## Maybe there is Hope

The Republic of Malawi is a former part of British Central Africa. It acquired independence from the United Kingdom in 1964. One of the independence leaders, Hastings Banda, became the first president of Malawi, serving from 1964 until 1994. During his tenure, Malawi was a shining example of how a strong authoritarian president could make life in the country much better. However, the lack of democracy during those 30 years left Malawi unfamiliar with its practice.

Did Malawi put together a solid, free and fair election in 2014? Guest writer, Uduak-Obong Ekanem, explores this question.

Malawian President Arthur Peter Mutharika

Being both African and Nigerian, I must say that the data from the 2014 Malawi Presidential elections gave me a lot of hope in the credibility of African election results. I analyzed the 2014 Presidential elections with Weighted Least Square (WLS) and Binomial regression. Another regression method available was Ordinary Least Squares (OLS) regression, however, the ones being used are more advanced than the OLS.

Election results were obtained from the website of the Malawi Electoral Commission. The election featured 12 candidates. A total of 7,470,806 registered votes were counted. Of these registered voters, 5,228,583 valid votes were counted and 56,695 votes were invalidated. In the end, 5,285,278 votes were cast on election day. The Malawi Presidential elections were analyzed for any evidence of electoral unfairness. In investigating for electoral unfairness given the data, an analysis was carried out to test for any relationship between the invalidated rates and the candidate. WLS and Binomial regression were used to estimate the dependence (if any). As usual, the null hypothesis is that there is no relationship between a ballot being invalidated and whom that ballot was cast for.

The candidates of concern were Dr. Lazarus McCarthy Chakwera and Prof. Peter Mutharika. The 2014 Presidential election was won by Mutharika with a total of 1,904,399 votes (36.4%) while Chakwera came in second place with 1,455,880 votes (27.8%). Banda was third with only 20% of the vote. Mutharika was strong in the south, while Chakwera had much of his support in the north.

Mutharika support in each of Malawi's 28 districts.

Apart from being more advanced than OLS, WLS is more efficient in adjusting for certain types of heteroskedasticity. The dependent variable, the invalidation rate, will be regressed against the independent variable, candidate support. Although there were 12 candidates, the analysis was limited to Peter Mutharika, as he was the incumbent president and best able to unfairly influence the outcome of the election.

## Results

The analysis was done with the R Statistical Environment. Prior to analysis, the independent and dependent variables were transformed using the logit function. This approach was taken to take care of any violations in the assumptions such as Normality. The assumptions of the WLS include: the residuals are from a Normal distribution, have a constant expected value, and have a constant variance.

A scatter plot and regression table regressed the transformed invalidation rate weighted with the total votes cast and level of support for Peter Mutharika producing the following results in both cases: the residuals of the relationship, the regression equation of y = 0.2326x − 4.6408 for Mutharika. Although these values are representative of the plot, the main value of concern is the p-value. The p-value is important in evaluating how much the sample supports the null hypothesis (that there is no statistical relationship between the dependent and independent variable). The p-value is compared to the alpha level of 0.05.

The p-value in this case (0.2060) leads to the conclusion that there is no detected relationship between the independent variable and the dependent variable. However, this conclusion is not enough because in performing this analysis, certain assumptions were made. To appropriately conclude this "interesting" result, the assumptions made for WLS were tested for reasonability.

The first assumptions involving the residuals concerned constant variance and expected value. To test the assumption, graphical and numerical methods were used. A graphical method included a scatter plot of the residuals against the independent variable (level of candidate support). Additionally, the Breusch-Pagan test of the model was carried out as a numerical test for homoskedastic residuals. This test returned a p-value of 0.3231 for Mutharika, indicating no evidence of heteroskedasticity.

Testing for normality is always dreaded. It is one assumption in my own little experience that is easily violated. It is important to note that if at least one of the assumptions is violated, then the model will be changed or if models or other analytical tools are exhausted then a final conclusion on the election will be made. To test the residuals are from a Normal distribution, both graphical and numerical tools were employed For the numerical tool, I used the Shapiro-Wilk test, which returned a p-value of 0.9093 for the Mutharika support model. The conclusion is that we fail to reject the hypothesis of Normality of the residuals in both cases. Furthermore, just like the p-value in the Breusch-Pagan analysis, it is extremely high.

Although the WLS showed tremendous results in the analysis of the 2014 Presidential elections, I still ran a Binomial regression. The Binomial regression served more as an additional check of the WLS. It served more to bolster the results of the WLS analysis. Three assumptions are tested in the Binomial Regression. They include: constant expected value and overdispersion. The constant expected value assumption is tested using a residuals plot or the runs test.

Statisticians know that the deviance of a model approximately follows a chi-square distribution. Knowing this, we can create an upper bound for the observed residual deviance under the assumption that it is 1. That critical value is 38.9. The observed residual deviance is 7326.7, thus indicating severe overdispersion in the model.

A solution to overdispersion is to use maximum quasi-likelihood estimation instead of the typical maximum likelihood estimation.

With this adjustment, this model was not able to detect a statistical relationship between the invalidation rate and the support level for Mutharika (p-value = 0.2920). Thus, we did not detect unfairness using this test.

The following invalidation plot illustrates these findings. Because a horizontal line fits entirely in the Working-Hotelling (1929) confidence bands, there is not sufficient evidence to conclude that the relationship between the invalidation rate and support level for Mutharika is different from none.

Invalidation plot for Peter Mutharika. Note that the slope of the line is shallow. This supports the contention that there was no differential invalidation in this election.

## Conclusion

The results from the Binomial and WLS regression show that with these analysis techniques, we can begin to trust or confer credibility in some elections in Africa. It signifies that the tunnel to fairness and honesty is not too far away.

While Malawi elevates our heart, we will turn to South Africa and Uganda's elections to see if they do the same or return us to square 1. Stay tuned on the next post.