class statsmodels.stats.outliers_influence.MLEInfluence(results, resid=None, endog=None, exog=None, hat_matrix_diag=None, cov_params=None, scale=None)[source]

Global Influence and outlier measures (experimental)

resultsinstance of results class

This only works for model and results classes that have the necessary helper methods.

other arguments

Those are only available to override default behavior and are used instead of the corresponding attribute of the results class. By default resid_pearson is used as resid.


MLEInfluence uses generic definitions based on maximum likelihood models.

MLEInfluence produces the same results as GLMInfluence for canonical links (verified for GLM Binomial, Poisson and Gaussian). There will be some differences for non-canonical links or if a robust cov_type is used. For example, the generalized leverage differs from the definition of the GLM hat matrix in the case of Probit, which corresponds to family Binomial with a non-canonical link.

The extension to non-standard models, e.g. multi-link model like BetaModel and the ZeroInflated models is still experimental and might still change. Additonally, ZeroInflated and some threshold models have a nondifferentiability in the generalized leverage. How this case is treated might also change.

Warning: This does currently not work for constrained or penalized models, e.g. models estimated with fit_constrained or fit_regularized.

This has not yet been tested for correctness when offset or exposure are used, although they should be supported by the code.

status: experimental, This class will need changes to support different kinds of models, e.g. extra parameters in discrete.NegativeBinomial or two-part models like ZeroInflatedPoisson.

hat_matrix_diag (hii)This is the generalized leverage computed as the

local derivative of fittedvalues (predicted mean) with respect to the observed response for each observation. Not available for ZeroInflated models because of nondifferentiability.

d_paramsChange in parameters computed with one Newton step using the

full Hessian corrected by division by (1 - hii). If hat_matrix_diag is not available, then the division by (1 - hii) is not included.

dbetaschange in parameters divided by the standard error of parameters

from the full model results, bse.

cooks_distancequadratic form for change in parameters weighted by

cov_params from the full model divided by the number of variables. It includes p-values based on the F-distribution which are only approximate outside of linear Gaussian models.

resid_studentizedIn the general MLE case resid_studentized are

computed from the score residuals scaled by hessian factor and leverage. This does not use cov_params.

d_fittedvalueslocal change of expected mean given the change in the

parameters as computed in d_params.

d_fittedvalues_scaledsame as d_fittedvalues but scaled by the standard

Change in fittedvalues scaled by standard errors.

params_oneis the one step parameter estimate computed as params

from the full sample minus d_params.


plot_index([y_var, threshold, title, ax, idx])

index plot for influence attributes

plot_influence([external, alpha, criterion, ...])

Plot of influence in regression.

resid_score([joint, index, studentize])

Score observations scaled by inverse hessian.


Score residual divided by sqrt of hessian factor.


Creates a DataFrame with influence results.



Cook's distance and p-values.


Change in expected response, fittedvalues.


Change in fittedvalues scaled by standard errors.


Approximate change in parameter estimates when dropping observation.


Scaled change in parameter estimates.


Diagonal of the generalized leverage


Diagonal of the hat_matrix using only exog as in OLS


Parameter estimate based on one-step approximation.


studentized default residuals.

Last update: Jul 16, 2024