Acknowledgement

The content of this GitHub repo is a product of a research project funded by Duolingo, Inc. through Competitive Research Grant Program to support topics of interest related to Duolingo's English Test's ongoing research agenda.

Repository Overview

This repository contains the code and resources associated with the following paper:

Zopluoglu, C., Lockwood, J.R. (under review). A Comparative Study of Item Response Theory Models for Mixed Discrete-Continuous Responses. Journal of Intelligence.

For a tutorial-style introduction to the analyses conducted in the paper, please visit:

https://czopluoglu.github.io/Duolingo_paper/

Directory Structure and Contents

1. /data/:

   • Contains simulated datasets in both long and wide formats for the Beta, Simplex, and SB IRT models.

2. /script/beta_irt/:

   • R script for simulating the dataset based on the Beta IRT model.

   • Scripts for fitting the model in Stan and evaluating model fit using posterior predictive checks.

   • Includes the Stan model syntax (beta.stan) and its compiled version for the cmdstanr package.

3. /script/simplex_irt/:

   • R script for simulating the dataset based on the Simplex IRT model.

   • Scripts for fitting the model in Stan and evaluating model fit using posterior predictive checks.

   • Includes the Stan model syntax (simplex.stan) and its compiled version for the cmdstanr package.

4. /script/sb_irt/:

   • R script for simulating the dataset based on the SB IRT model.

   • Scripts for fitting the model in Stan and evaluating model fit using posterior predictive checks.

   • Includes the Stan model syntax (sb.stan) and its compiled version for the cmdstanr package.

5. /docs/:

   • Contains the Rmarkdown file and the rendered HTML for the tutorial page.