gkwreg (version 2.1.6)

MockJurors: Confidence of Mock Jurors in Their Verdicts

Description

Data from a study examining factors that influence mock juror confidence in verdicts for criminal trials. The experiment manipulates verdict options (two-option vs. three-option) and presence of conflicting testimonial evidence.

Usage

MockJurors

Format

A data frame with 104 observations on 3 variables:

confidence

numeric. Juror confidence in their verdict, scaled to the open unit interval (0, 1). Original scale was 0-100.

verdict

factor indicating whether a two-option verdict (guilty vs. acquittal) or three-option verdict (with Scottish 'not proven' alternative) was requested. Sum contrast coding is employed.

conflict

factor. Is there conflicting testimonial evidence? Values are no or yes. Sum contrast coding is employed.

Details

The data were collected by Deady (2004) among first-year psychology students at Australian National University. The experiment examined how the availability of a third verdict option ('not proven') and conflicting evidence affect juror confidence.

Smithson and Verkuilen (2006) employed the data, scaling the original confidence (on a scale 0-100) to the open unit interval using the transformation: ((original_confidence/100) * 103 - 0.5) / 104.

Important note: The original coding of conflict in the data provided from Smithson's homepage is -1/1 which Smithson and Verkuilen (2006) describe to mean no/yes. However, all their results (sample statistics, histograms, etc.) suggest that it actually means yes/no, which was employed in the corrected MockJurors dataset.

References

Deady, S. (2004). The Psychological Third Verdict: 'Not Proven' or 'Not Willing to Make a Decision'? Unpublished honors thesis, The Australian National University, Canberra.

Smithson, M., and Verkuilen, J. (2006). A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables. Psychological Methods, 11(1), 54--71.

Examples

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

data(MockJurors)

# Example 1: Main effects model with heteroscedasticity
# Confidence depends on verdict options and conflicting evidence
# Variability may also depend on these factors
fit_kw <- gkwreg(
  confidence ~ verdict + conflict |
    verdict * conflict,
  data = MockJurors,
  family = "kw"
)
summary(fit_kw)

# Interpretation:
# - Alpha (mean): Additive effects of verdict type and conflict
#   Three-option verdicts may reduce confidence
#   Conflicting evidence reduces confidence
# - Beta (precision): Interaction suggests confidence variability
#   depends on combination of verdict options and evidence type

# Example 2: Full interaction in mean model
fit_kw_interact <- gkwreg(
  confidence ~ verdict * conflict |
    verdict * conflict,
  data = MockJurors,
  family = "kw"
)
summary(fit_kw_interact)

# Interpretation:
# - Full interaction: Third verdict option may have different effects
#   depending on whether evidence is conflicting

# Test interaction significance
anova(fit_kw, fit_kw_interact)

# Example 3: McDonald distribution for extreme confidence patterns
# Jurors may show very high confidence (ceiling effects) or very low
# confidence depending on conditions
fit_mc <- gkwreg(
  confidence ~ verdict * conflict | # gamma: full interaction
    verdict * conflict | # delta: full interaction
    verdict + conflict, # lambda: additive extremity effects
  data = MockJurors,
  family = "mc",
  control = gkw_control(
    method = "BFGS",
    maxit = 1500,
    reltol = 1e-8
  )
)
summary(fit_mc)

# Interpretation:
# - Lambda: Models asymmetry and extreme confidence
#   Some conditions produce more polarized confidence (very high or very low)

# Example 4: Exponentiated Kumaraswamy alternative
fit_ekw <- gkwreg(
  confidence ~ verdict * conflict | # alpha
    verdict + conflict | # beta
    conflict, # lambda: conflict affects extremity
  data = MockJurors,
  family = "ekw",
  control = gkw_control(
    method = "BFGS",
    maxit = 1500
  )
)
summary(fit_ekw)

# Compare 3-parameter models
AIC(fit_ekw, fit_mc)
# }