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LECTURE 14 OUTLIERS AND MULTICOLLINEARITYPowerPoint Presentation

LECTURE 14 OUTLIERS AND MULTICOLLINEARITY

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LECTURE 14OUTLIERS AND MULTICOLLINEARITY

- OUTLIER ANALYSIS
- 1. VISUAL DISPLAY
- 2. INTERACTIVE INSPECTION:
http://www.stat.uiuc.edu/~stat100/java/guess/PPApplet.html

OUTLIERS

- LEVERAGE
- hii= 1/n + (Score – Mx)/x2 (single predictor)
Should be close to 1/n

- Centered: h*ii= hii- 1/n

OUTLIERS

- Test: t(case I deleted)= [resid(i)/ 1- hij] / [MSres(i)/(1- hij )]
- Where resid(i) = residual of Y-Ymni with case i removed
- SPSS- take case i out, run analysis with SAVE

OUTLIERS

- MAHALANOBIS (Euclidean) distance of DV score from centroid of IVs
- Cook’s D: C = (Y – Yi)2 /[(k-1)*MSres]
- DFFITSi = (Y – Yi) /SQRT[MSresi hii]

OUTLIERS

- SPSS: GENERAL LINEAR MODEL OPTIONS: ‘SAVE’
(check ‘Leverage Values’ and ‘Cooks’ to get hii and C

Plot C and h against the cases

OUTLIERS – WHAT TO DO

- DELETE
- REVISE MODEL
- TRANSFORM VARIABLES (LOG, SQRT, LOGIT, ARCSIN, ETC.)
- ROBUST METHODS:
- LTS (LEAST TRIMMED SQUARES)
- VARIANT: WINDSORIZE (REMOVE TOP 5%, BOTTOM 5%)

- M-estimation: weight least squares for each case by deviation from regression line

MULTICOLLINEARITY

- EXACT COLLINEARITY: One IV is predicted perfectly from another set of IVs
- MULTICOLLINEARITY: high correlation between one IV and another or set of other IVs

MULTICOLLINEARITY Measures

- VIF- Variance Inflation Factor
VIF(i) = 1 / [ 1 – R2(i.1,2,3,…k)

Calculates the R-square for each predictor from all the rest of the predictors

- TOLERANCE
= 1 / VIF

- CONDITION INDEX
= max / min

= largest eigenvalue over smallest

CRITICAL CONDITIONS

- VIF- Variance Inflation Factor > 10
- TOLERANCE
= 1 / VIF < .10

- CONDITION INDEX > 30

FIXING MULTICOLLINEARITY

- REVISE MODEL
- NEW DATA
- RIDGE REGRESSION: SPSS Macro
- PRINCIPAL COMPONENTS REGRESSION
- STANDARDIZE PREDICTORS
- GET PRINCIPAL COMPONENT WEIGHTS
- CREATE NEW PRIN.COMP. SCORES, USE AS PREDICTORS

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