PLEBISCITE FOR PEACE IN COLOMBIA: STATISICAL ANALYSIS USING - - PowerPoint PPT Presentation
Introduction Applied exercise Discussion PLEBISCITE FOR PEACE IN COLOMBIA: STATISICAL ANALYSIS USING COMPOSITIONAL DATA CoDaWork 2017 CATALINA PLATA RINC ON & ANDR ES FELIPE ORTIZ RICO UNIVERSITY SANTO TOM AS June 9 2017
Introduction Applied exercise Discussion
CoDaWork 2017
CATALINA PLATA RINC´ ON & ANDR´ ES FELIPE ORTIZ RICO UNIVERSITY SANTO TOM´ AS
June 9 2017
Introduction Applied exercise Discussion
Introduction Applied exercise Discussion
Motivation: The similar behavior observed at the geographical level bet- ween the three electoral processes was the main motivation for the deve- lopment of this exercise.
Figura 1: Geographical comparision
Introduction Applied exercise Discussion
Description of the variables used through the exercise:
Introduction Applied exercise Discussion
Introduction Applied exercise Discussion
Introduction Applied exercise Discussion
Figura 2: Second round and plebiscite
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Linear model that predicts the result of the plebiscite Cluster analysis for plebiscite results Discriminant analysis for the results of the plebiscite
Introduction Applied exercise Discussion
The model equation in the simplex is: Yi = a ⊕ X1i ⊙ B1 ⊕ X2i ⊙ B2 ⊕ x3i ⊙ b3 ⊕ x4i ⊙ b4 ⊕ x5i ⊙ b5 ⊕ εi (1) In the real space, the equation of the model is: ilr(Yi) = ilr(a) + ilr(X1i)B1 + ilr(X2i)B2 + x3ib3 + x4ib4 + x5ib5 + εi (2) X1i: Composition of the first presidential round X2i: Composition of the second presidential round Yi: Composition of the plebiscite x3i: Population projected to the 2014 x4i: Voters potential in 2014 x5i Unsatisfied needs index 2008
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Graphical display of the result of the model adjustment to the data:
Figura 3: Model adjustment vs Observed data
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Geographical comparison at the departmental level of the original results versus those obtained with the model.
Figura 4: Geographical comparison of maps at departmental level: observed vs model
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The following table gives a global look to the results: The model indicate although with a small difference that the winning re- sult was the NO, a result that coincides with the observed results of the plebiscite, although as observed in the geographical comparison, there are 3 departments in which the model does not coincide with the reality.
Introduction Applied exercise Discussion
To determine each municipality or department to which cluster belonged (Yes-No), the information that was taken into account were only the com- positions referring to the 2 presidential rounds, later, the individuals were coloured considering the clasiffication made by the cluster.
Introduction Applied exercise Discussion
The result is shown below:
Figura 5: Ternary diagram at the departmental level with the adjustment by the cluster
Introduction Applied exercise Discussion
Geographical comparison at the municipal level of the original results com- pared to those obtained with the cluster.
Figura 6: Geographical comparison at municipal level: observed vs cluster
Introduction Applied exercise Discussion
Geographical comparison at the departmental level of the original results compared to those obtained with the cluster.
Figura 7: Geographical comparison at departmental level: observed vs cluster
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The table below shows the percentage of successes of this method at the municipal level and at the departmental level: The two exercises at both the departmental and municipal level have very good results since in both cases the percentage of success is above 80 %.
Introduction Applied exercise Discussion
For this exercise, all available variables were used and the grouping variable was a dummy that indicated which outcome had been the winner for each municipality or department. (Yes - No)
Introduction Applied exercise Discussion
It is important to notice that even though is clear that are more red in- dividuals (YES), it doesn’t mean that this was the winner result. The demographic density of the population of each department has to be take into account.
Figura 8: Ternary diagram at the departmental level with the adjustment by the discriminant analysis
Introduction Applied exercise Discussion
Geographical comparison at the municipal level of the original results com- pared to those obtained with discriminant analysis.
Figura 9: Geographical comparison at municipal level: observed vs. discriminant
Introduction Applied exercise Discussion
Geographical comparison at the departmental level of the original results compared to those obtained with discriminant analysis.
Figura 10: Geographical comparison at departmental level: observed vs. discriminant
Introduction Applied exercise Discussion
The table below shows the percentage of successes of this method at the municipal level and at the departmental level: The results at both the departmental and municipal level have very good results since in both cases the percentage of success is above 80 %; At least at the departmental level this method is better than the cluster, but it is important to remember that this exercise unlike the cluster, makes use
Introduction Applied exercise Discussion
The results of the three exercises applied in this case (the model, the cluster and the discriminant analysis) allow to highlight the great benefits and capacities of the techniques for CoDa. Although the objective of this exercise was not to find the best fit to the results of the electoral process, it should be pointed out that, with the variables used as the basis for the analysis, a good approximation is achieved to the real data.
Introduction Applied exercise Discussion