# Towards a Predictive Analytics-Based Intelligent Malaria Outbreak Warning System+
## 2 Assessment of Hidden Ecological Factors
### Presentation of Results
These results revealed some clear indications that the malaria transmission in the study area at Lag 0 and Lag 2 suffered a negative effect, which might be attributed to the bi-annual rainfall pattern, low relative humidity--say less than 50%--and inability of mosquitoes completing the EIP cycle. In general, the result showed that maximum temperature, minimum temperature, and relative humidity were related to the malaria incidence at lagged effects of 1 month (i.e., a month in advance) except precipitation which has a negative association in the study area. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Mal. Incid.** & **Max. Temp.** & **Min. Temp.** & **Precip.** & **Rel. Humid** & **Solar Rad.** & **Wind Speed** \\ \hline
**Mal. Incid.** & 1.00 & - & - & - & - & - & - \\
**Max. Temp.** & 0.28 & 1.00 & - & - & - & - & - \\
**Min. Temp.** & 0.68 & 0.04 & 1.00 & - & - & - & - \\
**Precip.** & \(-\)0.21 & \(-\)0.36 & 0.22 & 1.00 & - & - & - \\
**Rel. Humid.** & 0.51 & \(-\)0.24 & 0.90 & 0.38 & 1.00 & - & - \\
**Solar Rad.** & 0.19 & 0.54 & \(-\)0.33 & \(-\)0.10 & \(-\)0.44 & 1.00 & - \\
**Wind Speed** & \(-\)0.16 & 0.07 & 0.45 & 0.17 & 0.39 & 0.01 & 1.00 \\ \hline \hline \end{tabular} Note: (1) Malaria incidence, (2) Maximum temperature, (3) Minimum temperature, (4) Precipitation, (5) Relative humidity, (6) Solar radiation and (7) Wind speed.  
\end{table} 
Table 1: Correlation matrix of climate drivers and malaria incidence. Figure 4: The Cattell scree plot presents the eigenvalues of the components and threshold for identifying the number of hidden ecological factors to be considered using the information in Table 1.  
Some important summary statistics are presented in Table 2, which describe the distributional pattern of the climate indicators of malaria incidence and variance inflated factor (VIF). In factor analysis, multicollinearity can be used as a diagnostics check prior to application of regression analysis, whereby variables with high-factor loadings are typically multicollinear. We compute VIF of the climate variables to measure the degrees of multicollinearity and identify those factors that are independent of the magnitude of their VIF. In Table 2, the minimum temperature and relative humidity have VIF of 8.7919 and 9.0065 that gives a high degree of multicollinearity. The results revealed a high independent predictor of malaria incidence in the study area, and the degree to which they are independent gives evidence to accurately determine the major factors. However, the values of kurtosis (see Table 2) indicate a high peak of the climate variables with positive values across all the indicators except the wind speed which indicates a flat distribution. Positive values, generally listed in Table 2, indicate that the peakedness of distribution of the climate variables particularly influences the malaria incidence. Also, the standard error estimates provide information on the statistical accuracy of the climate variables; the larger the standard error, the wider the confidence interval of the statistic and vice-versa. Non-normality of the dataset is one necessity for adopting PLS-SEM, and it is very robust when used on extremely non-normal data [39]. We examined the degree to which the data on malaria incidence are non-normal using the Shapiro-Wilk tests by invoking R software (3.4.1, University of Auckland, New Zealand). The results show that the null hypothesis (Ho) is rejected, indicating that the malaria incidence dataset is non-normal as suggested by the following indices W = 0.9486, \(p\)-value = 0.0134 and \(\alpha\) = 0.05, respectively. This method is particularly chosen and useful in smaller samples sizes, less than 2000 [40], and the null hypothesis is that the data are from a normal distribution. Similarly, we used a graphical approach called quantile-quantile (Q-Q) plot [41] and tested for normality of the dataset in similar fashion. The approach creates a plot from the ranked samples of the dataset against a similar number of ranked theoretical samples from a normal distribution.