# srre: Stochastic Restricted Ridge Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

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

## Usage

 `1` ```srre(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 `srre` returns the Stochastic Restricted Ridge 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 `srre` returns all the scalar MSE values and corresponding parameter values of Stochastic Restricted Ridge Estimator.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

Revan, M. (2009) A stochastic restricted ridge regression estimator in Journal of Multivariate Analysis, volume 100, issue 8, pp. 1706–1716

`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) srre(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 Stochastic Restricted Ridge 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(srre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd), main=c("Plot of MSE of Stochastic Restricted Ridge 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(srre(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

```\$`*****Stochastic Restricted Ridge Estimator*****`
Estimate Standard_error t_statistic pvalue
X1   2.1924         0.1167     11.8330  0.000
X2   1.1535         0.0289     24.0598  0.000
X3   0.7580         0.1008      4.7521  0.001
X4   0.4864         0.0343          NA     NA

\$`*****Mean square error value*****`
MSE
0.0258
```

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