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CPS2174 Septian R. et al.
Therefore, the prediction of the each model candidate can be formulated
below.
̂ = ( ); = 1,2, … ,
∗

Then, the averaging of the model candidate is

̂ = ∑ ̂

=1
with indicates the weight of -th model candidate, and ∑ = 1. [5]

=1

2.3 Proposed Method
In case of binary response variable, ×1 = [ ]; ∈ {0,1}, the model

candidate constructed by implementing the logistic regression to averaged in
model averaging process. The model candidate in this case can be described
below.
( ̂ ) = ( ); = 1,2, … ,
∗

where ∗ × contains predictor variables that randomly selected from
. Then, the next step is averaging of probability prediction each model
candidates ( ) using the AIC weight,

= ∑

=1
before it transforms to be the class of response variable. In this research,
AIC weight applied to average the prediction each model candidates that is
based on the value of AIC in each model candidates. Suppose there are
model candidates, therefore the – th AIC weight follows
1
( )

= 2 1

∑ ( )

2
=1
where denotes the value of AIC in the – th model candidates, and ≥

0 ; ∑ =1 = 1 [6].

In practices, the data set separated to be two parts; training data for
constructing the model, and testing data for evaluating the prediction. The
observation that selected to be the content of testing data selected randomly
with size about 40% of observations that is 100 observations, therefore
training data has 187 observations. There are three used in this research,
= {50,100,150} with = 50 that to be evaluated by 100 replications in each
processes. In detail the randomly process for selecting observation in testing
data and for selecting predictor in model candidate are applied in each
replictions.

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