Analysis code for looking at the relationship between project goal and % success from #SciFund. Note, I did it with my own private data set that has a lot of merged fields in it, but you can run this analysis or something like it with Zen's data at http:

goal_success_scifund.R

source("./sciFundFunctions.r")
library(gridExtra)

#################################################
#######HISTOGRAMS
#################################################
#total raised histogram distribution
raised<-qplot(total, data=projects) +
  theme_bw(base_size=16) +
  xlab("\nTotal Raised") +
  ylab("Count")

mean(projects$total)
median(projects$total)


#total asked for
asked<-qplot(Goal, data=projects)+
  theme_bw(base_size=16) +
  xlab("\nTotal Asked For") +
  ylab("Count")

mean(projects$Goal)
median(projects$Goal)



#################################################
#####goal influence
#################################################

a<-qplot(Goal, percent,data=projects, size=I(4))+
  theme_bw(base_size=16) +
  xlab("\nGoal") +
  ylab("Percent Raised") +
  geom_vline(xintercept=7500, colour="red", lty=2, size=2) +
  geom_text(aes(x=15000, y=150, label="Zone of Failure?"), size=8)

b<-qplot(Goal, percent,data=projects, size=I(4))+
  theme_bw(base_size=16) +
  xlab("\nGoal") +
  ylab("Percent Raised") +
  stat_smooth(method="glm", family=gaussian(link="log"), size=2)

grid.arrange(a,b,ncol=2)


##ANALYSIS OF CURVES
aglm<-glm(percent ~ Goal, family=gaussian(link="log"), data=projects)

Anova(aglm)
summary(aglm)
summary(lm(percent ~ aglm$fitted.values , data=projects))$r.squared #r2=0.22


####BOX

#get the likelihood of the data given some breakpoint
boxFun<-function(params){
  breakpoint<-params[1]
  sdlog<-abs(params[2])
  sd3<-abs(params[3])
  prec<-projects$percent
  idx<-which(projects$Goal>breakpoint)
  -2*sum(dlnorm(prec[-idx], mean(prec[-idx]), sdlog, log=T))+sum(dlnorm(prec[idx], 0, sd3, log=T))
}

#brute force solve - yes, it's brute force, but, optim was being squirely with my function above 
x<-7500
m<- boxFun(c(x,5,6))
  for(y in seq(1,100,.1)){
   for(z in seq(1,100,.1)){
    a<-boxFun(c(x,y,z))
    if(a<m) {
      b<-c(x,y, z)
      m<-a
    }
  }}

######AIC comparison
m+2*2 - AICc(aglm)