Belsley collinearity diagnostics
collintest(X)
collintest(X,Name,Value)
sValue = collintest(___)
[sValue,condIdx,VarDecomp]
= collintest(___)
collintest(ax,___)
[sValue,condIdx,VarDecomp,h]
= collintest(___)
collintest(
displays Belsley collinearity
diagnostics for assessing the strength and sources of collinearity
among variables in the matrix or table X
)X
at the command
line.
collintest(
uses
additional options specified by one or more name-value pair arguments. For
example, X
,Name,Value
)collintest(X,'plot','on')
plots the results to a
figure.
returns the
singular values in
decreasing order using any of the input argument combinations in the previous
syntaxes.sValue
= collintest(___)
[
additionally returns the condition indices
and variance decomposition
proportions.sValue
,condIdx
,VarDecomp
]
= collintest(___)
collintest(
plots on the axes specified by ax
,___)ax
instead
of the current axes (gca
). ax
can precede any of the input
argument combinations in the previous syntaxes.
For purposes of collinearity diagnostics, Belsley [1] shows that column scaling of the design matrix, X
,
is always desirable. However, he also shows that centering the data
in X
is undesirable. For models with an intercept,
if you center the data in X
, then the role of the
constant term in any near dependency is hidden, and yields misleading
diagnostics.
Tolerances for identifying large condition indices
and variance-decomposition proportions are comparable to critical
values in standard hypothesis tests. Experience determines the most
useful tolerance, but experiments suggest the collintest
defaults
are good starting points [1].
[1] Belsley, D. A., E. Kuh, and R. E. Welsh. Regression Diagnostics. New York, NY: John Wiley & Sons, Inc., 1980.
[2] Judge, G. G., W. E. Griffiths, R. C. Hill, H. Lϋtkepohl, and T. C. Lee. The Theory and Practice of Econometrics. New York, NY: John Wiley & Sons, Inc., 1985.