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

Local Influence and outlier measures (experimental)

This currently subclasses GLMInfluence instead of the other way. No common superclass yet. This is another version before checking what is common

resultsinstance of results class

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

other arguments are only 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 produces the same results as GLMInfluence (verified for GLM Binomial and Gaussian). There will be some differences for non-canonical links or if a robust cov_type is used.

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.

d_paramsChange in parameters computed with one Newton step using the

full Hessian corrected by division by (1 - hii).

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.


Creates a DataFrame with influence results.



Cook's distance and p-values


Change in expected response, fittedvalues


Change in fittedvalues scaled by standard errors


Change in parameter estimates


Scaled change in parameter estimates


Diagonal of the generalized leverage


Parameter estimate based on one-step approximation


Score residual divided by sqrt of hessian factor