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 FittingTest_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.