LISTEXAMPLE.RPF

LISTEXAMPLE.RPF does a sequence of regressions, removing from the sample each time just the most extreme outlier, so long as there is a data point with a standardized residual greater than 2.5. The LIST[INTEGER] called OUTLIERS is used to keep track of the entries as they are removed. This is provided as an example of how to use a LIST, which is a vector of objects of variable length.

Outside the loop, this creates a series which initially is all 1's (which will be the SMPL series for the regression, with dropped entries zeroed out) and declares an (empty) LIST[INTEGER] which will be used to keep track of the observations which are dropped.

set working = 1.0
dec list[integer] outliers

Inside the loop

   prj(xvx=px)
   set stdresids = abs(resids/sqrt(%seesq*(1-px)))
   ext(noprint) stdresids

computes the series of (absolute values of) the studentized residuals and uses EXTREMUM to locate the maximum value (and entry). Then this checks to see if any of the studentized residuals are greater than 2.5. If the largest one is above that limit, the first COMPUTE adds the entry number (%MAXENT) to the end of the outliers LIST. (That's what a + operation does on a LIST). The second COMPUTE zeroes out the entry in the series used in the SMPL option on the LINREG so it gets skipped in the next and later regressions. If none of the residual statistics is greater than the 2.5 limit, we're done.

   if %maximum>=2.5 {
      compute outliers=outliers+%maxent
      compute working(%maxent)=0
   }
   else
      break

This shows the list of outliers (%size returns the number of elements, which could be zero) and re-runs the final regression with the PRINT option on.

do i=1,%size(outliers)

?"Outlier at" outliers(i)

end do i

linreg(print,smpl=working) logy / resids

# constant logk logl

Full Program

open data zellner.prn

data(format=prn,org=columns) 1 25 valueadd capital labor nfirm

set logy = log(valueadd)

set logk = log(capital)

set logl = log(labor)

* Compute linear regression, and the standardized residuals.

set working = 1.0

dec list[integer] outliers

loop

linreg(noprint,smpl=working) logy / resids

# constant logk logl

prj(xvx=px)

set stdresids = abs(resids/sqrt(%seesq*(1-px)))

ext(noprint) stdresids

if %maximum>=2.5 {

compute outliers=outliers+%maxent

compute working(%maxent)=0

}

else

break

end loop

do i=1,%size(outliers)

?"Outlier at" outliers(i)

end do i

linreg(print,smpl=working) logy

# constant logk logl

Output

Outlier at 4

Outlier at 10

Linear Regression - Estimation by Least Squares

Dependent Variable LOGY

Usable Observations 23

Degrees of Freedom 20

Skipped/Missing (from 25) 2

Centered R^2 0.9888884

R-Bar^2 0.9877772

Uncentered R^2 0.9994653

Mean of Dependent Variable 5.9323384337

Std Error of Dependent Variable 1.3638215667

Standard Error of Estimate 0.1507796992

Sum of Squared Residuals 0.4546903536

Regression F(2,20) 889.9576

Significance Level of F 0.0000000

Log Likelihood 12.4862

Durbin-Watson Statistic 1.8668

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 1.7642052396 0.1637986013 10.77058 0.00000000

2. LOGK 0.2094788550 0.0700712951 2.98951 0.00724489

3. LOGL 0.8519478678 0.0847732478 10.04973 0.00000000