﻿## Derived Indices

The dataset contains three derived indices: **Affect**, **Cognition**, and **Footprint**. All indices are computed from questionnaire items rated on a 4-point Likert scale (`1 = completely disagree`, `4 = completely agree`).

### Affect and Cognition

The Affect index is based on 7 questionnaire items (`Affekt1`–`Affekt7`), and the Cognition index is based on 10 items (`Kognition1`–`Kognition10`).

Responses are first transformed from the original 1–4 Likert scale to a 0–10 scale:

s(x)=\frac{(x-1)\cdot10}{3}

Some items are reverse-coded before aggregation. For reverse-coded items, the transformed score is inverted:

s_{rev}(x)=10-s(x)

The final index value is the arithmetic mean across all valid item scores for a participant/model.

### Footprint

The Footprint index is based on 8 behavioral items (`Verhalten2`–`Verhalten9`) representing activities with different estimated annual CO₂ reduction potentials.

Responses are transformed as follows:

* responses `1` and `2` → `0`
* response `3` → `0.5`
* response `4` → `1`

Equivalent formula:

f(x)=\max\left(0,\frac{x-2}{2}\right)

The transformed responses are multiplied by predefined CO₂ reduction weights (in tons CO₂e per year) and summed:

\mathrm{Footprint}=\sum_i f(x_i)\cdot w_i

with:

`w = [0.2, 0.8, 0.9, 0.5, 1.0, 0.6, 0.8, 0.5]`