# Q below was dropped from original draft


# Q3: Amorim-Neto and Cox. Interaction effects

## preparation of full dataset 
#rm(list=ls())
#load("AmorimNetoCox_full.RData")
#a
#anc <- subset(d,country != "BOLIVIA" & country != "HONDURAS" & country != "URUGUAY")
#b
#anc$proxXenpres <- anc$proximity*anc$enpres
#save.image("AmorimNetoCox.RData")


load("AmorimNetoCox.RData")

#d
reg.orig <- lm(enpv ~ lml + upp + proximity + proxXenpres, data=anc)
reg.full <- lm(enpv ~ lml + upp + proximity + enpres + proxXenpres, data=anc)
#d
#An additional effective pres. candidate increases the eff. number of el. parties
# only by .025 when proximity is zero, i.e. if the parl election is at midterm between the pres. elections
# e
# 0.025+2.15 = 2.175
# f

#Predictions with CIs (looks need to be improved)
cand <- c(seq(0,7,.1))
pr.min <- predict(reg.full,new=data.frame(lml=mean(anc$lml),upp=mean(anc$upp),proximity=0,enpres=cand,proxXenpres=0),interval="confidence")

pr.max <- predict(reg.full,new=data.frame(lml=mean(anc$lml),upp=mean(anc$upp),proximity=1,enpres=cand,proxXenpres=cand),interval="confidence")

plot(cand,pr.min[,1],type="l", ylim=c(-5,15))
lines(pr.min[,2]~cand,lty="dashed")
lines(pr.min[,3]~cand,lty="dashed")
lines(pr.max[,1]~cand)
lines(pr.max[,2]~cand,lty="dashed")
lines(pr.max[,3]~cand,lty="dashed")