# rrre: Restricted Ridge Regression Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

This function can be used to find the Restricted Ridge Regression Estimated values and corresponding scalar Mean Square Error (MSE) value. Further the variation of MSE can be shown graphically.

## Usage

 `1` ```rrre(formula, r, R, dpn, delt, k, data = NULL, na.action, ...) ```

## Arguments

 `formula` in this section interested model should be given. This should be given as a `formula`. `r` is a j by 1 matrix of linear restriction, r = Rβ + δ + ν. Values for `r` should be given as either a `vector` or a `matrix`. See ‘Examples’. `R` is a j by p of full row rank j ≤ p matrix of linear restriction, r = Rβ + δ + ν. Values for `R` should be given as either a `vector` or a `matrix`. See ‘Examples’. `dpn` dispersion matrix of vector of disturbances of linear restricted model, r = Rβ + δ + ν. Values for `dpn` should be given as either a `vector` (only the diagonal elements) or a `matrix`. See ‘Examples’. `delt` values of E(r) - Rβ and that should be given as either a `vector` or a `matrix`. See ‘Examples’. `k` a single numeric value or a vector of set of numeric values. See ‘Examples’. `data` an optional data frame, list or environment containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which the function is called. `na.action` if the dataset contain `NA` values, then `na.action` indicate what should happen to those `NA` values. `...` currently disregarded.

## Details

Since formula has an implied intercept term, use either `y ~ x - 1` or `y ~ 0 + x` to remove the intercept.

Use `plot` so as to obtain the variation of scalar MSE values graphically. See ‘Examples’.

## Value

If `k` is a single numeric values then `rrre` returns the Restricted Ridge Regression Estimated values, standard error values, t statistic values, p value and corresponding scalar MSE value.

If `k` is a vector of set of numeric values then `rrre` returns all the scalar MSE values and corresponding parameter values of Restricted Ridge Regression Estimator.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

Sarkara, N. (1992), A new estimator combining the ridge regression and the restricted least squares methods of estimation in Communications in Statistics - Theory and Methods, volume 21, pp. 1987–2000. DOI:10.1080/03610929208830893

`plot`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```## Portland cement data set is used. data(pcd) k<-0.05 r<-c(2.1930,1.1533,0.75850) R<-c(1,0,0,0,0,1,0,0,0,0,1,0) dpn<-c(0.0439,0.0029,0.0325) delt<-c(0,0,0) rrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd) # Model without the intercept is considered. ## To obtain variation of MSE of Restricted Ridge Regression Estimator. data(pcd) k<-c(0:10/10) r<-c(2.1930,1.1533,0.75850) R<-c(1,0,0,0,0,1,0,0,0,0,1,0) dpn<-c(0.0439,0.0029,0.0325) delt<-c(0,0,0) plot(rrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd), main=c("Plot of MSE of Restricted Ridge Regression Estimator"), type="b",cex.lab=0.6,adj=1,cex.axis=0.6,cex.main=1,las=1,lty=3,cex=0.6) mseval<-data.frame(rrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd)) smse<-mseval[order(mseval[,2]),] points(smse[1,],pch=16,cex=0.6) ```

### Example output

```\$`*****Restricted Ridge Regression Estimator*****`
Estimate Standard_error t_statistic pvalue
X1   0.2349         0.0283      1.2680 0.2366
X2  -0.0537         0.0070     -1.1194 0.2920
X3   0.1654         0.0233      1.0367 0.3269
X4  -0.0349         0.0047          NA     NA

\$`*****Mean square error value*****`
MSE
0.0014
```

lrmest documentation built on May 29, 2017, 9:02 a.m.