# Condition indexes and variance decomposition proportions

### Description

Calculates condition indexes and variance decomposition proportions in order to test for collinearity among the independent variables of a regression model and identifies the sources of collinearity if present

### Usage

1 2 3 4 |

### Arguments

`mod` |
A model object or data-frame |

`scale` |
If FALSE, the data are left unscaled. Default is TRUE |

`center` |
If TRUE, data are centered. Default is FALSE |

`add.intercept` |
if TRUE, an intercept is added. Default is TRUE |

`x` |
A |

`dec.places` |
number of decimal places to use when printing |

`fuzz` |
variance decomposition proportions less than |

`fuzzchar` |
character for small variance decomposition proportion values |

`...` |
arguments to be passed on to or from other methods |

### Details

`Colldiag`

is an implementation of the regression collinearity diagnostic procedures found in Belsley, Kuh, and Welsch (1980). These procedures examine the “conditioning” of the matrix of independent variables.

`Colldiag`

computes the condition indexes of the matrix. If the largest condition index (the condition number) is *large* (Belsley et al suggest 30 or higher), then there may be collinearity problems. All *large* condition indexes may be worth investigating.

`Colldiag`

also provides further information that may help to identify the source of these problems, the *variance decomposition proportions* associated with each condition index. If a large condition index is associated two or more variables with *large* variance decomposition proportions, these variables may be causing collinearity problems. Belsley et al suggest that a *large* proportion is 50 percent or more.

### Value

A colldiag object

`condindx` |
A vector of condition indexes |

`pi` |
A matrix of variance decomposition proportions |

`print.colldiag`

prints the condition indexes as the first column of a table with the variance decomposition proportions beside them. `print.colldiag`

has a `fuzz`

option to suppress printing of small numbers. If fuzz is used, small values are replaces by a period “.”. `Fuzzchar`

can be used to specify an alternative character.

### Note

Colldiag is based on the Stata program `coldiag`

by Joseph Harkness joe.harkness@jhu.edu, Johns Hopkins University.

### Author(s)

John Hendrickx John_Hendrickx@yahoo.com

### References

D. Belsley, E. Kuh, and R. Welsch (1980). Regression Diagnostics. Wiley.

Belsley, D.A. (1991). Conditioning diagnostics, collinearity and weak data in regression. New York: John Wiley & Sons.

### See Also

`lm`

, `scale`

, `svd`

, `[car]`

`vif`

, `[rms]`

`vif`

, `perturb`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
# Belsley (1991). "Conditioning Diagnostics"
# The Consumption Function (pp. 149-154)
data(consumption)
ct1 <- with(consumption, c(NA,cons[-length(cons)]))
# compare (5.3)
m1 <- lm(cons ~ ct1+dpi+rate+d_dpi, data = consumption)
anova(m1)
summary(m1)
# compare exhibit 5.11
with(consumption, cor(cbind(ct1, dpi, rate, d_dpi), use="complete.obs"))
# compare exhibit 5.12
cd<-colldiag(m1)
cd
print(cd,fuzz=.3)
## Not run:
# Example of reading UCLA data files from
# http://www.ats.ucla.edu/stat/r/dae/rreg.htm
library(foreign)
elemapi <- read.dta("http://www.ats.ucla.edu/stat/data/elemapi2.dta")
attach(elemapi)
# Example of SAS collinearity diagnostics from
# http://www.ats.ucla.edu/stat/sas/webbooks/reg/chapter2/sasreg2.htm
# 2.4 Tests for Collinearity
m2 <- lm(api00 ~ acs_k3+avg_ed+grad_sch+col_grad+some_col)
summary(m2)
library(car)
vif(m2)
library(perturb)
cd2<-colldiag(m2,add.intercept=FALSE,center=TRUE)
print(cd2,dec.places=5)
# Same data, SPSS example at
# http://www.ats.ucla.edu/stat/spss/webbooks/reg/chapter2/spssreg2.htm
colldiag(m2,add.intercept=TRUE)
## End(Not run)
``` |