LD_calc <- function(proportion,model.object,intercept,linear.parameter,quad.parameter=NULL,x.min=NULL,x.max=NULL){	
		post <- rethinking::sample.naive.posterior(model.object)
	a <- post[[which(names(post)==intercept)]]
	b <- post[[which(names(post)==linear.parameter)]]
	if(!is.null(quad.parameter)){
		c <- post[[which(names(post)==quad.parameter)]]
		post.LD.low  	<- 	sapply(proportion,function(z)( (-b - sqrt(b^2-4*c*a+4*c*log(z/(1-z))))/(2*c)))
		post.LD.low.mean	<- mean(post.LD.low)
		post.LD.low.CI <- rethinking::HPDI(post.LD.low,prob=0.95)
		post.LD.high 	<- 	sapply(proportion,function(z)( (-b + sqrt(b^2-4*c*a+4*c*log(z/(1-z))))/(2*c)))
		post.LD.high.mean	<- mean(post.LD.high)
		post.LD.high.CI <- rethinking::HPDI(post.LD.high,prob=0.95)
		LD_results <- list("LD_low" = post.LD.low.mean,
							"LD_low_CI" = post.LD.low.CI,
							"LD_high" = post.LD.high.mean,
							"LD_high_CI" = post.LD.high.CI)
		if(!is.null(x.min)){
			if(LD_results$LD_low < x.min){
				warning("the predicted lower LD bound is outside of the range of your data")
			}
		}
		if(!is.null(x.max)){
			if(LD_results$LD_high > x.max){
				warning("the predicted higher LD bound is outside of the range of your data")
			}
		}
	} else if(is.null(quad.parameter)){
		post.LD <- sapply(proportion,function(z)(log(z/(1-z))-post$a)/post$b)
		post.LD.mean <- mean(post.LD)
		post.LD.CI <- rethinking::HPDI(post.LD,prob=0.95)
		LD_results <- list("x" = post.LD.mean,
								"x_CI" = post.LD.CI)
		if(!is.null(x.max)){
			if(post.LD.CI[2] > x.max){
				warning("the predicted LD is outside of the range of your data")
			}
		}
	}
	return(LD_results)
}