'Memory-based incremental exploration in a stochastic environment'
(AsPredicted #77128)
Download PDF

---

---

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?
Which decision variable best predicts participant's table choices in the exploration phase of the color card game? We will compare three variables derived from rational analysis of the task: exposure (visitation count), current uncertainty, and expected information gain (EIG). Additionally we ask whether the use of the best candidate variable is modulated by working memory load or total uncertainty of choice-options?
Based on a previous experiment, we expect current uncertainty to be the best candidate decision variable. We expect to see its influence diminish with working memory load. We expect to see the largely-positive effect of current uncertainty on choice become negative when total-uncertainty is high.

3) Describe the key dependent variable(s) specifying how they will be measured.
Our main dependent variables will be exploration-phase table choices and reaction times for these choices. We will also analyse test-phase choices and confidence ratings for these choices.

4) How many and which conditions will participants be assigned to?
Participants will play four sessions of the color-card game, consisting of 19 individual games. Each game comprises an exploration phase, and a test phase. On each trial of the exploration phase, participants will be presented with 2 out 4 table choice options. Choosing a table reveals the two decks of cards associated with it. Choosing a deck reveals the color of one card. Participants will repeat this for a varying number of trials in each game (game length was drawn from a geometric distribution with parameter 1/44). After the exploration phase, one of the colors will be randomly designated as rewarding, and participants will have to point out the deck with the most rewarding-color cards on each table. After choosing a deck at all four tables, participants report their confidence in the accuracy of each choice on a 1-5 Likert scale.
Before each game, participants are shown the tables for the game, and the decks associated with each table. They are repeatedly tested on the associations on a 2AFC task until achieving perfect accuracy in assigning each deck to the table belonging to it. After each test phase the proportion of color cards for each deck is revealed as a spread of 10 cards, together with accuracy feedback for the test choice.
Participants complete a practice game with only 2 tables at the beginning of the first session.

5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.
We will derive current uncertainty and EIG from an ideal Bayesian observer model of the task.
All models described below will be multilevel, with maximal random effect structure. Regularization priors used: std_normal() for all standardized predictors, normal(0,40) for total uncertainty, and normal(0,3) for the inflection point.
We will fit the following models:

1. A logistic regression model predicting test-phase accuracy from uncertainty after the final trial of the exploration phase.
2. An ordered-logistic regression predicting test-phase confidence ratings from uncertainty after the final trial of the exploration phase, and accuracy of choice (correct/error/no-information).
3. Three logistic regression models, predicting the tendency to choose the table on the right in the exploration phase from the R-L difference in current uncertainty, EIG, and the L-R difference in exposure. We will compare these three models using PSIS-LOO.
4. The models from 3, adding a stay-choice predictor (1 for right table was last chosen, -1 for left), again using PSIS-LOO to compare them.
5. A logistic regression model predicting table choice from the best candidate decision variable, a stay-choice predictor, and a step-wise interaction with total uncertainty (no interaction until an inflection point, after which an interaction occurs. Both interaction and inflection point are free parameters).
6. We will correlate the participant-wise goodness of fit of model 5. with test phase performance.
7. Model 5, without a stay-choice, but including a trial number covariate.
8. Model 5, without a stay-choice, but including a block number covariate.
9. A logistic regression model predicting table choice from the best candidate variable and WM load, operationalized as the minimal number of trials since each of the table options was last chosen. The model will also include the candidate variable x WM load interaction.
10. We will plot reaction times (RTs) as a function of the best candidate variable. We will fit RTs with a lognormal model with total uncertainty and WM load as predictors. We will plot RTs as a function of best candidate variable and stay-choice status.
11. A logistic regression model predicting current choice from best candidate decision variable, stay-choice predictor, and stay-choice predictor for previous trial, and standardized RT predictor for previous trial.

6) Describe exactly how outliers will be defined and handled, and your precise rule(s) for excluding observations.
We will exclude participants who did not finish the task, due to getting more than 10 warnings during the game for very quick responses, missing response deadlines, or interacting with applications outside the experiment.
We will exclude trials aborted due to warnings.
We will exclude participants who didn't choose from both decks - if the average proportion of choosing their favorite deck on each table, weighted by number of trials, was more than 0.8.
We will exclude participants whose memory for deck-table association after a game is not significantly above chance.

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.
Will will collect data until we have 190 participants who satisfy the criteria above. This is 3 times the sample size for the original experiment (N=62), rounded up.

8) Anything else you would like to pre-register?
(e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)
We will fit the RT data with variants of sequential sampling models.