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# Nominal/Categorical Metrics
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Statistical measures for analyzing associations and agreements between categorical variables, useful for evaluating classification models and understanding categorical data relationships.
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## Capabilities
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### Association Measures
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Metrics for measuring strength of association between categorical variables.
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```python { .api }
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class CramersV(Metric):
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    def __init__(
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        self,
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        num_classes: int,
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        bias_correction: bool = True,
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        **kwargs
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    ): ...
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class TheilsU(Metric):
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    def __init__(
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        self,
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        num_classes: int,
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        **kwargs
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    ): ...
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class TschuprowsT(Metric):
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    def __init__(
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        self,
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        num_classes: int,
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        bias_correction: bool = True,
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        **kwargs
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    ): ...
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class PearsonsContingencyCoefficient(Metric):
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    def __init__(
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        self,
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        num_classes: int,
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        **kwargs
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    ): ...
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```
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### Agreement Measures
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Metrics for evaluating inter-rater agreement and consistency.
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```python { .api }
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class FleissKappa(Metric):
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    def __init__(
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        self,
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        mode: str = "counts",
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        **kwargs
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    ): ...
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```
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## Usage Examples
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```python
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import torch
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from torchmetrics.nominal import CramersV, FleissKappa, TheilsU
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# Association between two categorical variables
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cramers_v = CramersV(num_classes=3)
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theil_u = TheilsU(num_classes=3)
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# Sample categorical data
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preds = torch.randint(0, 3, (100,))  # Predicted categories
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target = torch.randint(0, 3, (100,))  # True categories
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# Compute association measures
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cv_score = cramers_v(preds, target)
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tu_score = theil_u(preds, target)
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print(f"Cramer's V: {cv_score:.4f}")
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print(f"Theil's U: {tu_score:.4f}")
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# Inter-rater agreement
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fleiss_kappa = FleissKappa(mode="counts")
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# Rating counts: (subjects, categories)
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# Each row represents how many raters assigned each category to a subject
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ratings = torch.tensor([
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    [0, 0, 0, 0, 14],  # Subject 1: all 14 raters chose category 5
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    [0, 2, 6, 4, 2],   # Subject 2: mixed ratings
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    [0, 0, 3, 5, 6],   # Subject 3: mixed ratings
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])
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kappa_score = fleiss_kappa(ratings)
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print(f"Fleiss' Kappa: {kappa_score:.4f}")
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```
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## Types
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```python { .api }
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CategoricalData = Tensor  # Integer categorical labels
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RatingCounts = Tensor     # Inter-rater agreement count matrix
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```