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### This function is a component of astrochron: An R Package for Astrochronology
### Copyright (C) 2016 Stephen R. Meyers
###
###########################################################################
### divTrend: divide data value by linear trend - (SRM: March 29, 2012; Oct. 11, 2012;
### May 20, 2013; June 21, 2013;
### July 22, 2016)
###
### motivated by Bloomfield (2000), pg 134.
###########################################################################
divTrend <- function (dat,genplot=T,verbose=T)
{
if(verbose) cat("\n----- DIVIDE STRATIGRAPHIC SERIES BY LINEAR TREND-----\n")
dat=data.frame(dat)
### use least-squares fit to remove linear trend
lm.0 <- lm(dat[,2] ~ dat[,1])
if(verbose) cat(" * Slope=",lm.0$coeff[2],"\n")
if(verbose) cat(" * y-intercept=",lm.0$coeff[1],"\n")
y.predict <-predict(lm.0, se= TRUE)
out <- dat
out[2] <- dat[2]/y.predict$fit
if(genplot)
{
### plot detrended data
par(mfrow=c(2,2))
plot(dat,cex=0.5, xlab="Location", ylab="Value", main="Data with Trend Line"); lines(dat[,1],y.predict$fit,col="red")
plot(out,cex=0.5, xlab="Location", ylab="Value", main="Data/Trend"); lines(out)
### plot the denisty and the histogram together
hist(out[,2],freq=F, xlab="Value", main="Distribution of Data/Trend Values"); lines(density(out[,2], bw="nrd0"),col="red"); grid()
### boxplot
boxplot(out[,2], ylab="Value", main="Boxplot of Data/Trend Values")
### Normal probabilty plot (Normal Q-Q Plot)
# qqnorm(out[,2]); qqline(out[,2], col="red")
}
return(out)
### END function divTrend
}
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