gkwreg (version 2.1.6)

ImpreciseTask: Imprecise Probabilities for Sunday Weather and Boeing Stock Task

Description

Data from a cognitive psychology experiment where participants estimated upper and lower probabilities for events to occur and not to occur. The study examines judgment under uncertainty with imprecise probability assessments.

Usage

ImpreciseTask

Format

A data frame with 242 observations on 3 variables:

task

factor with levels Boeing stock and Sunday weather. Indicates which task the participant performed.

location

numeric. Average of the lower estimate for the event not to occur and the upper estimate for the event to occur (proportion).

difference

numeric. Difference between upper and lower probability estimates, measuring imprecision or uncertainty.

Details

All participants in the study were either first- or second-year undergraduate students in psychology at Australian universities, none of whom had a strong background in probability theory or were familiar with imprecise probability theories.

For the Sunday weather task, participants were asked to estimate the probability that the temperature at Canberra airport on Sunday would be higher than a specified value.

For the Boeing stock task, participants were asked to estimate the probability that Boeing's stock would rise more than those in a list of 30 companies.

For each task, participants were asked to provide lower and upper estimates for the event to occur and not to occur.

References

Smithson, M., Merkle, E.C., and Verkuilen, J. (2011). Beta Regression Finite Mixture Models of Polarization and Priming. Journal of Educational and Behavioral Statistics, 36(6), 804--831. tools:::Rd_expr_doi("10.3102/1076998610396893")

Smithson, M., and Segale, C. (2009). Partition Priming in Judgments of Imprecise Probabilities. Journal of Statistical Theory and Practice, 3(1), 169--181.

Examples

# \donttest{
require(gkwreg)
require(gkwdist)

data(ImpreciseTask)

# Example 1: Basic model with task effects
# Probability location varies by task type and uncertainty level
fit_kw <- gkwreg(location ~ task * difference,
  data = ImpreciseTask,
  family = "kw"
)
summary(fit_kw)

# Interpretation:
# - Alpha: Task type and uncertainty (difference) interact to affect
#   probability estimates
# - Different tasks may have different baseline probability assessments

# Example 2: Heteroscedastic model
# Precision of estimates may vary by task and uncertainty
fit_kw_hetero <- gkwreg(
  location ~ task * difference |
    task + difference,
  data = ImpreciseTask,
  family = "kw"
)
summary(fit_kw_hetero)

# Interpretation:
# - Beta: Variability in estimates differs between tasks
#   Higher uncertainty (difference) may lead to less precise estimates

# Example 3: McDonald distribution for extreme uncertainty
# Some participants may show very extreme probability assessments
fit_mc <- gkwreg(
  location ~ task * difference | # gamma: full interaction
    task * difference | # delta: full interaction
    task, # lambda: task affects extremity
  data = ImpreciseTask,
  family = "mc",
  control = gkw_control(
    method = "BFGS",
    maxit = 1500
  )
)
summary(fit_mc)

# Interpretation:
# - Lambda varies by task: Weather vs. stock may produce
#   different patterns of extreme probability assessments
# }