APD: Average Proportional Distance for Item Analysis from Scales

The APD package provides functions to compute the Average Proportional Distance, a measure of internal consistency based on pairwise proportional differences between item scores.
This approach focuses on the average discrepancy between item responses (in agreement with Sturman et al., 2009) and complements inter-item correlation average indices.

Features

• Compute Average Proportional Distance (APD) for item sets.
• Supports bootstrap confidence intervals for APD.
• Provides group comparisons based on confidence intervals of the difference (MOVER method).
• Computes average inter–item correlation and group comparison, more equivalent indices.

Installation

You can install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("cmerinos/APD")

Example

###### Example 1 ######
library(APD)

## Toy data: 10 persons x 5 items
set.seed(123)
dat.example1 <- matrix(sample(1:5, 50, replace = TRUE), ncol = 5)

## compute APD
APD(dat.example1, ncat = 5, ci = TRUE, level = 0.95, B = 500)

###### Example 2 ######
library(psych)

## Loading data
data("bfi")

## Choosing variables (Neuroticism factor items, more demographics)
data.bfi <- bfi[, c("N1", "N2", "N3", "N4", "N5", "gender", "age")]

## Clean for missing values
data.bfi <- data.bfi[complete.cases(data.bfi), ]


## APD for total sample
APD(data = data.bfi[, 1:5],
      ncat = 5, 
      ci = T, 
      B = 500, 
      cimethod = "perc",
      conf.level = .95)

## Item-level APD
APDitem(data = data.bfi[, 1:5], group = data.bfi$gender, 
        ncat = 5, 
        ci = T)

## Inter-item average correlation (iia) for total sample
iiacor(data = data.bfi[, 1:5])

## APD and iia for sex groups
data.bfi$gender <- as.factor(data.bfi$gender)

APDmg(data = data.bfi[, 1:5],
      ncat = 5, 
      ci = T, 
      B = 1000, 
      cimethod = "perc",
      group = data.bfi$gender, 
      conf.level = .95)

iiacor(data = data.bfi[, 1:5], group = data.bfi$gender)


## APD and iia for customized age groups
DescTools::Freq(data.bfi$age)

table(cut(data.bfi$age, breaks = c(0, 20, 30, 40, 50, 90)))

data.bfi$age4lev <- cut(data.bfi$age, breaks = c(0, 20, 30, 40, 50, 90))

APDmg(data = data.bfi[, 1:5],
      ncat = 5, 
      ci = T, 
      B = 500, 
      cimethod = "perc",
      group = data.bfi$age4lev, 
      conf.level = .95)


iiacor(data = data.bfi[, 1:5], 
       group = data.bfi$age4lev, 
       nboot = 500)

Package Structure

• APD() – Compute Average Proportional Distance, for total group.
• APDmg() – Compute Average Proportional Distance for multiple groups.
• APDitem() – Compute item-level Average Proportional Distance (APD).
• APDitemmg() – Compute item-level Average Proportional Distance (APD).
• aiicor() – Inter–item average, total and multigroup, more supplementary information.
• rmsiic() – Root-Mean-Square Inter-Item Correlation, based on the squared correlation matrix.
• aiicorEigen() – the average inter-item association and equivalent first eigenvalue.

Citation

If you use this package, please cite:

Merino Soto C (2026). APD: Average Proportional Distance for Item Analysis from Scales. R package version 0.3.0, https://github.com/cmerinos/APD.

You can also obtain the citation in R:

citation("APD")

References

Sturman, D., Cribbie, R. A., & Flett, G. L. (2009).
The average distance between item values: A novel approach for estimating internal consistency.
Educational and Psychological Measurement, 69(6), 913–932. https://doi.org/10.1177/0734282908330937

Briggs, S.R. and Cheek, J.M. (1986).
The role of factor analysis in the development and evaluation of personality scales.
Journal of Personality, 54, 106–148. https://doi.org/10.1111/j.1467-6494.1986.tb00391.x

Clark, L. A., & Watson, D. (1995).
Constructing validity: Basic issues in objective scale development.
Psychological Assessment, 7(3), 309–319. https://doi.org/10.1037/1040-3590.7.3.309

Piedmont, R.L. (2014). Inter-item correlations.
In A.C. Michalos (Ed.), Encyclopedia of Quality of Life and Well-Being Research.
Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0753-5_1493

License

This package is released under the MIT License.