Download presentation

Published byVicente Yandle Modified over 4 years ago

1
**Multicollinearity in Regression Principal Components Analysis**

Standing Heights and Physical Stature Attributes Among Female Police Officer Applicants S.Q. Lafi and J.B. Kaneene (1992). “An Explanation of the Use of Principal Components Analysis to Detect and Correct for Multicollinearity,” Preventive Veterinary Medicine, Vol. 13, pp

2
Data Description Subjects: 33 Females applying for police officer positions Dependent Variable: Y ≡ Standing Height (cm) Independent Variables: X1 ≡ Sitting Height (cm) X2 ≡ Upper Arm Length (cm) X3 ≡ Forearm Length (cm) X4 ≡ Hand Length (cm) X5 ≡ Upper Leg Length (cm) X6 ≡ Lower Leg Length (cm) X7 ≡ Foot Length (inches) X8 ≡ BRACH (100X3/X2) X9 ≡ TIBIO (100X6/X5)

3
Data

4
**Standardizing the Predictors**

5
**Correlations Matrix of Predictors and Inverse**

6
**Variance Inflation Factors (VIFs)**

VIF measures the extent that a regression coefficient’s variance is inflated due to correlations among the set of predictors VIFj = 1/(1-Rj2) where Rj2 is the coefficient of multiple determination when Xj is regressed on the remaining predictors. Values > 10 are often considered to be problematic VIFs can be obtained as the diagonal elements of R-1 Not surprisingly, X2, X3, X5, X6, X8, and X9 are problems (see definitions of X8 and X9)

7
**Regression of Y on [1|X*]**

Note the surprising negative coefficients for X3*, X5*, and X9*

8
**Principal Components Analysis**

While the columns of X* are highly correlated, the columns of W are uncorrelated The ls represent the variance corresponding to each principal component

9
**Police Applicants Height Data - I**

10
**Police Applicants Height Data - II**

11
Regression of Y on [1|W] Note that W8 and W9 have very small eigenvalues and very small t-statistics Condition indices are 63.5 and 85.2, Both well above 10

12
Reduced Model Removing last 2 principal components due to small, insignificant t-statistics and high condition indices Let V(g) be the p×g matrix of the eigenvectors for the g retained principal components (p=9, g=7) Let W(g) = X*V(g) Then regress Y on [1|W(g)]

13
**Reduced Regression Fit**

14
**Transforming Back to X-scale**

15
**Comparison of Coefficients and SEs**

Original Model Principal Components

Similar presentations

Presentation is loading. Please wait....

OK

An introduction to Principal Component Analysis (PCA)

An introduction to Principal Component Analysis (PCA)

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on natural numbers 0 Ppt on laser diode Free download ppt on surface chemistry Ppt on ip address classes ppt Ppt on ganga action plan download Ppt on youth leadership Ppt on eye osce Converter pub to ppt online student Synonyms interactive ppt on the writing Ppt on limits and continuity ppt