Commit de40914e authored by linushof's avatar linushof
Browse files

Revised Method section

parent c8ee5ed2
......@@ -15,8 +15,6 @@ output:
# load packages
pacman::p_load(repro,
tidyverse,
R2jags,
mcmcplots,
knitr)
```
......@@ -27,11 +25,12 @@ pacman::p_load(repro,
# Abstract
Synthetic choice data from decisions from experience (DfE) is generated by applying different strategies of sample integration to 2-prospect gambles. The synthetic data is explored for characteristic choice patterns produced by comprehensive and piecewise forms of sample integration under varying structures of the environment (prospect features) and aspects of the sampling- and decision behavior (model parameters).
Synthetic choice data from decisions from experience (DfE) is generated by applying different strategies of sample integration to 2-prospect gambles.
The synthetic data is explored for characteristic choice patterns produced by comprehensive and piecewise forms of sample integration under varying structures of the environment (gamble features) and aspects of the sampling- and decision behavior (model parameters).
# Summary
Provide short summary of pilot study results.
Provide short summary of simulation study results.
# Introduction
......@@ -41,27 +40,29 @@ A formal introduction to sampling in DfE and the data generating models of this
## Test set
Under each condition, i.e., strategy-parameter combinations, all gambles are played by 100 synthetic agents. We test a set of gambles, in which one of the prospects contains a safe outcome and the other two risky outcomes (*safe-risky gambles*). Therefore, 60 gambles from an initial set of 10,000 are sampled. Both, outcomes and probabilities are drawn from uniform distributions, ranging from 0 to 20 for outcomes and from .01 to .99 for probabilities of the lower risky outcomes $p_{low}$. The probabilities of the higher risky outcomes are $1-p_{low}$, respectively. To omit dominant prospects, safe outcomes fall between both risky outcomes. The table below contains the test set of 60 gambles. Sampling of gambles was stratified, randomly drawing an equal number of 20 gambles with no, an attractive, and an unattractive rare outcome. Risky outcomes are considered *"rare"* if their probability is $p < .2$ and *"attractive"* (*"unattractive"*) if they are higher (lower) than the safe outcome.
Under each condition, i.e., strategy-parameter combinations, all gambles are played by 100 synthetic agents. We test a set of gambles, in which one of the prospects contains a safe outcome and the other two risky outcomes (*safe-risky gambles*).
Therefore, 60 gambles from an initial set of 10,000 are sampled.
Both outcomes and probabilities are drawn from uniform distributions, ranging from 0 to 20 for outcomes and from .01 to .99 for probabilities of the lower risky outcomes $p_{low}$.
The probabilities of the higher risky outcomes are $1-p_{low}$, respectively.
To omit dominant prospects, safe outcomes fall between both risky outcomes.
The table below contains the test set of 60 gambles.
Sampling of gambles was stratified, randomly drawing an equal number of 20 gambles with no, an attractive, and an unattractive rare outcome. Risky outcomes are considered *"rare"* if their probability is $p < .2$ and *"attractive"* (*"unattractive"*) if they are higher (lower) than the safe outcome.
```{r}
sr_subset <- read_csv("./data/gambles/sr_subset.csv")
sr_subset <- read_csv("data/gambles/sr_subset.csv")
kable(sr_subset)
```
## Model Parameters
**Switching probability** $s$ is the probability increment added to the unbiased probability $p = .5$ with which agents draw the succesive single sample from the same prospect they get their most recent single sample from.
$s$ is varied between -.5 to .4 in increments of .1. To ease interpretation during data analysis, $s$ is transformed by $s_{rec}= 1-(p + s)$ after the simulation such that it ranges from .1 to 1.
**Switching probability** $s$ is the probability with which agents draw the following single sample from the prospect they did not get their most recent single sample from.
$s$ is varied between .1 to 1 in increments of .1.
The **boundary type** is either the minimum value any prospect's sample statistic must reach (absolute) or the minimum value for the difference of these statistics (relative).
Sample statistics are sums over outcomes (comprehensive strategy) and sums over wins (piecewise strategy), respectively.
For comprehensive integration, the **boundary value** $a$ is varied between 15 to 80 in increments of 5.
For piecewise integration $a$ is varied between 1 to 7 in increments of 2.
Representations of the sampled outcomes are assumed to be stochastical.
Therefore, **Gaussian noise** $\epsilon \sim N(0, \sigma)$ in units of outcomes is added.
To reduce computational load, $\sigma$ is fixed to .5.
For comprehensive integration, the **boundary value** $a$ is varied between 15 to 75 in increments of 15.
For piecewise integration $a$ is varied between 1 to 5 in increments of 1.
# Results
......
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