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# Probit Models
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Spatial probit regression for binary choice models with spatial dependence, supporting various spatial structures and diagnostic tests.
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## Capabilities
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### Spatial Probit Model
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```python { .api }
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class Probit:
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    def __init__(self, y, x, w=None, optim='newton', scalem='phimean', maxiter=100,
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                 vm=False, name_y=None, name_x=None, name_w=None, name_ds=None,
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                 latex=False, hard_bound=False):
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        """
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        Spatial probit regression for binary dependent variables.
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        Parameters:
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        - y (array): nx1 binary dependent variable (0/1)
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        - x (array): nxk independent variables
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        - w (sparse matrix, optional): Spatial weights for spatial probit
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        - optim (str): Optimization method ('newton' or 'bfgs')
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        - scalem (str): Scale method ('phimean' or 'xmean')
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        - maxiter (int): Maximum iterations for optimization
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        - vm (bool): Include variance-covariance matrix
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        - hard_bound (bool): Enforce spatial parameter bounds
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        Attributes:
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        - betas (array): Estimated coefficients
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        - rho (float): Spatial dependence parameter (if spatial)
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        - logl (float): Log-likelihood value
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        - predy (array): Predicted probabilities
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        - summary (str): Formatted results
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        """
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```
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## Usage Examples
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### Basic Probit Model
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```python
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import numpy as np
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import spreg
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# Binary dependent variable
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n = 100
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x = np.random.randn(n, 2)
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linear_combo = 1 + x[:, 0] + 2 * x[:, 1] + np.random.randn(n)
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y = (linear_combo > 0).astype(int).reshape(-1, 1)
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# Probit estimation
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probit_model = spreg.Probit(y, x, name_y='choice', name_x=['x1', 'x2'])
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print(probit_model.summary)
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```