betareg (version 3.2-1)

MockJurors: Confidence of Mock Jurors in Their Verdicts

Description

Data with responses of naive mock jurors to the conventional conventional two-option verdict (guilt vs. acquittal) versus a three-option verdict setup (the third option was the Scottish 'not proven' alternative), in the presence/absence of conflicting testimonial evidence.

Usage

data("MockJurors", package = "betareg")

Format

A data frame containing 104 observations on 3 variables.

verdict

factor indicating whether a two-option or three-option verdict is requested. (A sum contrast rather than treatment contrast is employed.)

conflict

factor. Is there conflicting testimonial evidence? (A sum contrast rather than treatment contrast is employed.)

confidence

jurors degree of confidence in his/her verdict, scaled to the open unit interval (see below).

Details

The data were collected by Daily (2004) among first-year psychology students at Australian National University. Smithson and Verkuilen (2006) employed the data scaling the original confidence (on a scale 0--100) to the open unit interval: ((original_confidence/100) * 103 - 0.5) / 104.

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 MockJurors.

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 Unpublished honors thesis, The Australian National University, Canberra.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, Verkuilen J (2006). A Better Lemon Squeezer? Maximum-Likelihood Regression with Beta-Distributed Dependent Variables. Psychological Methods, 11(7), 54--71.

See Also

betareg, ReadingSkills, StressAnxiety

Examples

data("MockJurors", package = "betareg")
library("lmtest")

## Smithson & Verkuilen (2006, Table 1)
## variable dispersion model
## (NOTE: numerical rather than analytical Hessian is used for replication,
##  Smithson & Verkuilen erroneously compute one-sided p-values)
mj_vd <- betareg(confidence ~ verdict * conflict | verdict * conflict,
  data = MockJurors, hessian = TRUE)
summary(mj_vd)

## model selection for beta regression: null model, fixed dispersion model (p. 61)
mj_null <- betareg(confidence ~ 1 | 1, data = MockJurors)
mj_fd <-   betareg(confidence ~ verdict * conflict | 1, data = MockJurors)
lrtest(mj_null, mj_fd)
lrtest(mj_null, mj_vd)
## McFadden's pseudo-R-squared
1 - as.vector(logLik(mj_null)/logLik(mj_vd))

## visualization
if(require("lattice")) {
  histogram(~ confidence | conflict + verdict, data = MockJurors,
    col = "lightgray", breaks = 0:10/10, type = "density")
}

## see demo("SmithsonVerkuilen2006", package = "betareg") for more details