# lte1: Type (1) Liu Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

This function can be used to find the Type (1) Liu Estimated values, corresponding scalar Mean Square Error (MSE) value and Prediction Sum of Square (PRESS) value in the linear model. Further the variation of MSE and PRESS values can be shown graphically.

## Usage

 `1` ```lte1(formula, k, d, press = FALSE, 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 ‘Examples’. `d` a single numeric value or a vector of set of numeric values. See ‘Examples’. `press` if “press=TRUE” then all the PRESS values and its corresponding parameter values are returned. Otherwise all the scalar MSE values and its corresponding parameter values are returned. `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 `matplot` so as to obtain the variation of scalar MSE values and PRESS values graphically. See ‘Examples’.

## Value

If `k` and `d` are single numeric values then `lte1` returns the Type (1) Liu Estimated values, standard error values, t statistic values, p value, corresponding scalar MSE value and PRESS value.

If `k` and `d` are vector of set of numeric values then `lte1` returns the matrix of scalar MSE values and if “press=TRUE” then `lte1` returns the matrix of PRESS values of Type (1) Liu Estimator by representing `k` and `d` as column names and row names respectively.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

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``` ```## Portland cement data set is used. data(pcd) k<-0.1650 d<--0.1300 lte1(Y~X1+X2+X3+X4-1,k,d,data=pcd) # Model without the intercept is considered. ## To obtain the variation of MSE of Type (1) Liu Estimator. data(pcd) k<-c(0:4/5) d<-c(0:25/10) msemat<-lte1(Y~X1+X2+X3+X4-1,k,d,data=pcd) matplot(d,lte1(Y~X1+X2+X3+X4-1,k,d,data=pcd),type="l",ylab=c("MSE"), main=c("Plot of MSE of Type (1) 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) ## Use "press=TRUE" to obtain the variation of PRESS of Type (1) Liu Estimator. ```