Page 26 - Contributed Paper Session (CPS) - Volume 7

CPS2020 Honeylet T. S.
regression model estimates without bootstrapping, (2) Poisson regression
model estimates using bootstrap within, and (3) Poisson regression model
estimates using bootstrap across.
Absolute relative bias (RBIAS) and mean absolute error (MAE) will be used
to evaluate the performance of matching and estimation procedures. Formula
for RBIAS and MAE are shown below:
̂
= | − ̂ | (2.2)

̂
where is the true value of the coefficient and is the coefficient estimate;
and
= ∑ | − ̂ | (2.3)
=1

ℎ
ℎ
where is the observation, ̂ is the predicted observation, and n is the

number of observations.

2.3. Simulation
To evaluate the performance of matching and estimation methods,
datasets with complete information are generated first. The complete dataset
consists of two common variables X1 and X2 with either high correlation or low
correlation, and specific variables Y and Z. Highly correlated X1 and X2 are
generated as follows:
~(2,1); = 0.99 + ℎ ~(0,1) (2.4)
1
2
1
Moreover, X1 and X2 with low correlation have the following characteristics:
~(2,1); = 2 + 0.01 + ℎ ~(0,1) (2.5)
2
1
1
Subsequently, specific variables Y and Z are Poisson distributed with log
means that are either linear or nonlinear functions of X1 and X2. For the linear
case, means of Y and Z are generated as follows:
= exp( + ); = exp( + ) (2.6)

1
1
2

2
where − vector of means of Y; − vector of means of Z;

− vector of observations of , = 1,2;

and – respective coefficients of , = 1,2.

Furthermore, coefficients of the X variables were made to vary. Specifically,
the effect of the X variables on Y can either be: (a) X1 dominating with = 0.8
1
and = 0.2 or (b) X1 and X2 have equal effects with = = 0.45. Similarly,
2
1
2
the effect of the X variables on Z can either be: (a) X1 dominating with = 0.7
1
and = 0.1 or (b) X1 and X2 have equal effects with = = 0.4.
2
1
2
For nonlinear case, means of Y and Z are generated as follows:
= exp[exp( ) + exp( )]; = exp[exp( ) + exp( )] (2.7)

1
1
2
2
where – vector of means of Y; – vector of means of Z;

– vector of observations of , = 1,2;

and – respective coefficients of , = 1,2.

In this case, the coefficients of the X variables in generating the means of
Y are: (a) = 0.2 and = 0.1 or (b) = = 0.14. The coefficients in
2
1
1
2
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