Models of choice Flashcards
How to model response times?
continuous distribution
How to model accuracy?
binomial distribution - you either are right or wrong
what is Bernoulli distribution?
discrete probability distribution that models binary outcome of one trial
how Bernoulli distribution differes from binomial distribution?
Bernoulli distribution assesses only one trial, whereas binomial distribution extends over multiple trials
What is characteristic of response times curve?
there is right skew
outliers in the right - some trials took longer than they should
Inverse Gaussian distribution can capture that
how to simulate Inverse Gaussian function in Python?
scipy.stats.invgauss(mu, loc=0, scale=1)
mu = shape parameter -> mean -> determines center of distribution
loc = optional, shifts distribution along the x-axis
scale = optional -> controls variance (spread of distribution)
- higher values = more narrow
What is good default of loc for response times?
information needs to reach V1 (40 ms) + you need time for motor response (50 ms)
therefore, response time should not be lower than 90 ms
in the example, 300 ms were chosen as cut-off point
model fitting
upon assuming certain model, we can estimate (measure) parameters from real data
Signal Detection Theory
cognitive model of accuracy
decision critierion - not for estimation
sensitivity (d’) parameter summarizes the difference between two distributions
How to calculate sensitivity? Signal Detection Theory
(1 / np.sqrt(2)) * (stats.norm.ppf(true positive - hit) - stats.norm.ppf(false positive - false alarm))
What if subject has very high accuracy?
- replace 1 in ppf (Gaussian) for 0.99
- good estimate of d’ - you shouldn’t get infinate
How does bootstrapping for sensitivity estimate loook like? What are necessary steps?
1) resampling data with replacement
2) calculating a statistic (in this case, d’)
3) using these bootstrapped estimates to derive a confidence interval
What does resampling with replacement mean?
some trials may be selected more than once, while others might not be selected in a particular bootstrap sample
therefore, each bootstrap sample contains random selection of original trials - some may appear multiple times, some not at all
Drift-diffusion model
cognitive model of accuracy AND response time!
if sb is really good at the task -> they may be both accurate AND fast (so those parameters might not be independent)
random walk
random walk process is a model in which the next step of process comes from random distribution which is then added to result of previous step
can be used to simulate both RT and accuracy!
Simulating Drift Diffusion model with specific kind of random walk -> Wiener process
Wiener process -> random walk with infinitely small time step (very small time step) - mostly for model fitting
moreover, boundaries are added around random walk -> when you reach the boundary you need to choose
both RT and accuracy depend on random walk
What does boundary reflect?
speed-accuracy tradeoff
What does drift rate reflect?
ability parameter
larger drift rate reflects faster and more accurate responses
What does relative start point reflect?
the amount of bias participant has to pick either choice
if we want to start unbiased, we set it to 0.5
About what informs boundary seperation?
high boundary seperation -> boundaries away from each other -> slower RT, but higher accuracy
boundaries close to each other -> small fluctuations may be enough to hit either boundary -> faster, but less accurate
About what informs non-decision time?
when you are not doing random walk process -> time to accummulate evidence (time needed for information to travel in the brain)
About what informs diffusion coefficient?
noise
What parameters measure (estimate) ability vs strategy in the Drift-Diffusion Model?
ability = drift-rate
strategy => boundary
How to relate drift-diffusion model to neural data?
studies with monkeys
monkeys were instructed to move their eyes when they saw the target (2 alternative forced choice task)
superior colliculus neurons showed evidence accumulation behavior
for easy task -> firing rate goes up really fast
for hard task -> firing rate is more steady
cognitive evidence = spikes per second
Why you shouldn’t use normal distribution for cognitive model of reaction time and accuracy?
because it is impossible to disentangle ability vs strategy
fitting a model
to discover a set of parameter estimates (or parameter uncertainties using Bayesian methods) that best decribe the data given the model
How can you use fitting model to test hypotheses?
1) by directly estimating and then evaluating parameters
2) by comparing multiple models’ ability to describe data
