5 + where , for are smooth coefficients (or functions of climate variability) and are the coefficients of the linear socio-economic control variables. Note that in this specification the interaction between temperature and precipitation is established through the variability in precipitation. In the second specification where the form of the nonlinear function is unknown, the empirical formulation of the model can be written as: Int. J. Environ. Res. Public Health 2011, 8 919 Although, this last specification is the most attractive for empirical investigation proposes because it nests all possible functional forms of the effect of climatic factors on malaria prevalence, it comes with the cost that higher dimensionality of the function might weaken the correct estimation of the marginal effects given the sample size in hand. Since we are fitting a three dimensional function with fewer data points (our current sample size is 305 observations) we can run into the risk of not having enough data points in some neighborhoods for a good fit. This problem is known as “curse of dimensionality” in non-parametric estimations [30]. That is, when more data become available (e.g., 500 observations at least) more general non-parametric models with fewer assumptions could be tested). 7. Results and Their Interpretation Results obtained from the two model specifications are similar in many aspects but because of possible “curse of dimensionality” issues only results from the first specification are presented. We use the natural log of malaria cases per 1,000 people as dependent variable. Results for the linear effects of the socio-economic variables on malaria cases are presented in Table 2. These effects are all statistically different from zero (except the effect of population density) and have expected signs. Also, the coefficients on these variables have the expected signs. An increase in GDP per capita and per capita expenditures on healthcare significantly reduce the number of malaria cases. In contrast, a higher Gini inequality index (meaning more unequal distribution of income) and count of hospital beds per 1,000 people lead to an increase in the number of reported malaria cases. We included number of hospital beds per 1,000 people for each country as a proxy for access to medical care. The assumption is that the number of hospital beds per 1,000 people indicates ability of an infected person to get to a health care facility and get treatment. Therefore, areas with more access to health care facilities are more likely to have cases reported and this needed to be controlled for. Note also that the socio-economic variables explain about 22% of the variations observed in the log of malaria cases per 1,000 people. (8) (9)