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# Diagnostic Functions
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Comprehensive diagnostic testing for spatial autocorrelation, heteroskedasticity, normality, multicollinearity, and model specification in spatial regression contexts.
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## Capabilities
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### Spatial Diagnostic Tests
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```python { .api }
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class LMtests:
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    def __init__(self, ols, w, tests=["all"]):
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        """
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        Lagrange Multiplier tests for spatial dependence.
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        Parameters:
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        - ols: OLS regression object
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        - w: Spatial weights object
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        - tests: list of strings specifying which tests to run
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            * 'all': runs all tests (default)
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            * 'lme': LM error test  
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            * 'rlme': Robust LM error test
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            * 'lml': LM lag test
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            * 'rlml': Robust LM lag test
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            * 'sarma': LM SARMA test
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            * 'lmwx': LM test for WX
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            * 'rlmwx': Robust LM WX test
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            * 'lmspdurbin': Joint test for SDM
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            * 'rlmdurlag': Robust LM Lag - SDM
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        Attributes:
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        - lme: tuple (statistic, p-value) for LM error test
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        - lml: tuple (statistic, p-value) for LM lag test
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        - rlme: tuple (statistic, p-value) for Robust LM error test
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        - rlml: tuple (statistic, p-value) for Robust LM lag test
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        - sarma: tuple (statistic, p-value) for SARMA test
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        - lmwx: tuple (statistic, p-value) for LM WX test
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        - rlmwx: tuple (statistic, p-value) for Robust LM WX test
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        - lmspdurbin: tuple (statistic, p-value) for Joint SDM test
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        - rlmdurlag: tuple (statistic, p-value) for Robust LM Lag - SDM test
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        """
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class MoranRes:
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    def __init__(self, ols, w, z=False):
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        """
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        Moran's I test for spatial autocorrelation in residuals.
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        Parameters:
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        - ols: OLS regression object
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        - w: Spatial weights object
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        - z: boolean, if True computes eI, vI and zI attributes
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        Attributes:
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        - I: float, Moran's I statistic
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        - eI: float, Moran's I expectation (if z=True)
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        - vI: float, Moran's I variance (if z=True)  
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        - zI: float, Moran's I standardized value (if z=True)
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        """
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class AKtest:
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    def __init__(self, iv, w, case='nosp'):
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        """
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        Anselin-Kelejian test for spatial dependence in IV residuals.
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        Parameters:
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        - iv: TSLS regression object
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        - w: Spatial weights object
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        - case: string, 'nosp' for no spatial endogenous regressors, 'gen' for general case
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        Attributes:
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        - mi: float, Moran's I statistic for IV residuals
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        - ak: float, Square of corrected Moran's I
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        - p: float, P-value of the test
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        """
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```
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### General Diagnostic Tests
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```python { .api }
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def jarque_bera(reg):
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    """Jarque-Bera test for normality of residuals."""
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def breusch_pagan(reg):
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    """Breusch-Pagan test for heteroskedasticity."""
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def white(reg):
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    """White test for heteroskedasticity."""
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def koenker_bassett(reg):
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    """Koenker-Bassett test for heteroskedasticity."""
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def vif(reg):
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    """Variance Inflation Factor for multicollinearity detection."""
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def f_stat(reg, z_stat=False):
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    """F-statistic or Wald statistic for overall model significance."""
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def t_stat(reg, z_stat=False):
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    """t-statistics or z-statistics for individual coefficients."""
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```
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## Usage Examples
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### Spatial Diagnostic Testing
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```python
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import numpy as np
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import spreg
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from libpysal import weights
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# OLS model for testing
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n = 100
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x = np.random.randn(n, 2)
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y = np.random.randn(n, 1)
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w = weights.KNN.from_array(np.random.randn(n, 2), k=5)
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ols_model = spreg.OLS(y, x, nonspat_diag=False, spat_diag=False)
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# Manual spatial diagnostic testing
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lm_tests = spreg.LMtests(ols_model, w)
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print("LM Error test:", lm_tests.lme)
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print("LM Lag test:", lm_tests.lml)
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print("Robust LM Error:", lm_tests.rlme)
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print("Robust LM Lag:", lm_tests.rlml)
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print("SARMA test:", lm_tests.sarma)
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# Decision rule for spatial dependence
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if lm_tests.lme[1] < 0.05 and lm_tests.lml[1] < 0.05:
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    if lm_tests.rlme[1] < lm_tests.rlml[1]:
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        print("Spatial error model recommended")
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    else:
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        print("Spatial lag model recommended")
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# Moran's I test on residuals
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moran_test = spreg.MoranRes(ols_model, w, z=True)
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print(f"Moran's I: {moran_test.I}, Z-score: {moran_test.zI}")
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# For TSLS models, use AKtest
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tsls_model = spreg.TSLS(y, x[:,:1], x[:,1:2], x[:,1:2])  # Simple IV example
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ak_test = spreg.AKtest(tsls_model, w)
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print(f"AK test statistic: {ak_test.ak}, p-value: {ak_test.p}")
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```