statsmodels.stats.outliers_influence.OLSInfluence#

class statsmodels.stats.outliers_influence.OLSInfluence(results)[source]#

Class to calculate outlier and influence measures for OLS result

Parameters:

resultsRegressionResults: currently assumes the results are from an OLS regression

Attributes:

cooks_distance

Cook’s distance

Uses original results, no nobs loop

Based on:

Eubank, R. L. (1999). Nonparametric regression and spline: smoothing. CRC press.
Cook’s distance. (n.d.). In Wikipedia. July 2019, from: https://en.wikipedia.org/wiki/Cook%27s_distance

cov_ratio

covariance ratio between LOOO and original

This uses determinant of the estimate of the parameter covariance from leave-one-out estimates. requires leave one out loop for observations

det_cov_params_not_obsi

determinant of cov_params of all LOOO regressions

dfbeta

dfbeta

uses results from leave-one-observation-out loop

dfbetas

dfbetas

uses results from leave-one-observation-out loop

dffits

dffits measure for influence of an observation

dffitsfloat: The dffits measure for each observation, which is a measure of the influence of a single data point on the predicted value of a model.
dffits_thresholdfloat: The threshold to determine if the influence of an observation is large. The threshold is 2 * sqrt(k / n).

based on resid_studentized_external, uses results from leave-one-observation-out loop.

It is recommended that observations with dffits large than a threshold of 2 sqrt{k / n} where k is the number of parameters, should be investigated.

Based on Wikipedia

dffits_internal

dffits measure for influence of an observation

based on resid_studentized_internal uses original results, no nobs loop

ess_press

Error sum of squares of PRESS residuals

hat_diag_factor

Factor of diagonal of hat_matrix used in influence

this might be useful for internal reuse h / (1 - h)

hat_matrix_diag

Diagonal of the hat_matrix for OLS

influence

Influence measure

matches the influence measure that gretl reports u * h / (1 - h) where u are the residuals and h is the diagonal of the hat_matrix

params_not_obsi

parameter estimates for all LOOO regressions

resid_press

PRESS residuals

resid_std

estimate of standard deviation of the residuals

See also resid_var.

resid_studentized

Studentized residuals using variance from OLS

alias for resid_studentized_internal for compatibility with MLEInfluence. This uses sigma from original estimate and does not require leave one out loop

resid_studentized_external

Studentized residuals using LOOO variance

this uses sigma from leave-one-out estimates

requires leave one out loop for observations

resid_studentized_internal

Studentized residuals using variance from OLS

this uses sigma from original estimate does not require leave one out loop

resid_var

estimate of variance of the residuals

sigma2 = sigma2_OLS * (1 - hii)

where hii is the diagonal of the hat matrix

sigma2_not_obsi

error variance for all LOOO regressions

This is ‘mse_resid’ from each auxiliary regression.

uses results from leave-one-observation-out loop

Methods

`get_resid_studentized_external`([sigma])	Calculate studentized residuals
`plot_index`([y_var, threshold, title, ax, idx])	Index plot for influence attributes
`plot_influence`([external, alpha, criterion, ...])	Plot of influence in regression.
`summary_frame`()	Creates a DataFrame with all available influence results
`summary_table`([float_fmt])	Create a summary table with all influence and outlier measures

Notes

One part of the results can be calculated without any auxiliary regression (some of which have the _internal postfix in the name). Other statistics require leave-one-observation-out (LOOO) auxiliary regression, and will be slower (mainly results with _external postfix in the name). For the auxiliary LOOO regression, only the required results are stored.

Using the LOO measures is currently only recommended if the data set is not too large. One possible approach for LOOO measures would be to identify possible problem observations with the _internal measures, and then run the leave-one-observation-out only with observations that are possible outliers. (However, this is not yet available in an automated way.)

This should be extended to general least squares.

The leave-one-variable-out (LOVO) auxiliary regression are currently not used.

Methods

`get_resid_studentized_external`([sigma])	Calculate studentized residuals
`plot_index`([y_var, threshold, title, ax, idx])	Index plot for influence attributes
`plot_influence`([external, alpha, criterion, ...])	Plot of influence in regression.
`summary_frame`()	Creates a DataFrame with all available influence results
`summary_table`([float_fmt])	Create a summary table with all influence and outlier measures

Properties

`cooks_distance`	Cook's distance
`cov_ratio`	covariance ratio between LOOO and original
`det_cov_params_not_obsi`	determinant of cov_params of all LOOO regressions
`dfbeta`()	uses results from leave-one-observation-out loop
`dfbetas`()	uses results from leave-one-observation-out loop
`dffits`	dffits measure for influence of an observation
`dffits_internal`	dffits measure for influence of an observation
`ess_press`	Error sum of squares of PRESS residuals
`hat_diag_factor`	Factor of diagonal of hat_matrix used in influence
`hat_matrix_diag`	Diagonal of the hat_matrix for OLS
`influence`	Influence measure
`params_not_obsi`	parameter estimates for all LOOO regressions
`resid_press`	PRESS residuals
`resid_std`	estimate of standard deviation of the residuals
`resid_studentized`	Studentized residuals using variance from OLS
`resid_studentized_external`	Studentized residuals using LOOO variance
`resid_studentized_internal`	Studentized residuals using variance from OLS
`resid_var`	estimate of variance of the residuals
`sigma2_not_obsi`	error variance for all LOOO regressions