# Towards a Predictive Analytics-Based Intelligent Malaria Outbreak Warning System+
## 2 Assessment of Hidden Ecological Factors
### Presentation of Results  
In the application of PLS-SEM, three weighting schemes such as centroid weighting, factorial weighting and path weighting are conceptually used for model specifications and estimations. The conceptual SEM presented in Figure 3a shows the hypothetical causal relationship between latent (hidden) variables and observed meteorological (manifest) variables to the occurrence of malaria incidence. For the identification of confounding hidden variables, we performed factor analysis using exploratory factor analysis (EFA) [34]. From the results, three hidden factors were identified: Factor I (related to the minimum temperature and relative humidity), Factor II (related to the maximum temperature and solar radiation) and Factor III (related to precipitation and wind speed). The identified factors accounted for 64% of the total variance, and at \(\alpha\) = 5% level of significance, \(\chi^{2}\) = 13.91, df = 8, Pvalue = 0.0841. This result provides sufficient evidence to explain malaria incidence in the study area. We also explored the Guttman-Kaiser Criterion [35] and Cattell scree plots [36], to determine the number of factors to extract, the result of which reconfirmed the existence of three hidden ecological factors to the incidence of malaria. In the Guttman-Kaiser Criterion, we have the eigenvalues 2.71, 1.53, 1.02, 0.82, 0.57, 0.29, 0.05 computed using the correlation matrix (see Table 1); however, the rule for extraction is based on the factors whose eigenvalues are greater than unity. We then discard those factors that have eigenvalues less than unity, and are left with three eigenvalues indicating the number of factors to be considered. Similarly, the Cattell scree plot presented in (Figure 4) facilitates decisions regarding the number of factors to retain. By analysing Table 1, we obtained the scree plot shown in Figure 4 which represents the relative proportion of variance accounted for by the components. In the scree plot, the eigenvalues of the first three components greater than unity can be seen from the parallel indicator, while the subsequent components below unity also line up beneath the parallel indicator. However, it is important to evaluate the variance accounted for by a few of the eigenvalues regarded as sufficient so that we can focus on them and discard the remaining insufficient factors as noise. In Table 2, we present Pearson's cross-correlation between meteorological variables and occurrence of malaria incidence at various lag effects from 0 to 3 months. The Lag 0, Lag 1 and Lag 2 (e.g., 0 month, 1 month and 2 month) presented in Table 2 which indicates the lagged correlation effects between climate variables and the incidence of malaria in the study area. We observed that at lag effects of 1 month, the minimum temperature, maximum temperature and relative humidity have positive association with malaria incidence as indicated by 0.321, 0.215 and 0.254 respectively. While the precipitation is negatively correlated with malaria incidence at lag effects of 1 month as indicated by \(-\)0.292. This explained that the climate drivers at lag of 1 month would be quite enough for the mosquitoes to reproduce and also complete their incubation periods (EIP) to becomes fully active in transmitting malaria infection. We found that the preceding result is consistent with other relevant studies on the influence of meteorological variables on the malaria incidence [37]. The 1 month time lag in the study area is sufficient to capture the pattern of malaria transmission for various strains of plasmodium parasites with definite lengths of EIP. This period usually takes about 10-15 days [38] and temporally varies over location, parasite species and climatic resolution. At Lag 0 and Lag 2, the minimum temperature, precipitation and relative humidity have negative lag effects at 0 month and 2 month except the maximum temperature which has effects of 0.284 and 0.092.