library(spatstat)

#############
# Null model
#############

null <- ppm(outbreaks.ppp, ~1) 
summary(null)

######################
# Inhomogeneous model
######################

inhom <- ppm(outbreaks.ppp, ~ x + y) 
summary(inhom)
valid.ppm(inhom)

# To gnerate likelihood ratio test for models above:
LR.1 <- anova(null, inhom)
summary(LR.1)
AIC(null)
AIC(inhom)

####################################
## Covariate Model with Interaction
####################################

# popmgvf.img = pixel image for population density:MGVF interaction
# bio1.africa.30.img = pixel image for mean annual temperature
# bio12.africa.30.img = pixel image for mean annual precipitation
# mgvf.2001.africa.img = pixel image for MGVF
# popdens2000.africa.30.img =  pixwl image for population density
# alt.africa.30.img = pixel image for altitude

spatial.m.int <- ppm(outbreaks.ppp, ~Cov1 + Cov2 + Cov3 + Cov4 + Cov5 + Cov6, covariates = list(Cov1 = popmgvf.img, 
	Cov2 = bio1.africa.30.img, Cov3 = bio12.africa.30.img, Cov4 = mgvf.2001.africa.img, Cov5 = popdens2000.africa.30.img,
	Cov6 = alt.africa.30.img))
spatial.m.int
exp(coef(spatial.m.int))
exp(confint(spatial.m.int))
AIC(spatial.m.int)
valid.ppm(spatial.m.int)


pInteract <- predict.ppm(spatial.m.int, covariates = list(Cov1 = popmgvf.img, 
	Cov2 = bio1.africa.30.img, Cov3 = bio12.africa.30.img, Cov4 = mgvf.2001.africa.img, 
	Cov5 = popdens2000.africa.30.img, Cov6 = alt.africa.30.img))