# liu: Liu Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

`liu` can be used to find the Liu Estimated values and corresponding scalar Mean Square Error (MSE) value in the linear model. Further the variation of MSE can be shown graphically.

## Usage

 `1` ```liu(formula, d, data = NULL, na.action, ...) ```

## Arguments

 `formula` in this section interested model should be given. This should be given as a `formula`. `d` 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 `d` is a single numeric values then `liu` returns the 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 `liu` returns all the scalar MSE values and corresponding parameter values of Liu Estimator.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

Liu, K. (1993) A new class of biased estimate in linear regression in Communications in Statistics-Theory and Methods 22, pp. 393–402.

`plot`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## Portland cement data set is used. data(pcd) d<-0.05 liu(Y~X1+X2+X3+X4-1,d,data=pcd) # Model without the intercept is considered. ## To obtain the variation of MSE of Liu Estimator. data(pcd) d<-c(0:10/10) plot(liu(Y~X1+X2+X3+X4-1,d,data=pcd),main=c("Plot of MSE of 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(liu(Y~X1+X2+X3+X4-1,d,data=pcd)) smse<-mseval[order(mseval[,2]),] points(smse[1,],pch=16,cex=0.6) ```

### Example output

```\$`*****Liu Estimator*****`
Estimate Standard_error t_statistic p_value
X1   2.1800         0.1837     11.8641  0.0000
X2   1.1563         0.0476     24.3039  0.0000
X3   0.7491         0.1583      4.7326  0.0011
X4   0.4883         0.0412     11.8477  0.0000

\$`*****Mean square error value*****`
MSE
0.0631
```

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