LinearModelAnalysis

class LinearModelAnalysis(*args)

Analyse a linear model.

Available constructors:

LinearModelAnalysis(linearModelResult)

Parameters:

linearModelResultLinearModelResult

A linear model result.

See also

LinearModelResult

Notes

This class relies on a linear model result structure and performs diagnostic of linearity. This diagnostic mainly relies on graphics and a summary like function (pretty-print)

By default, on graphs, labels of the 3 most significant points are displayed. This number can be changed by modifying the ResourceMap key (LinearModelAnalysis-Identifiers).

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Normal()
>>> Xsample = distribution.getSample(30)
>>> func = ot.SymbolicFunction(['x'], ['2 * x + 1'])
>>> Ysample = func(Xsample) + ot.Normal().getSample(30)
>>> algo = ot.LinearModelAlgorithm(Ysample, Xsample)
>>> result = algo.getResult()
>>> analysis = ot.LinearModelAnalysis(result)

Methods

drawCookDistance()	Accessor to plot of Cook's distances versus row labels.
drawCookVsLeverages()	Accessor to plot of Cook's distances versus leverage/(1-leverage).
drawModelVsFitted()	Accessor to plot of model versus fitted values.
drawQQplot()	Accessor to plot a Normal quantiles-quantiles plot of standardized residuals.
drawResidualsVsFitted()	Accessor to plot of residuals versus fitted values.
drawResidualsVsLeverages()	Accessor to plot of residuals versus leverages that adds bands corresponding to Cook's distances of 0.5 and 1.
drawScaleLocation()	Accessor to a Scale-Location plot of sqrt(abs(residuals)) versus fitted values.
getClassName()	Accessor to the object's name.
getCoefficientsConfidenceInterval([level])	Accessor to the confidence interval of level for the coefficients of the linear expansion
getCoefficientsPValues()	Accessor to the coefficients of the p values.
getCoefficientsTScores()	Accessor to the coefficients of linear expansion over their standard error.
getFisherPValue()	Accessor to the Fisher p value.
getFisherScore()	Accessor to the Fisher test.
getId()	Accessor to the object's id.
getLinearModelResult()	Accessor to the linear model result.
getName()	Accessor to the object's name.
getNormalityTestCramerVonMises()	Performs Cramer-Von Mises test.
getNormalityTestResultAndersonDarling()	Performs Anderson-Darling test.
getNormalityTestResultChiSquared()	Performs Chi-Square test.
getNormalityTestResultKolmogorovSmirnov()	Performs Kolmogorov test.
getShadowedId()	Accessor to the object's shadowed id.
getVisibility()	Accessor to the object's visibility state.
hasName()	Test if the object is named.
hasVisibleName()	Test if the object has a distinguishable name.
setName(name)	Accessor to the object's name.
setShadowedId(id)	Accessor to the object's shadowed id.
setVisibility(visible)	Accessor to the object's visibility state.

__init__(*args)

drawCookDistance()

Accessor to plot of Cook’s distances versus row labels.

Returns:

graphGraph

drawCookVsLeverages()

Accessor to plot of Cook’s distances versus leverage/(1-leverage).

Returns:

graphGraph

drawModelVsFitted()

Accessor to plot of model versus fitted values.

Returns:

graphGraph

drawQQplot()

Accessor to plot a Normal quantiles-quantiles plot of standardized residuals.

Returns:

graphGraph

drawResidualsVsFitted()

Accessor to plot of residuals versus fitted values.

Returns:

graphGraph

drawResidualsVsLeverages()

Accessor to plot of residuals versus leverages that adds bands corresponding to Cook’s distances of 0.5 and 1.

Returns:

graphGraph

drawScaleLocation()

Accessor to a Scale-Location plot of sqrt(abs(residuals)) versus fitted values.

Returns:

graphGraph

getClassName()

Accessor to the object’s name.

Returns:

class_namestr

The object class name (object.__class__.__name__).

getCoefficientsConfidenceInterval(level=0.95)

Accessor to the confidence interval of level for the coefficients of the linear expansion

Returns:

confidenceIntervalInterval

getCoefficientsPValues()

Accessor to the coefficients of the p values.

Returns:

pValuesPoint

getCoefficientsTScores()

Accessor to the coefficients of linear expansion over their standard error.

Returns:

tScoresPoint

getFisherPValue()

Accessor to the Fisher p value.

Returns:

fisherPValuefloat

getFisherScore()

Accessor to the Fisher test.

Returns:

fisherScorefloat

getId()

Accessor to the object’s id.

Returns:

idint

Internal unique identifier.

getLinearModelResult()

Accessor to the linear model result.

Returns:

linearModelResultLinearModelResult

The linear model result which had been passed to the constructor.

getName()

Accessor to the object’s name.

Returns:

namestr

The name of the object.

getNormalityTestCramerVonMises()

Performs Cramer-Von Mises test.

The statistical test checks the Gaussian assumption of the model (null hypothesis).

Returns:

testResultTestResult

Test result class.

Notes

We check that the residual is Gaussian thanks to NormalityTest::CramerVonMisesNormal.

getNormalityTestResultAndersonDarling()

Performs Anderson-Darling test. The statistical test checks the Gaussian assumption of the model (null hypothesis).

Returns:

testResultTestResult

Test result class.

Notes

We check that the residual is Gaussian thanks to NormalityTest::AndersonDarling.

getNormalityTestResultChiSquared()

Performs Chi-Square test. The statistical test checks the Gaussian assumption of the model (null hypothesis).

Returns:

testResultTestResult

Test result class.

Notes

The Chi-Square test is a goodness of fit test which objective is to check the normality assumption (null hypothesis) of residuals (and thus the model).

Usually, Chi-Square test applies for discrete distributions. Here we rely on the ChiSquared() to check the normality.

getNormalityTestResultKolmogorovSmirnov()

Performs Kolmogorov test.

Performs Kolmogorov test to check Gaussian assumption of the model (null hypothesis).

Returns:

testResultTestResult

Test result class.

Notes

We check that the residual is Gaussian thanks to FittingTest::Kolmogorov.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

idint

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns:

visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns:

hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool

True if the name is not empty and not the default one.

setName(name)

Accessor to the object’s name.

Parameters:

namestr

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visiblebool

Visibility flag.

Examples using the class

Build and validate a linear model

Build and validate a linear model

Create a linear model

Create a linear model

Perform stepwise regression

Perform stepwise regression