perturb.n: Perturbation and estimation in a multiple linear model
In multiColl: Collinearity detection in a multiple linear regression model

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

The function quantifies the variations in the estimations of the coefficients of a multiple linear regression when a perturbation is introduced in the quantitative data set.

1	perturb.n(data, n, mu, dv, tol = 0.01, pos = NULL)

`data`	Data set `(y, X)` where `y` and `X` contain, respectively, the observations of the dependent variable and independients variables (intercept included) of the multiple linear regression.
`n`	Number of times that perturbation is performed.
`mu`	Any real number.
`dv`	Any real positive number.
`tol`	A value between 0 and 1. By default `tol=0.01`.
`pos`	A numeric vector that indicates the position of the independent variables to disturb once you eliminate in `data` the dependent variable and the intercept. By default `pos=NULL`.

`tols`	A vector presenting the percentage of disturbance induced in the variables indicated in each iteration.
`norms`	A vector presenting the percentage of variation in the estimations of the coefficients in each iteration.

tols must be a constant vector equal to tol. It is obtained to check if data have been correctly perturbed.

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

D. Belsley (1982). Assessing the presence of harmfull collinearity and other forms of weak data throught a test for signal-to-noise. Journal of Econometrics, 20, 211-253.

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.

perturb.

tol = 0.01
mu = 10
dv = 10

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

iterations = 5

perturb.n.T = perturb.n(theil.y.X, iterations, mu, dv, tol, pos = c(1,2))
perturb.n.T
mean(perturb.n.T[,1])
mean(perturb.n.T[,2])
c(min(perturb.n.T[,2]), max(perturb.n.T[,2]))

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

iterations = 1000

perturb.n.KG = perturb.n(KG.y.X, iterations, mu, dv, tol, pos = c(1,2,3))
mean(perturb.n.KG[,1])
mean(perturb.n.KG[,2])
c(min(perturb.n.KG[,2]), max(perturb.n.KG[,2]))

      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
           cte income relprice twentys
[1,]  99.2   1   96.7    101.0       1
[2,]  99.0   1   98.1    100.1       1
[3,] 100.0   1  100.0    100.0       1
[4,] 111.6   1  104.9     90.6       1
[5,] 122.2   1  104.9     86.5       1
[6,] 117.6   1  109.5     89.7       1
     tols   normas
[1,]    1 4.214807
[2,]    1 3.430323
[3,]    1 2.777928
[4,]    1 3.965039
[5,]    1 2.300320
[1] 1
[1] 3.337683
[1] 2.300320 4.214807
  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
  KG[, 1] cte wage.income non.farm.income farm.income
1    62.8   1       43.41           17.10        3.96
2    65.0   1       46.44           18.65        5.48
3    63.9   1       44.35           17.09        4.37
4    67.5   1       47.82           19.28        4.51
5    71.3   1       51.02           23.24        4.88
6    76.6   1       58.71           28.11        6.37
[1] 1
[1] 3.128441
[1] 0.2094383 9.3379935