tolerance

[Buhi, Eric]

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[Swank, Paul R]

Tolerance is usually defined as 1 – R squared where R squared is for one predictor  regressed on all the other predictors. Thus a tolerance of 0 indicates perfect collinearity. The variance inflation factor, on the other hand, measures the effect of the variable on the variances used to estimate the standard error for each parameter and is given by 1/tolerance. Thus it has the opposite scale and a value of one means no collinearity and larger values mean problems, particularly values above 10 or so.

 

Paul R. Swank, Ph.D

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center

Houston, TX 77038

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Buhi, Eric
Sent: Tuesday, February 03, 2009 8:37 AM
To: [hidden email]
Subject: tolerance

 

Can anyone clarify how to interpret “tolerance” when investigating multicollinearity?

 

Tabachnick and Fidell (Using Multivariate Statistics, 2007) note that “even tolerances as high as .5 or .6 may pose difficulties in testing and interpreting regression coefficients” (p. 125). However, G. David Garson notes on his Statnotes: Topics in Multivariate Analysis site: “The higher the intercorrelation of the independents, the more the tolerance will approach zero. As a rule of thumb, if tolerance is less than .20, a problem with multicollinearity is indicated” (http://faculty.chass.ncsu.edu/garson/PA765/regress.htm#toleranc). So, does a high tolerance value equate to multicollinearity or is it that a lower tolerance value equates to multicollinearity?

 

Thanks!

 

 

Eric R. Buhi, MPH, PhD, CHES

Assistant Professor

Department of Community and Family Health

College of Public Health

University of South Florida

13201 Bruce B. Downs Blvd., MDC 56

Tampa, Florida 33612

Phone: [phone]

[hidden email]

http://publichealth.usf.edu/cfh/

 

[Reutter, Alex]

Hi Eric,

 

The two statements don’t contradict one another.  “As a rule of thumb, if tolerance is less than .20, a problem with multicollinearity is indicated”; however, “even tolerances as high as .5 or .6 may pose difficulties”.

 

Cheers,

Alex

 

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Buhi, Eric
Sent: Tuesday, February 03, 2009 8:37 AM
To: [hidden email]
Subject: tolerance

 

Can anyone clarify how to interpret “tolerance” when investigating multicollinearity?

 

Tabachnick and Fidell (Using Multivariate Statistics, 2007) note that “even tolerances as high as .5 or .6 may pose difficulties in testing and interpreting regression coefficients” (p. 125). However, G. David Garson notes on his Statnotes: Topics in Multivariate Analysis site: “The higher the intercorrelation of the independents, the more the tolerance will approach zero. As a rule of thumb, if tolerance is less than .20, a problem with multicollinearity is indicated” (http://faculty.chass.ncsu.edu/garson/PA765/regress.htm#toleranc). So, does a high tolerance value equate to multicollinearity or is it that a lower tolerance value equates to multicollinearity?

 

Thanks!

 

 

Eric R. Buhi, MPH, PhD, CHES

Assistant Professor

Department of Community and Family Health

College of Public Health

University of South Florida

13201 Bruce B. Downs Blvd., MDC 56

Tampa, Florida 33612

Phone: [phone]

[hidden email]

http://publichealth.usf.edu/cfh/

 

[SR Millis-3]

I think that it is much more informative to use the 2-step method of Belsley et al. to investigate collinearity: first, see whether there are any condition indexes > 30. Next, for the indexes, see whether there are any variables with variance-decomposition proportions greater than .50. VIF/TOL isn't able to distinguish among several coexisting near dependencies.  In addition, as this discussion shows, there's varying opinions regarding which values of VIF are high.

Scott R Millis, PhD, MEd, ABPP (CN,CL,RP), CStat
Professor & Director of Research
Dept of Physical Medicine & Rehabilitation
Wayne State University School of Medicine
261 Mack Blvd
Detroit, MI 48201
Email:  [hidden email]
Tel: [phone]
Fax: [phone]


--- On Tue, 2/3/09, Buhi, Eric <[hidden email]> wrote:

> From: Buhi, Eric <[hidden email]>
> Subject: tolerance
> To: [hidden email]
> Date: Tuesday, February 3, 2009, 9:36 AM
> Can anyone clarify how to interpret "tolerance"
> when investigating multicollinearity?
>
> Tabachnick and Fidell (Using Multivariate Statistics, 2007)
> note that "even tolerances as high as .5 or .6 may pose
> difficulties in testing and interpreting regression
> coefficients" (p. 125). However, G. David Garson notes
> on his Statnotes: Topics in Multivariate Analysis site:
> "The higher the intercorrelation of the independents,
> the more the tolerance will approach zero. As a rule of
> thumb, if tolerance is less than .20, a problem with
> multicollinearity is indicated"
> (http://faculty.chass.ncsu.edu/garson/PA765/regress.htm#toleranc).
> So, does a high tolerance value equate to multicollinearity
> or is it that a lower tolerance value equates to
> multicollinearity?
>
> Thanks!
>
>
> Eric R. Buhi, MPH, PhD, CHES
> Assistant Professor
> Department of Community and Family Health
> College of Public Health
> University of South Florida
> 13201 Bruce B. Downs Blvd., MDC 56
> Tampa, Florida 33612
> Phone: [phone]
> [hidden email]<mailto:[hidden email]>
> http://publichealth.usf.edu/cfh/

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