From: The role of ENSO in understanding changes in Colombia's annual malaria burden by region, 1960–2006
Poisson Model (PM) | Negative Binomial Regression Model (NBRM) | Link Function |
---|---|---|
E(Y t /X t ) = λ t = exp(X t β) > 0 | E(Y t /X t ) = λ t = exp(X t β) > 0 | Log |
V(Y t /X t ) = λ t = exp(X t β) > 0 | V(Y t /X t ) = λ t + α (λ t )2-k; k = 0,1 | Log |
E(Y t /X t ): Expected value of number of malaria cases in year t given the information of X t . | ||
V(Y t /X t ): Variance of the number of malaria cases in year t given the information of X t . | ||
β: unknown set of parameters | ||
α: dispersion parameter [α > 0 over-dispersion; α < 0 under-dispersion] | ||
Y t : dependent variable: Number of Malaria cases per year (Total, R1,..., R5) | ||
X t : set of independent or explanatory variables. | ||
Y t : {Mal_Tot, Mal_R1,..., Mal_R5}: set of dependent variables. | ||
X t : {Base Line Trend, ENSO Measure} = {BLT, ENSO} | ||
BLT: {Intercept, Trend1, Trend2, Vextre}: some or all of them | ||
ENSO: {ENSO_Avg, ENSO_Dom}: one of them | ||
Probability Distribution (PD) | ||
Poisson PD: | ||
Negative Binomial PD: |