Statistical Analysis of fMRI Data: GLM Flashcards
What are the vertical plots about? and the ß1-3?
The image shows a linear model of voxel activity. Voxel activity is being modelled by the experimental conditions which each have a coefficient ß1 and ß2 that modulate the importance of the conditions in terms of explaining the observed activity. Lastly, there is an “implicit baseline” which is also estimated by the coefficient ß3 and noise.
The coefficients are adjusted to make the model look as similar as possible to the observed data.
How can we interpret ß1 and ß2?
ß1 estimated regressor for condition 1
ß2 estimated regressor for condition 2
As ß1 is larger than ß2, it indicates that condition 1 elicits larger activity in the specific voxel than condition 2.
What are y, X, ß and e in the GLM as shown in the picture?
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what is n and p?
y is the observed activity
X is the design matrix (contains parameters that provide information about experimentally controlled factors such as conditions, but also potential confounds)
ß is a matrix of regression coefficient. One coefficient per parameter in X
e is error
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n = number of scans p = number of parameters (conditions, hemodynamic response function, linear drift function)
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Which function is sometimes used to fit the GLM?
Ordinary Least Squares (OLS)
OLS is a method of fitting a linear model, where the objective is to minimize the sum of squared errors. That is, the linear model is optimized by altering the ß-values until the point where the error between the model and the observed data is as small as possible.
What is the difference between a T-contrast and an F-contrast?
A T-contrast is basically like a t.test asking “Is there a difference between the two conditions?
An F-contrast on the other hand can test linear relationships between your parameters and the data. Thus, we ask “is there a relationship between the data and any of the parameters?”
Low-frequency drift
What is it?
When using an MRI scanner, the output will always have artifacts characterized by gradual signal degradation and scan intensity changes over time. Thereby, the signal measured in the beginning of a session will look different than the signals measured later in the session.
Low-frequency drift
How do we fix it?
We regress it out of the signal! That is, we add a parameter to our design matrix, which can take care of the scanner drift. This is done using a Discrete Cosine Transform, and is called “temporal filtering”
Why is the Hemodynamic response function taken into account? and how?
While our conditions are usually coded as 0 and 1, we know that the signal shows a specific signal during activation, which is not a binary 0 and 1.
The brain signal has been modelled and is called the hemodynamic reponse function. The hemodynamic response function and the stimulus functions are convolved, resulting in regressors that resemble brain activity more accurately.
How do we handle residual movement effects?
Residual movement effects are movement artifacts which could not be taken care of in the preprocessing using realignment. However, it is possible to extract the alignment parameters from the preprocessing and use them in the design matrix. Thereby, 6 parameters describing different movement directions are added to the GLM.
What is the problem of serial auto-correlations?
In almost all time series data, the data points are correlated serially. That is, the activation in a voxel at timepoint t is correlated to the activation at the same voxel at t+1.
When doing fMRI analyses with a GLM, an underlying assumptions is that the error in the model is independent and identically distributed for all scans. However due to auto-correlation, the error values are not independent.
This is solved by including an auto-regressive model in the error term.
How do we deal with the problem of serial auto-correlations?
Instead of using a simple noise model, where we assume that errors are independent and identically distributed, we create a noise model where the error distribution is derived from the actual data. Thereby, the errors are predicted both as random noise, but also as an “autoregressive” model, where the errors from earlier time points have an influence on the model.
What’s your problem, Multiple Comparisons?
With an alpha level of 0.05, there will be a lot of spurious results, as often many thousand tests are run when using fMRI data.
This can be solved by using different correction methods for the alpha level, in fMRI usually Gaussian random field theory is utilised
Gaussian random field theory (RFT) correction
Used to correct for multiple comparisons.
As e.g. Bonferroni correction is too conservative for many thousand tests, RFT is used. RFT assumes that the noise in neighbouring voxels is correlated, which is almost always is due to the smoothing which is done in the preprocessing. RFT can then be used to model the distribution of noise throughout the brain, and output how many “resolution elements” are in the brain. Resolution elements are also called Resels, and take the size of the “smallest spatially resolved region in an image”. So, basically it divides the brain into clusters of voxels that are highly correlated (resels), which lowers the number of “elements” in the brain which have to be taken into account when correcting for multiple comparisons.
Parametric modulators what are they?
If we know that there is trial-wise variability possibly influencing the BOLD signal, such as brighter images or emotional content in some trials more than others, it should be included in the model.
This can be done using parametric modulators, which fits HRF-convolved regressors to data about trial-wise intensity.
What is second-level GLMs used for?
Testing differences in activation at the group-level. Everything until now has revolved around single-subject analyses, but most often we also want to compare activation between groups.
This can be done by using the contrasts from the first level analysis, which is then analysed by making a new GLM, where the activity from a specific voxel is switched out so it is by subject instead of by time.
Different design matrices can then be used to carry out well-known statistical tests such as t-tests, regression or ANOVA
