Periodic GLM or GLMM
Let take an example: # generate data jo <- 1:800 trans_trigo <- 10+sin((jo/365.25)*2*pi)*1+ cos((jo/365.25)*2*pi)*5 obs <- rnorm(n=800, mean=trans_trigo, sd=2) # plot the data plot(jo, obs, bty="n", xlim=c(1,800), ylim=c(0,20)) par(new=TRUE) plot(jo, trans_trigo, bty="n", xlim=c(1,800), ylim=c(0,20), xlab="", ylab="", axes=FALSE, col="violet", type="l", lwd=2) # group is per month observation mydat <- data.frame(obs=obs, jour=jo, jour2=jo*jo, group=round(jo/27)) # glm with ordinal day as linear factor mod <- glm(obs ~ jour, data=mydat, family=gaussian) summary(mod) newdata <- data.frame(jour=1:800) preddf2 <- predict(mod, type="response", newdata=newdata, se.fit=FALSE) par(new=TRUE) plot(jo, preddf2, bty="n", xlim=c(1,800), ylim=c(0,20), xlab="", ylab="", axes=FALSE, col="red", type="l") # glm with ordinal day as