Determining significant changes in slope in a GAM

by James White   Last Updated August 10, 2018 11:19 AM

I've read various online blogs and forums about obtaining this information, but I cannot seem to get the code to work. I have annual measurements and want to plot where significant changes in slope occur. I have read somewhere that scaling both the response and explanatory variable between 0-1 and examining where the gradient is >-1 or <1 denotes a significant period of changes, and first-order derivatives should be used for this. Can anyone verify this approach? And if so, suggest code how is best to achieve this? Ultimately, I would like to identify and plot (by highlighting in a different colour) periods of significant change, for two types of datasets like those outlined below. I have seen Gavin Simpson's helpful blog on this ( ) but I cannot get it to work for my own data.

Example 1) Using a very basic dataset I can construct the following GAM and (I think) obtain first order derivatives. But I am not sure what to do from here.

##Create data and scale between 0 and 1
DF <- = 1950, to = 2000, by = 1))
colnames(DF)[1] <- "YEAR"
DF$AVERAGE <- c(1:20,20,20,20,20,20,20:1,1,1,1,1,2,3)
range01 <- function(x){(x-min(x))/(max(x)-min(x))}
DF$YEAR <- range01(DF$YEAR)

###Create GAM
GAM <- gam(AVERAGE ~ s(YEAR), data=DF)
newDF <- with(DF, data.frame(YEAR = unique(YEAR)))
X0 <-, newDF, type = 'lpmatrix'))

Example 2) I'd like to also identify and plot significant changes in slope for two GAM time series whereby values are nested within a factor (SITE here).

DF_NEW <- = 1950, to = 2000, by = 1))
colnames(DF_NEW)[1] <- "YEAR"

DF_NEW <- rbind(DF,DF_NEW)
DF_NEW$SITE <- as.factor(rep(c("A","B"),each = 51))
DF_NEW$YEAR <- range01(DF$YEAR)

GAM2 <- gam(AVERAGE ~ s(YEAR, by = SITE), data = DF_NEW)

Thank you in advance for any help / suggestions.

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