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Samenvatting les 5 colleges
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Samenvatting les 5 colleges
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LES 5Multicollinearity (H8)
Y i=β 0 + β 1 X 1 i+ β 2 X 2 i+ …+ui
^
Estimate parameters: β j
o Based on covariances between X ji and Y i
o To identify unique parameters, we need unique covariances
o If there is correlation between X 1 i and X 2 i , the covarianceXY is not
unique, but shared! reeksen bewegen samen, hangen af van mekaar
1. No MC
2. Perfect MC X1 en X2 hebben een
bepaald verband op Y
perfecte MC X1 en X2
liggen op mekaar
1
, verbanden zijn niet meer uniek?
wat gebeurt er voor het ontstaan van
een perfect verband? => X1 en X2
zijn hetzelfde dus ik kan er geen
deeleffecten meer uithalen
Examples perfect MC
Distance in meters and in kilometers
Distance in kilometers and in miles
Share of females and share of males
Percent of voters ‘yes’, ‘no’ and ‘abstention’
Temperature in °C and in °F
3. Non-perfect MC
klein driehoekje => is dit nu effect X1 of
X2 => kunnen we niet
toewijzen (want we weten het niet)
Strong relationship between two or more explanatory variables, but no perfect
linear combination
Parameters can still be estimated
Predictions are still good
However…
Parameters estimates are not nice ‘marginal effects’ any longer
Parameter estimates become highly sensitive to small changes:
observaties bijvoegen parameters veranderen heel snel en zijn heel
gevoelig
Standard errors of the parameters become larger
variantie is afh. van de onderlinge
samenhang van de X
=> wordt groter door MC
2
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