---
title: "Scoring the Probability Discounting Questionnaire (PDQ)"
author: "Brent Kaplan"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Scoring the Probability Discounting Questionnaire (PDQ)}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 7, fig.height = 4.2)
library(beezdiscounting)
```

The 30-item Probability Discounting Questionnaire (PDQ; Madden, Petry, &
Johnson, 2009) measures preference between smaller guaranteed rewards and
larger probabilistic rewards. Items form three 10-question blocks (\$20 for
sure vs. a chance of \$80, \$40 vs. \$100, and \$40 vs. \$60), each an
ascending ladder of discount rates (h) at indifference under the
hyperbolic odds-against model V = A / (1 + h * theta), where
theta = (1 - p) / p (Rachlin, Raineri, & Cross, 1991).

## Scoring

`score_pdq()` expects long-form data with `subjectid`, `questionid`
(1-30, the administered order), and `response` (0 = guaranteed,
1 = risky). Each block is scored independently by the same
consistency-maximization algorithm used for the MCQ; the implementation
reproduces the Gray et al. (2016) scoring syntax for every possible
response pattern.

```{r score}
score_pdq(pdq)
```

`block1_h`-`block3_h` are the per-block discount rates; `mean_h` is the
arithmetic mean recommended by Gray et al. (2016) and `geomean_h` the
geometric mean. `block*_proportion` is the risky choice ratio (RCR).
`overall_h` is a beezdiscounting extension. The published scoring has
no overall 30-item ladder, so `overall_h` pools all 30 items into a
single ascending ladder and applies the same consistency-maximization
(see `?score_pdq` for the pooling conventions); prefer `mean_h` when
following the published scoring exactly. Gray et al. recommend excluding
subjects below 80% consistency on any block.

## Proportions by h rank

`prop_sc()` reports the proportion choosing the *guaranteed* reward at
each h rank (the complement of the risky choice ratio above).

```{r prop-sc}
prop_sc(pdq)
plot(prop_sc(pdq))
```

## Trial-level modeling bridge

`pdq_to_choice()` reshapes responses into one row per choice with the
item design attached (including `theta`, the odds against winning),
ready for trial-level modeling of probability discounting:

```{r to-choice}
head(pdq_to_choice(pdq))
```

## The item design

```{r lookup}
get_lookup_table(instrument = "pdq")
```

## References

Gray, J. C., Amlung, M. T., Palmer, A. A., & MacKillop, J. (2016). Syntax
for calculation of discounting indices from the monetary choice
questionnaire and probability discounting questionnaire. *Journal of the
Experimental Analysis of Behavior, 106*(2), 156-163.

Madden, G. J., Petry, N. M., & Johnson, P. S. (2009). Pathological
gamblers discount probabilistic rewards less steeply than matched
controls. *Experimental and Clinical Psychopharmacology, 17*(5), 283-290.

Rachlin, H., Raineri, A., & Cross, D. (1991). Subjective probability and
delay. *Journal of the Experimental Analysis of Behavior, 55*(2), 233-244.