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CPS2084 Siti Aisyah Mohd Padzil et al.
2.2 Multiple Binary Logit
Multiple Binary Logit (MBL) or often called as Logistic Regression is a
variation to ordinary linear regression and is used when the dependent
variable is binary taking on values 0 and 1. The basic general model of MBL
was defined by (Kutner et al. 2008) s in Equation (1).

where represent the response variable, β0 is the constant coefficient, is
the number of covariates and is the random error for the model.
The results of success/ failure for MBL is presented in forms of probability
values which is in between 0 and 1. For example, probability of 0.75 explain
that there are 75% chances of success (1) to occur and vice versa. Unlike
Multiple regression, the do not gives the probability results, instead the
probability, can be obtain using Equation (2).

2.3 Model Averaging and Alternative Model Averaging
Model Averaging discussed in (Claeskens and Hjort, 2008) was proposed
to deal with underestimation of parameter estimates issue which come from
Model Selection. MA applies weights to all possible models, so that the final
best model will include all variables being studied and covariates with higher
importance will receive more weight. According to Posada and Buckley (2004),
MA will shrink the estimates of a weaker variables. In this study, the weight
calculation will be based on and as in (Hurvich and Tsai,1989) and
(Schawarz, 1978) respectively. The formula for weight, is as in Equation
(3).

where m is all possible models, = 1, 2, 3 …, and is the model selection
criterion. MA aims to incorporate the estimates of potentially good
model by averaging the weights of all possible models to produce
estimator for the best model. Equation (4) shows the formula to obtain
coefficients estimates for each covariate which average the weights for
all possible models.

where ̂ (,) is the estimate of βp under model for m = 1,2,…, M.
Figure 1 summarized the step and procedure of obtaining MA best model
based on (Aisyah et al. 2018) as well as AMA procedure.

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