Aungkana Hukharnsusatrue

pp. 1311 - 1325

Abstract

The objective of this research is to compare multiple regression coefficients estimating methods with
existence of multicollinearity among independent variables. The estimation methods are Ordinary Least
Squares method (OLS), Restricted Least Squares method (RLS), Restricted Ridge Regression method (RRR)
and Restricted Liu method (RL) when restrictions are true and restrictions are not true. The study used
the Monte Carlo Simulation method. The experiment was repeated 1,000 times under each situation. The
analyzed results of the data are demonstrated as follows.
CASE 1: The restrictions are true.
In all cases, RRR and RL methods have a smaller Average Mean Square Error (AMSE) than OLS
and RLS method, respectively. RRR method provides the smallest AMSE when the level of correlations is
high and also provides the smallest AMSE for all level of correlations and all sample sizes when standard
deviation is equal to 5. However, RL method provides the smallest AMSE when the level of correlations is
low and middle, except in the case of standard deviation equal to 3, small sample sizes, RRR method provides
the smallest AMSE. The AMSE varies with, most to least, respectively, level of correlations, standard deviation and
number of independent variables but inversely with to sample size.
CASE 2: The restrictions are not true.
In all cases, RRR method provides the smallest AMSE, except in the case of standard deviation equal
to 1 and error of restrictions equal to 5%, OLS method provides the smallest AMSE when the level of correlations is low or median and there is a large sample size, but the small sample sizes, RL method provides
the smallest AMSE. In addition, when error of restrictions is increased, OLS method provides the smallest
AMSE for all level, of correlations and all sample sizes, except when the level of correlations is high and
sample sizes small. Moreover, the case OLS method provides the smallest AMSE, the most RLS method has
a smaller AMSE than RRR and RL methods when the level of correlations is low or median and sample sizes
are large.
The AMSE varies with, most to least, respectively, error of restrictions, level of correlations, standard
deviation and number of independent variables but inversely with to sample sizes, except that error of
restrictions does not affect AMSE of OLS method.

Keywords

• multicollinearity
• Ordinary Least Squares
• Restricted Least Squares
• Restricted Ridge Regression
• Restricted Liu