# ogalt3: Ordinary Generalized Type (3) Adjusted Liu Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

This function can be used to find the Ordinary Generalized Type (3) Adjusted Liu Estimatd values, corresponding scalar Mean Square Error (MSE) value in the linear model. Further the variation of MSE values can be shown graphically.

## Usage

 `1` ```ogalt3(formula, k, d, aa, data = NULL, na.action, ...) ```

## Arguments

 `formula` in this section interested model should be given. This should be given as a `formula`. `k` a single numeric value or a vector of set of numeric values. See ‘Example’. `d` a single numeric value or a vector of set of numeric values. See ‘Example’. `aa` this is a set of scalars belongs to real number system. Values for “aa” should be given as a `vector`, format. See ‘Details’. `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.

In order to get the best results, optimal values for `k`,`d` and `aa` should be selected.

The way of finding `aa` can be determined from Rong,Jian-Ying (2010) Adjustive Liu Type Estimators in linear regression models in communication in statistics-simulation and computation, volume 39

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

## Value

If `k` and `d` are single numeric values then `ogalt3` returns the Ordinary Generalized Type (3) Adjusted Liu Estimated values, standard error values, t statistic values, p value, corresponding scalar MSE value.

If `k` and `d` are vector of set of numeric values then `ogalt3` returns the matrix of scalar MSE values of Ordinary Generalized Type (3) Adjusted Liu Estimator by representing `k` and `d` as column names and row names respectively.

## 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

Rong,Jian-Ying (2010) Adjustive Liu Type Estimators in linear regression models in communication in statistics-simulation and computation, volume 39 DOI:10.1080/03610918.2010.484120

`matplot`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## Portland cement data set is used. data(pcd) k<-0.1650 d<--0.1300 aa<-c(0.958451,1.021155,0.857821,1.040296) ogalt3(Y~X1+X2+X3+X4-1,k,d,aa,data=pcd) # Model without the intercept is considered. ## To obtain the variation of MSE of Ordinary Generalized # Type (3) Adjusted Liu Estimator. data(pcd) k<-c(0:5/10) d<-c(-420:-380/10) aa<-c(0.958451,1.021155,0.857821,1.040296) msemat<-ogalt3(Y~X1+X2+X3+X4-1,k,d,aa,data=pcd) matplot(d,ogalt3(Y~X1+X2+X3+X4-1,k,d,aa,data=pcd),type="l",ylab=c("MSE"), main=c("Plot of MSE of Ordinary Generalized Type (3) Adjusted Liu Estimator"),cex.lab=0.6,adj=1,cex.axis=0.6,cex.main=1,las=1,lty=3) text(y=msemat[1,],x=d[1],labels=c(paste0("k=",k)),pos=4,cex=0.6) ```