AFM simulations

This repo contains the code used in PhD thesis Exploring Statistical Biases in Educational Data: A Simulation-Based Approach. It consists of the following four main part.

1. Custom implementation of Additive Factors Model (AFM).
2. Implementation of simulation framework.
3. Description of scenarios in JSON format.
4. Analysis scripts that produce various figures.

How to use

This repository is also a Python package managed by Poetry. The easiest way to run the code is to install poetry package

pip install poetry

install the package

poetry install

and run one of the available scripts

poetry run figure-X-Y

that reproduce figures from the thesis.

Available scripts

Parameter stability

• Scripts figure-3-2 and figure-3-3 reproduce heatmaps from section about stability of estimated AFM parameters. Some of these heatmaps are shown in Figure 3.2 and Figure 3.3.

Effects of cheating

• Script figure-4-1 reproduces scatter plots of estimated β and γ parameters with increasing number of cheating students shown in Figure 4.1.
• Script figure-4-2 reproduces histograms with estimate student α parameters as seen in Figure 4.2.
• Script figure-4-3 reproduces learning curves shown in Figure 4.3.

Effects of item ordering

• Script figure-5-3 reproduces scatter plots with estimated β and γ parameters under fixed and random item ordering depicted in Figure 5.3.
• Script figure-5-4 reproduces barplots with various performance metrics comparing performance of AFM with correct and misspecified Q-matrix from Figure 5.4.
• Script figure-5-5 reproduces scatter plots showing detailed estimated values of β and γ parameters for AFM with correct and misspecified Q-matrix from Figure 4.2.