Week 5: First and high level analyses Flashcards
What is the difference between fixed effects and group effects analysis?
Fixed effects analysis focuses on a single participant while group effects analysis compares results across participants
Difference between within and between subject variance
The within subject variance describes the relative distribution of a random variable around its expected value (mean) for a single subject, while between subject variance describes the distribution of a variable around its mean across multiple people.
Fixed effects variance
Fixed effect variance equals the within subject variance divided by the amount of subjects and samples we are considering (e.g., number of voxels); it allows us to make inferences only about the specific subjects that we are analysing and does not allow to generalize our inference to the greater population
Fixed effects = variables that are constant across individuals
Mixed effects variance
Mixed effect variance equals the fixed effect variance + the between subject variance divided by the amount of subjects; with mixed effects, we make the assumption that the subjects were randompy pulled from a distribution, which itself has a variance; this allows us to extend our inference to the overall population. It treats subjects as random effects, meaning that it treats them as variables whose value of interest is not constant.
What happens if we ignore the random effect?
Then we are effectively conducting a fixed effect analysis, because if we ignore the random effect, we restrict our inference to the sample of subjects we have available and won’t be able to generalise to the population. Also, if we ignore random effects, we will only be relying on the within subject variance and hence assuming that subjects are fixed effects.
What happens to the overall variance when you include a between subject variance?
It will increase; on the contrary, increasing within-subject variance will have little impact on the overall variance. This also shows that it is better to try to get more subjects rather than increasing the trials for each subject.
Difference between fixed, random and mixed effects
Fixed effects: considers within subjects variance only
Random effects: consider between subject variance only
Mixed effects: consider both
Mixed model on fMRI data
The goal here is to estimate the variance of the effect, and to do so we need the variance of the estimates from each level of our analysis. Ideally, we would place all the data from our analysis (X and y) in a single GLM and estimate the parameters and their variance that way, but this is computationally unfeasible. This is why scientists came up with an approximation of the mixed effect model, called 2 summary stat approach.
Two summary statistics approach
Assume we want to research whether there is activation difference when viewing faces versus houses between the two groups (patients and controls).
Our model will have 2 levels:
1. at the first level, we model the data for each subject separately; the output of this model is subject-specific estimates of the faces–houses contrast and within-subject variance estimates for this contrast
2. the second-level model then takes as input
the subject-specific parameter estimates and variance estimates from the first-level
model. For example, in the face vs houses example above, the model estimates a mean for each group and the contrast tests whether the faces–houses activation is stronger in the first group relative to the second group and is an example of a two-sample t-test.
The between-subject variance is estimated in the [first/second]-level analysis
Second
How is a high mixed effects variance subject treated compared to a low mixed effects variance subject?
A subject with higher mixed effect variance will be downweighted compared to a sibject with lower mixed effect variance, because we want as little variance as possible for our estimates (?).
When your goal is to perform a group-analysis, the most efficient way to reduce variance is to include….
more subjects; this is becaise more subjects means that we will have a better estimate of the population distribution around the mean and also, looking at the MXF variance formula, adding more subjects will reduce it.
Fixed effects model
Used when when each subject has multiple runs of data and the runs need to be combined
1. run level (first level)
2. subject level (second level) = a weighted average of the first level effects, uses a fixed effects model
3. group level (third level)
Second level analysis - subject level
combines the per run estimates using a fixed effects model, which is a weighted linear regression with weights simply given by the inverse of the within-run standard deviations that were estimated in the first-level analysis;
Mean centering continuous covariates (=predictors)
does not change the quality of the fit of the model, it does change the interpretation of some of the parameter estimates; beta_0 becomes the mean BOLD activation for the subjects in the analysis, while beta_1 does not change > the goodness of the fit does not change.
