Collinearity
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Collinearity. The Problem of Large Correlations Among the Independent Variables. What is collinearity? Why is it a problem?. How do I know if I’ve got it? What can I do about it?. Skill Set. Collinearity Defined.

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Collinearity

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Collinearity

Collinearity

The Problem of Large Correlations Among the Independent Variables


Skill set

What is collinearity?

Why is it a problem?

How do I know if I’ve got it?

What can I do about it?

Skill Set


Collinearity defined

Collinearity Defined

  • Within the set of IVs, one or more IVs are (nearly) totally predicted by the other IVs.

  • In such a case, the b or beta weights are poorly estimated.

  • Problem of the “Bouncing Betas.”


Diagnostics

Diagnostics

1. Variance Inflation Factor (VIF).

Standard error of the b weight with 2 IVs:

Sampling Variance of b weight

VIF


Vif 2

VIF (2)

Standard Error with k predictors:

Large values of VIF are trouble. Some say values > 10 are high.


Tolerance

Tolerance

Tolerance is

Small values are trouble. Maybe .10?


Condition index

Number

Eigenval

Condition

Variance Proportions

Index

Constant

X1

X2

X3

1

3.771

1.00

.004

.006

.006

.008

2

.106

5.969

.003

.029

.268

.774

3

.079

6.90

.000

.749

.397

.066

4

.039

9.946

.993

.215

.329

.152

Condition Index

Lambda is an eigenvalue.

Number refers to a linear combination of the predictors.

Eigenvalue refers to the variance of that combination.

Collinearity is spotted by finding 2 or more variables that have large proportions of variance (.50 or more) that correspond to large condition indices. A rule of thumb is to label as large those condition indices in the range of 30 or larger. No apparent problem here.


Condition index 2

Number

Eigenval

Condition

Variance Proportions

Index

Constant

X1

X2

X3

1

3.819

1.00

.004

.006

.002

.002

2

.117

5.707

.043

.384

.041

.087

3

.047

9.025

.876

.608

.001

.042

4

.017

15.128

.077

.002

.967

.868

Condition Index (2)

The last condition index (15.128) is highly associated with X2 and X3. The b weights for X2 and X3 are probably not well estimated.


Dealing with collinearity

Dealing with Collinearity

  • Lump it. Admit ambiguity; SE of b weights. Refer also to correlations.

  • Select or combine variables.

  • Factor analyze set of IVs.

  • Use another type of analysis (e.g., path analysis).

  • Use another type of regression (ridge regression).

  • Unit weights (no longer regression).


Review

Review

  • What is collinearity?

  • Why is collinearity a problem?

  • What is the VIF?

  • What is Tolerance?

  • What is a condition index?

  • What are some things you can do to deal with collinearity?


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