# ogsrliu: Ordinary Generalized Stochastic Restricted Liu Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

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

## Usage

 `1` ```ogsrliu(formula, r, R, dpn, delt, d, 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’. `d` a single numeric value or a vector of set of numeric values. See ‘Example’. `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 `d` is a single numeric values then `ogsrliu` returns the Ordinary Generalized Stochastic Restricted Liu Estimated values, standard error values, t statistic values, p value and corresponding scalar MSE value.

If `d` is a vector of set of numeric values then `ogsrliu` returns all the scalar MSE values and corresponding parameter values of Ordinary Generalized Stochastic Resticted Liu Estimator.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

Arumairajan, S. and Wijekoon, P. (2015) ] Optimal Generalized Biased Estimator in Linear Regression Model in Open Journal of Statistics, pp. 403–411

Hubert, M.H. and Wijekoon, P. (2006) Improvement of the Liu estimator in the linear regression medel, Chapter (4-8)

`plot`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```## Portland cement data set is used. data(pcd) d<-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) ogsrliu(Y~X1+X2+X3+X4-1,r,R,dpn,delt,d,data=pcd) # Model without the intercept is considered. ## To obtain the variation of MSE of Ordinary Generalized Stochastic # Restricted Liu Estimator. data(pcd) d<-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(ogsrliu(Y~X1+X2+X3+X4-1,r,R,dpn,delt,d,data=pcd), main=c("Plot of MSE of Ordinary Generalized Stochastic Restricted Liu 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(ogsrliu(Y~X1+X2+X3+X4-1,r,R,dpn,delt,d,data=pcd)) smse<-mseval[order(mseval[,2]),] points(smse[1,],pch=16,cex=0.6) ```