.uk/Imaging/Common/rikSPM-GLM.ppt Previous years Presentations H Spiers, A Liston, H den Ouden, E Chu, in addition to previous Additional references Characterizing stimulus-response function using nonlinear regressors in parametric fMRI experiments, Buchel et al, Neuroimage, 1998 Using parametric regressors to disentangle properties of multi-feature processes, Wood et al, Behavioural in addition to Brain Functions, 2008

Temporal Basis Functions Methods as long as Dummies 21st Jan 2009 Antoinette Nicolle In linear algebra, a basis is used to describe a point in space. A basis function is the combining of a number of functions to describe a more complex function. Whats a basis function then Fourier analysis The complex wave at the top can be decomposed into the sum of the three simpler waves shown below. f(t)=h1(t)+h2(t)+h3(t) f(t) h1(t) h2(t) h3(t) In fMRI we need to describe a function of % signal change over time. There are various different basis sets that we could use to approximate the signal. Temporal Basis Functions as long as fMRI Finite Impulse Response (FIR) Fourier

Putting them into your design matrix Thanks to Rik Hensons slides: www.mrc-cbu.cam.ac.uk/Imaging/Common/rikSPM-GLM.ppt Previous years presenters slides Guillaume Fl in addition to in

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