rthor 0.2.1
Python implementation of RTHOR (Randomization test of hypothesized order relations)
Requires Python: >=3.11

# rthor

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**rthor** is a Python implementation of RTHOR (Randomization Test of Hypothesized Order Relations), a statistical test for circumplex and circular models in correlation matrices.

## Features

- **Exact Parity with RTHORR**: Produces numerically identical results to the original [RTHORR package](https://github.com/michaellynnmorris/RTHORR)
- **Multiple Input Formats**: Works with files, pandas DataFrames, or numpy arrays
- **Flexible Analysis**: Test single matrices or compare multiple matrices pairwise
- **Fast Performance**: Vectorized operations using NumPy for efficient computation

## Quick Start

```python
import rthor

# Test from correlation matrix file
df = rthor.test(
    "correlations.txt",
    order="circular6",
    n_matrices=3,
    n_variables=6,
    labels=["Sample 1", "Sample 2", "Sample 3"]
)

# View results (returns a pandas DataFrame)
print(df)
```

<div>
<table border="1" class="dataframe">
  <thead>
    <tr style="text-align: right;">
      <th></th>
      <th>matrix</th>
      <th>predictions</th>
      <th>agreements</th>
      <th>ties</th>
      <th>ci</th>
      <th>p_value</th>
      <th>label</th>
      <th>n_permutations</th>
      <th>n_variables</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th>0</th>
      <td>1</td>
      <td>72</td>
      <td>59</td>
      <td>1</td>
      <td>0.652778</td>
      <td>0.016667</td>
      <td>Sample 1</td>
      <td>720</td>
      <td>6</td>
    </tr>
    <tr>
      <th>1</th>
      <td>2</td>
      <td>72</td>
      <td>53</td>
      <td>1</td>
      <td>0.486111</td>
      <td>0.033333</td>
      <td>Sample 2</td>
      <td>720</td>
      <td>6</td>
    </tr>
    <tr>
      <th>2</th>
      <td>3</td>
      <td>72</td>
      <td>56</td>
      <td>3</td>
      <td>0.597222</td>
      <td>0.016667</td>
      <td>Sample 3</td>
      <td>720</td>
      <td>6</td>
    </tr>
  </tbody>
</table>
</div>

```python
df[df['ci'] > 0.5]  # Filter results
```

<div>
<table border="1" class="dataframe">
  <thead>
    <tr style="text-align: right;">
      <th></th>
      <th>matrix</th>
      <th>predictions</th>
      <th>agreements</th>
      <th>ties</th>
      <th>ci</th>
      <th>p_value</th>
      <th>label</th>
      <th>n_permutations</th>
      <th>n_variables</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <th>0</th>
      <td>1</td>
      <td>72</td>
      <td>59</td>
      <td>1</td>
      <td>0.652778</td>
      <td>0.016667</td>
      <td>Sample 1</td>
      <td>720</td>
      <td>6</td>
    </tr>
    <tr>
      <th>2</th>
      <td>3</td>
      <td>72</td>
      <td>56</td>
      <td>3</td>
      <td>0.597222</td>
      <td>0.016667</td>
      <td>Sample 3</td>
      <td>720</td>
      <td>6</td>
    </tr>
  </tbody>
</table>
</div>

```python
# Or print formatted results
rthor.print_results(df)
```

<pre style="white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><span style="font-style: italic">                                   </span><span style="color: #008080; text-decoration-color: #008080; font-weight: bold; font-style: italic">RTHOR Test Results</span><span style="font-style: italic">                                    </span>
<span style="font-style: italic">              </span><span style="color: #7f7f7f; text-decoration-color: #7f7f7f; font-style: italic">3 matrices • 6 variables • 72 predictions • 720 permutations</span><span style="font-style: italic">               </span>
╭──────────────┬────┬───────┬────────────────┬──────────────┬─────────────┬─────────────╮
│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Matrix       </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    CI </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Interpretation </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Significance </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">   Satisfied </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    Violated </span>│
├──────────────┼────┼───────┼────────────────┼──────────────┼─────────────┼─────────────┤
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> [1] Sample 1 </span>│ <span style="color: #00ff00; text-decoration-color: #00ff00">↗</span>  │<span style="font-weight: bold"> </span><span style="color: #00ff00; text-decoration-color: #00ff00; font-weight: bold">0.653</span><span style="font-weight: bold"> </span>│ Good fit       │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #008000; text-decoration-color: #008000"> 59/72 (82%) </span>│<span style="color: #800000; text-decoration-color: #800000"> 12/72 (17%) </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> [2] Sample 2 </span>│ <span style="color: #808000; text-decoration-color: #808000">→</span>  │<span style="font-weight: bold"> </span><span style="color: #808000; text-decoration-color: #808000; font-weight: bold">0.486</span><span style="font-weight: bold"> </span>│ Moderate fit   │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #008000; text-decoration-color: #008000"> 53/72 (74%) </span>│<span style="color: #800000; text-decoration-color: #800000"> 18/72 (25%) </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> [3] Sample 3 </span>│ <span style="color: #00ff00; text-decoration-color: #00ff00">↗</span>  │<span style="font-weight: bold"> </span><span style="color: #00ff00; text-decoration-color: #00ff00; font-weight: bold">0.597</span><span style="font-weight: bold"> </span>│ Good fit       │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #008000; text-decoration-color: #008000"> 56/72 (78%) </span>│<span style="color: #800000; text-decoration-color: #800000"> 13/72 (18%) </span>│
╰──────────────┴────┴───────┴────────────────┴──────────────┴─────────────┴─────────────╯
<span style="color: #7f7f7f; text-decoration-color: #7f7f7f; font-style: italic">                ℹ️  Higher CI values indicate better fit (range: -1 to +1)                </span>
</pre>

### Test from DataFrames

```python
df = rthor.test(
[df1, df2, df3],
order="circular6",
labels=["Group A", "Group B", "Group C"],
print_results=True # Print formatted results automatically
)
```

<pre style="white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><span style="font-style: italic">                                   </span><span style="color: #008080; text-decoration-color: #008080; font-weight: bold; font-style: italic">RTHOR Test Results</span><span style="font-style: italic">                                    </span>
<span style="font-style: italic">              </span><span style="color: #7f7f7f; text-decoration-color: #7f7f7f; font-style: italic">3 matrices • 6 variables • 72 predictions • 720 permutations</span><span style="font-style: italic">               </span>
╭─────────────┬────┬───────┬────────────────┬──────────────┬──────────────┬─────────────╮
│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Matrix      </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    CI </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Interpretation </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Significance </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    Satisfied </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    Violated </span>│
├─────────────┼────┼───────┼────────────────┼──────────────┼──────────────┼─────────────┤
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> [1] Group A </span>│ <span style="color: #00ff00; text-decoration-color: #00ff00">✓</span>  │<span style="font-weight: bold"> </span><span style="color: #00ff00; text-decoration-color: #00ff00; font-weight: bold">1.000</span><span style="font-weight: bold"> </span>│ Excellent fit  │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #008000; text-decoration-color: #008000"> 72/72 (100%) </span>│<span style="color: #800000; text-decoration-color: #800000">   0/72 (0%) </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> [2] Group B </span>│ <span style="color: #00ff00; text-decoration-color: #00ff00">↗</span>  │<span style="font-weight: bold"> </span><span style="color: #00ff00; text-decoration-color: #00ff00; font-weight: bold">0.583</span><span style="font-weight: bold"> </span>│ Good fit       │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #008000; text-decoration-color: #008000">  57/72 (79%) </span>│<span style="color: #800000; text-decoration-color: #800000"> 15/72 (21%) </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> [3] Group C </span>│ <span style="color: #800000; text-decoration-color: #800000">⚠</span>  │<span style="font-weight: bold"> </span><span style="color: #800000; text-decoration-color: #800000; font-weight: bold">0.056</span><span style="font-weight: bold"> </span>│ Minimal fit    │   <span style="color: #7f7f7f; text-decoration-color: #7f7f7f">p=0.433</span>    │<span style="color: #008000; text-decoration-color: #008000">  38/72 (53%) </span>│<span style="color: #800000; text-decoration-color: #800000"> 34/72 (47%) </span>│
╰─────────────┴────┴───────┴────────────────┴──────────────┴──────────────┴─────────────╯
<span style="color: #7f7f7f; text-decoration-color: #7f7f7f; font-style: italic">                ℹ️  Higher CI values indicate better fit (range: -1 to +1)                </span>
</pre>

### Compare multiple matrices

```python
individual, pairwise = rthor.compare(
[df1, df2, df3],
order="circular6",
print_results=True
)
```

<pre style="white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><span style="font-style: italic">                                </span><span style="color: #008080; text-decoration-color: #008080; font-weight: bold; font-style: italic">RTHOR Matrix Comparison</span><span style="font-style: italic">                                </span>
<span style="font-style: italic">             </span><span style="color: #7f7f7f; text-decoration-color: #7f7f7f; font-style: italic">3 matrices • 6 variables • 72 predictions • 720 permutations</span><span style="font-style: italic">              </span>
╭────────────┬────┬────────┬─────────────────┬──────────────┬───────┬────────┬────────╮
│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Comparison </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">    </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">     CI </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Result          </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Significance </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold">  Both </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Only 1 </span>│<span style="color: #008080; text-decoration-color: #008080; font-weight: bold"> Only 2 </span>│
├────────────┼────┼────────┼─────────────────┼──────────────┼───────┼────────┼────────┤
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> Matrix 1   </span>│ <span style="color: #00ff00; text-decoration-color: #00ff00">✓</span>  │<span style="font-weight: bold">  </span><span style="color: #00ff00; text-decoration-color: #00ff00; font-weight: bold">1.000</span><span style="font-weight: bold"> </span>│ Excellent fit   │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #7f7f7f; text-decoration-color: #7f7f7f"> 72/72 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      — </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      — </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> Matrix 2   </span>│ <span style="color: #00ff00; text-decoration-color: #00ff00">↗</span>  │<span style="font-weight: bold">  </span><span style="color: #00ff00; text-decoration-color: #00ff00; font-weight: bold">0.583</span><span style="font-weight: bold"> </span>│ Good fit        │   <span style="color: #008000; text-decoration-color: #008000">p&lt;.05 *</span>    │<span style="color: #7f7f7f; text-decoration-color: #7f7f7f"> 57/72 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      — </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      — </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> Matrix 3   </span>│ <span style="color: #800000; text-decoration-color: #800000">⚠</span>  │<span style="font-weight: bold">  </span><span style="color: #800000; text-decoration-color: #800000; font-weight: bold">0.056</span><span style="font-weight: bold"> </span>│ Minimal fit     │   <span style="color: #7f7f7f; text-decoration-color: #7f7f7f">p=0.433</span>    │<span style="color: #7f7f7f; text-decoration-color: #7f7f7f"> 38/72 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      — </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      — </span>│
├────────────┼────┼────────┼─────────────────┼──────────────┼───────┼────────┼────────┤
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> 1 vs 2     </span>│ <span style="color: #008000; text-decoration-color: #008000">↓</span>  │<span style="font-weight: bold"> </span><span style="color: #008000; text-decoration-color: #008000; font-weight: bold">-0.208</span><span style="font-weight: bold"> </span>│ Matrix 1 better │   <span style="color: #7f7f7f; text-decoration-color: #7f7f7f">p=0.933</span>    │<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">    57 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">     15 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      0 </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> 1 vs 3     </span>│ <span style="color: #008000; text-decoration-color: #008000">↓</span>  │<span style="font-weight: bold"> </span><span style="color: #008000; text-decoration-color: #008000; font-weight: bold">-0.472</span><span style="font-weight: bold"> </span>│ Matrix 1 better │   <span style="color: #7f7f7f; text-decoration-color: #7f7f7f">p=0.983</span>    │<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">    38 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">     34 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      0 </span>│
│<span style="color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold"> 2 vs 3     </span>│ <span style="color: #008000; text-decoration-color: #008000">↓</span>  │<span style="font-weight: bold"> </span><span style="color: #008000; text-decoration-color: #008000; font-weight: bold">-0.264</span><span style="font-weight: bold"> </span>│ Matrix 2 better │   <span style="color: #7f7f7f; text-decoration-color: #7f7f7f">p=0.967</span>    │<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">    37 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">     20 </span>│<span style="color: #7f7f7f; text-decoration-color: #7f7f7f">      1 </span>│
╰────────────┴────┴────────┴─────────────────┴──────────────┴───────┴────────┴────────╯
<span style="color: #7f7f7f; text-decoration-color: #7f7f7f; font-style: italic">   Info: Positive CI means matrix 2 fits better, negative means matrix 1 fits better   </span>
</pre>

## Installation

See [Installation Instructions](docs/installation.md) for more details.

```sh
pip install rthor
```

## What is RTHOR?

RTHOR (Randomization Test of Hypothesized Order Relations) is a statistical method for testing whether correlation matrices conform to a hypothesized ordering of variables [@Tracey2025RTHORR;@Tracey1997RANDALL]. This is particularly useful for:

- **Circumplex Models**: Variables arranged in a circular pattern (e.g., interpersonal behavior, emotions)
- **Circular Structures**: Testing theoretical predictions about variable ordering
- **Correlation Patterns**: Validating expected patterns in correlation matrices

The test uses a randomization approach to compute p-values, comparing the observed Correspondence Index (CI) with values from permuted data. CI ranges from -1 (perfect disagreement) to +1 (perfect agreement).

## Key Functions

### `rthor.test()`

Test whether correlation matrices conform to a hypothesized ordering.

**Parameters:**

- `data`: Input data (file path, list of DataFrames, or numpy array)
- `order`: Hypothesized ordering ("circular6", "circular8", or custom list)
- `labels`: Optional descriptive labels for matrices
- `n_matrices`: Number of matrices (required for file input)
- `n_variables`: Number of variables (required for file input)
- `print_results`: If True, print formatted results table

**Returns:** pandas DataFrame with columns: matrix, predictions, agreements, ties, ci, p_value, label, n_permutations, n_variables

### `rthor.compare()`

Compare multiple correlation matrices pairwise to determine which fits the hypothesis better.

**Parameters:** Same as `rthor.test()` but requires at least 2 matrices

**Returns:** Tuple of two pandas DataFrames: (individual_results, pairwise_comparisons)

## Documentation

Full documentation is available at [https://drandrewmitchell.com/rthor](https://drandrewmitchell.com/rthor)

### Validation Against Original Paper

The implementation has been validated against the original Hubert & Arabie (1987) [@Hubert1987Evaluating] paper. See [docs/examples/paper-validation.py](docs/examples/paper-validation.py) for a detailed demonstration that replicates Table 1 from the paper and confirms exact agreement with the expected results:

- ✓ 72 predictions, 61 agreements, 11 violations
- ✓ p-value = 0.0167 (12/720)
- ✓ CI = 0.694

## Testing

Run tests across all supported Python versions:

```sh
tox
```

Run tests in current environment:

```sh
pytest tests
```

Run tests with coverage:

```sh
pytest --cov --cov-report=xml
```

## Development

This project uses:

- **uv** for dependency management
- **ruff** for linting and formatting
- **pytest** for testing
- **mkdocs** with Material theme for documentation
- **pre-commit** hooks (via prek) for code quality

Install development dependencies:

```sh
uv sync --all-extras
```

Run pre-commit hooks:

```sh
uv run prek run -a
```

Build documentation:

```sh
uv run mkdocs serve
```

## Project Team

**Andrew Mitchell** ([andrew.mitchell.research@gmail.com](mailto:andrew.mitchell.research@gmail.com))

### Research Software Engineering Contact

Centre for Advanced Research Computing, University College London
([arc.collaborations@ucl.ac.uk](mailto:arc.collaborations@ucl.ac.uk))

## Citation

If you use rthor in your research, please cite both this package and the original method paper:

**rthor (Python implementation):**

```bibtex
@software{Mitchell2025rthor,
  author  = {Mitchell, Andrew},
  license = {MIT},
  title   = {{rthor: Python implementation of RTHOR (Randomization test of hypothesized order relations)}},
  url     = {https://github.com/MitchellAcoustics/rthor}
}
```

**Original RTHOR method:**

```bibtex
@article{Hubert1987Evaluating,
  author  = {Hubert, Lawrence and Arabie, Phipps},
  year    = {1987},
  month   = {07},
  pages   = {172-178},
  title   = {Evaluating Order Hypotheses Within Proximity Matrices},
  volume  = {102},
  journal = {Psychological Bulletin},
  doi     = {10.1037/0033-2909.102.1.172}
}
```

**R RTHORR package:**

```bibtex
@software{Tracey2025RTHORR,
  title  = {RTHORR: randomization test of hypothesized order relations (RTHOR) and
            comparisons},
  author = {Terence J. G. Tracey and Michael L. Morris},
  year   = {2025},
  note   = {R package version 0.1.3, commit c3edb36287c77733ec0a23236b478cc53c1cac0f},
  url    = {https://github.com/michaellynnmorris/RTHORR}
}
```

## License

MIT License. See [LICENSE.md](LICENSE.md) for details.

## Acknowledgments

This project is developed in collaboration with the
[Centre for Advanced Research Computing](https://ucl.ac.uk/arc), University College London.

`rthor` is a Python port of the R package RTHORR by Michael B. Gurtman. The implementation maintains exact numerical parity with the original R version while providing a Pythonic interface and improved performance through vectorization.