#10917 | AsPredicted

As Predicted:Learning under uncertainty (#10917)


Created:       05/15/2018 06:39 AM (PT)

This is an anonymized version of the pre-registration.  It was created by the author(s) to use during peer-review.
A non-anonymized version (containing author names) should be made available by the authors when the work it supports is made public.

1) Have any data been collected for this study already?
No, no data have been collected for this study yet.

2) What's the main question being asked or hypothesis being tested in this study?
Question 1: In a noisy but otherwise stable environment, how does people’s subjective uncertainty about stimulus-outcome contingencies change over time, as more outcomes are observed?
- And (how) does the adaptation of uncertainty over time differ between young adolescents (12-15 years old) and adults (18-30 years old)?
Question 2: In a noisy but otherwise stable environment, (how) do people adapt their learning rate over time?
- And (how) does the adaptation of learning rate over time differ between young adolescents and adults?
Question 3: In a noisy but otherwise stable environment, does subjective uncertainty predict learning rate?
- And (how) does the relationship between subjective uncertainty and learning rate differ between young adolescents and adults?
To address these questions, we will examine the effects of trial (number of previous observations) and noise level (outcome variance) on participants’ learning rates and uncertainty ratings, using regression analyses. In addition, to characterize the latent processes that give rise to these effects, we will fit a computational model to the data.

3) Describe the key dependent variable(s) specifying how they will be measured.
We will examine trial-to-trial changes in estimation uncertainty and learning rate during a predictive-inference task. In this task, participants repeatedly observe a value sampled from a Gaussian distribution with a fixed mean and SD. After each observation, participants predict the mean of the value-generating distribution (by typing a number using the keyboard) and rate their confidence in that prediction (on an 11-point vertical scale with lower and upper anchors of “completely unconfident” and “completely confident”, respectively, using the mouse). This procedure allows us to directly estimate the prediction error on each trial (observationt – predictiont) and the prediction update from each trial to the next (difference between two successive predictions, i.e., predictiont+1– predictiont).
Dependent variables:
1. Estimation uncertainty is defined on each trial based on participants’ reported confidence about their prediction of the mean. Confidence will be rated on a scale ranging from 0 (completely unconfident) to 10 (completely confident); we will transform these ratings into uncertainty ratings (10 - confidence rating).
2. Learning rate is defined on each trial t as the prediction update from that trial to the next, divided by the most recent prediction error (PE): learning ratet = (predictiont+1– predictiont)/PEt. Trials on which PE is 0 will be excluded, as learning rate cannot be computed on those trials. In addition, trials on which the participant’s prediction is larger than 100 will be excluded, as this likely reflects a typing error.

4) How many and which conditions will participants be assigned to?
The predictive-inference task consists of ten blocks of fifteen trials. The mean of the value-generating distribution varies across blocks (between 15 and 85). The standard deviation of the value-generating distribution is 4 (low noise) in blocks 1-5 and 8 (high noise) in blocks 6-10, or vice versa, in counterbalanced order. Blocks 1 and 6 are preceded by a practice block (not analyzed) to familiarize participants with the amount of outcome variability in the upcoming blocks.

5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.
1. We will fit a power function, SU= a*(x)b+c, to participants’ uncertainty (inverse confidence) ratings using nonlinear regression. The first uncertainty rating in each block will be excluded from this analysis.
We will fit the power function to each participant’s confidence ratings, separately for the two noise conditions, and test for group (adolescents vs. adults), noise (high vs. low) and group*noise effects on estimates of b (rate of change), a+c (initial value, after one observation), and c (asymptotic value), in 3 separate linear regression models.
2. We will repeat Analysis 1, using estimated learning rate as the dependent variable. The last trial of each block will be excluded as learning rate cannot be estimated on those trials. The most accurate estimate of the mean value in our task is the average of all previous outcomes observed in the current task block. This ‘sample-average’ method can be implemented by reducing learning rate as a function of the number of previous observations in the current block (x), according to LR = 1/x. This corresponds to power function LR = a*(x)b+c, with a = 1, b = -1, and c = 0. We will test whether the estimated b parameter of the power function differs from -1, and whether the estimated c parameter differs from 0, using one-sample t-tests (separately for each age group in case the previous analyses revealed significant group differences).
3. We will regress single-trial measures of estimated learning rate on subjective uncertainty (derived from participants’ confidence ratings) using multilevel regression, with age group as a second-level predictor.

Computational modeling: We will also fit two computational models to the observed data: (i) a Kalman filter, which adapts the effective learning rate on each trial depending on the precision of the current expectation; and (ii) a reinforcement-learning model with a constant learning rate.
We will use hierarchical Bayesian parameter estimation, and models will be fitted separately to the adolescent and adult groups. We will fit the Kalman filter model to participants’ trial-to-trial sequences of predictions and confidence ratings. We will fit the reinforcement learning model to participants’ predictions only. To compare the performance of the 2 models, we will also fit the Kalman filter to participants’ predictions only.
To examine evidence for age differences, we will compare the posterior distributions of the population mean for each parameter between the two age groups.
We will compare the performance of the Kalman filter and the reinforcement learning model, separately for the adolescent and adult group, using the DIC.

6) Describe exactly how outliers will be defined and handled, and your precise rule(s) for excluding observations.
Participants will be healthy adolescents (VWO/gymnasium students; 12-15 years old) and adults (university/HBO students, 18-30 years old). People with psychiatric or neurological disorders, and people who used alcohol or recreational drugs on the testing day will be excluded.
Participants who use learning rates higher than 0.9 on more than 90% of the trials (i.e. almost always update their prediction to the most recent observation) and participants who use negative learning rates on more than 30% of the trials will be excluded, as those behaviors suggest a misunderstanding of the task structure. Participants who do not complete all blocks will be excluded as well.

7) How many observations will be collected or what will determine sample size?
No need to justify decision, but be precise about exactly how the number will be determined.

We aim to collect data from 35 participants per group (excluding outlier participants, who will be replaced) before 31 October 2018. However, if we have only tested between 25 and 35 participants per group by 31 October 2018, we will end data collection and hence have a sample size between 25 and 35. If we have tested less than 25 participants per group by 31 October 2018, we will continue data collection until at least 25 participants per group have been tested.

8) Anything else you would like to pre-register?
(e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)

Secondary analyses:
• We will test for a potential difference in the first confidence rating in the predictive-inference task (before any outcome has been observed) between the 2 age groups, using an independent-samples t-test.
• We will examine potential effects of sex (male vs. female) by adding sex, and its interaction with age group, as additional regressors to Analyses 1, 2 and 3.
• We will examine whether individual differences in intolerance for uncertainty, as measured by the Dutch version of the Intolerance of Uncertainty Scale–Short version (IUS-12), predict individual differences in subjective uncertainty and/or learning rate. IUS-12 scores range from 12 to 60, with higher scores indicating greater intolerance for uncertainty. We will repeat Analyses 1, 2 and 3 while adding a regressor coding for individual differences in intolerance for uncertainty.