multiCol: Collinearity detection in a linear regression model
In multiColl: Collinearity detection in a multiple linear regression model

Description Usage Arguments Value Note Author(s) References See Also Examples

The function collects all existing measures to detect worrying multicollinearity in the package multiCol.

1	multiCol(X, dummy = F, pos = NULL)

`X`	A numeric design matrix that should contain more than one regressor (intercept included).
`dummy`	A logical value that indicates if there are dummy variables in the design matrix `X`. By default `dummy=F`.
`pos`	A numeric vector that indicates the position of the dummy variables, if these exist, in the design matrix `X`. By default `pos=NULL`.

If X contains two independent variables (intercept included) see SLM function.

If X contains more than two independent variables (intercept included):

`CV`	Coeficients of variation of quantitative variables in `X`.
`Prop`	Proportion of ones in the dummy variables.
`R`	Matrix correlation of the quantitative variables in `X`.
`detR`	Determinant of the matrix correlation of the quantitative variables in `X`.
`VIF`	Variance Inflation Factors of the quantitative variables in `X`.
`CN`	Condition Number of `X`.
`ki`	Stewart's index of the quantitative variables in `X`.

For more detail, see the help of the functions in See Also.

R. Salmer<f3>n (romansg@ugr.es) and C. Garc<ed>a (cbgarcia@ugr.es).

L. R. Klein and A.S. Goldberger (1964). An economic model of the United States, 1929-1952. North Holland Publishing Company, Amsterdan.

H. Theil (1971). Principles of Econometrics. John Wiley & Sons, New York.

SLM, CV, PROPs, RdetR, VIF, CN, ki.

# Henri Theil's textile consumption data modified
data(theil)
head(theil)
cte = array(1,length(theil[,2]))
theil.X = cbind(cte,theil[,-(1:2)])
multiCol(theil.X, TRUE, pos = 4)

# Klein and Goldberger data on consumption and wage income
data(KG)
head(KG)
cte = array(1,length(KG[,1]))
KG.X = cbind(cte,KG[,-1])
multiCol(KG.X)

# random
x1 = array(1,25)
x2 = rnorm(25,100,1)
x = cbind(x1,x2)
head(x)
multiCol(x)

# random
x1 = array(1,25)
x2 = sample(cbind(array(1,25),array(0,25)),25)
x = cbind(x1,x2)
head(x)
multiCol(x, TRUE)

      obs consume income relprice twentys
[1,] 1923    99.2   96.7    101.0       1
[2,] 1924    99.0   98.1    100.1       1
[3,] 1925   100.0  100.0    100.0       1
[4,] 1926   111.6  104.9     90.6       1
[5,] 1927   122.2  104.9     86.5       1
[6,] 1928   117.6  109.5     89.7       1
$`Coeficients of Variation`
[1] 0.04993766 0.21441845

$`Proportion of ones in the dummys variable`
[1] 41.17647

$`R and det(R)`
$`R and det(R)`$`Correlation matrix`
            income  relprice
income   1.0000000 0.1788467
relprice 0.1788467 1.0000000

$`R and det(R)`$`Correlation matrix's determinant`
[1] 0.9680139


$`Variance Inflation Factors`
  income relprice 
1.033043 1.033043 

$CN
$CN$`Condition Number without intercept`
[1] 24.15423

$CN$`Condition Number with intercept`
[1] 53.39671

$CN$`Increase (in percentage)`
[1] 54.76458


$ki
$ki$`Stewart index`
[1] 403.20963 415.28266  23.50258

$ki$`Proportion of essential collinearity in i-th independent variable (without intercept)`
[1] 0.2487566 4.3954455

$ki$`Proportion of non-essential collinearity in i-th independent variable (without intercept)`
[1] 99.75124 95.60455


  consumption wage.income non.farm.income farm.income
1        62.8       43.41           17.10        3.96
2        65.0       46.44           18.65        5.48
3        63.9       44.35           17.09        4.37
4        67.5       47.82           19.28        4.51
5        71.3       51.02           23.24        4.88
6        76.6       58.71           28.11        6.37
$`Coeficients of Variation`
[1] 0.2660921 0.2503487 0.2867863

$`Proportion of ones in the dummys variable`
[1] "At least one qualitative independent variable are needed (excluding the intercept)"

$`R and det(R)`
$`R and det(R)`$`Correlation matrix`
                wage.income non.farm.income farm.income
wage.income       1.0000000       0.9431118   0.8106989
non.farm.income   0.9431118       1.0000000   0.7371272
farm.income       0.8106989       0.7371272   1.0000000

$`R and det(R)`$`Correlation matrix's determinant`
[1] 0.03713592


$`Variance Inflation Factors`
    wage.income non.farm.income     farm.income 
      12.296544        9.230073        2.976638 

$CN
$CN$`Condition Number without intercept`
[1] 30.2987

$CN$`Condition Number with intercept`
[1] 35.88644

$CN$`Increase (in percentage)`
[1] 15.57062


$ki
$ki$`Stewart index`
[1]  17.86327 185.96422 156.50013  39.16836

$ki$`Proportion of essential collinearity in i-th independent variable (without intercept)`
[1] 6.612317 5.897805 7.599598

$ki$`Proportion of non-essential collinearity in i-th independent variable (without intercept)`
[1] 93.38768 94.10219 92.40040


     x1        x2
[1,]  1 102.53548
[2,]  1 101.20446
[3,]  1  99.75182
[4,]  1 100.68300
[5,]  1  98.74066
[6,]  1 100.46400
$`Coeficient of Variation`
[1] 0.009759725

$`Variance Inflation Factor`
[1] 1

$`Condition Number`
[1] 204.9287

$`Stewart index`
[1] 10499.44 10499.44

     x1 x2
[1,]  1  1
[2,]  1  1
[3,]  1  1
[4,]  1  1
[5,]  1  0
[6,]  1  0
$`Proportion of ones in the dummy variable`
[1] 44

$`Condition Number`
[1] 2.222711