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Belsley collinearity diagnostics

`collintest(X)`

`collintest(X,Name,Value)`

`sValue = collintest(___)`

```
[sValue,condIdx,VarDecomp]
= collintest(___)
```

`collintest(`

displays Belsley
collinearity diagnostics for assessing the strength and sources
of collinearity among variables in the matrix or tabular array `X`

)`X`

.

`collintest(`

uses
additional options specified by one or more `X`

,`Name,Value`

)`Name,Value`

pairs.

returns
the singular values in
decreasing order, using any of the previous input arguments.`sValue`

= collintest(___)

`[`

additionally returns the condition indices and variance
decomposition proportions.`sValue`

,`condIdx`

,`VarDecomp`

]
= collintest(___)

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.

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