Page 154 - Contributed Paper Session (CPS) - Volume 3

CPS1979 Francisco N. de los R.
2. Methodology
The Dissimilarity Index. Let the spatial areal data be denoted by
= ( , . . . , ) and = ( , . . . , ), which respectively denote the number
1
1

of people who voted and the number of registered voters for each of the n
areal units. Here, the areal units are the provinces, both regular and special
provinces as determined by the Commission on Elections (COMELEC), as well
as the districts in the National Capital Region. Define voter turnout as the
proportion of registered voters who actually voted. Let = ( , . . . , ) denote
1

the true voter turnout in each areal unit. The Dissimilarity index is given by Lee
et al (2015) as

| − |
= ∑
2 (1 − )

=1

where = ∑ and are the total population of registered voters and

=1
overall voter turnout in 2016 for the entire Philippines. The value of D lies in
the interval [0, 1], where 0 conveys parity and 1 means full disparity (or
segregation). The unknown true proportions are typically estimated by their
⁄
sample equivalents, that is ̂ = and ̂ = (∑ )/ ∑

=1

.

=1
Sampling variation is clearly present if ( , ) emanates from a survey, since

they are based on a random sample in areal unit . For the elections data,
variation may be alluded to measurement errors due to misreporting,
misrecording or computation as in the case of manual tallying.
Bayesian Modelling. The estimator ̂ is both the method of moments

estimator and the maximum likelihood estimator under the model
∼ ( , ). However, this model assumes that data among areal

units are independent, something which is not valid in the presence of spatial
autocorrelation. To accommodate this dependence, a Conditional
Autoregressive (CAR) model will be used to model the spatial autocorrelation
in the data. In this study, the methodology proposed by Lee, Minton and Pryce
(2015) was followed. Lee, et al. proposed a global smoothing model for
spatially autocorrelated data using a binomial generalized linear mixed model
(GLMM), where the random effects are spatially autocorrelated. The full model
is given by Lee et al (2015) as follows:
∼ ( , )

2
−1
( ) = + ; ~(0, (, ) )
1 − 0

~(0, ),

~ (, )
2

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