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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.