emtrends and piecewise regression

I want to obtain four slopes for piecewise regression. Two slopes for each release type before 365 days, and after 365 days. I also know I should use the emmeans package.

Here is a dummy dataset.

 df <- data.frame (tsr = c(0,0,9,10,19,20,20,21, 30,30,100,101,200,205,350,360, 400,401,500,501,600,605,700,710,800,801,900,902,1000,1001,1100,1105,2000,2250,2500,2501),
              release_type = c('S','H','S','H','S','S','H','S','H','S','S','H','S','H','S','S','H','S','H','S','S','H','S','H','S','S','H','S','H','S','S','H','S','H','S', 'H'),
              cond = c(250,251,250,251,300,301,351,375,250,249,216,257,264,216,250,251,250,251,300,301,351,375,250,249,216,257,264,216, 250,251,250,251,300,301,351,375),
              notch = c('A','B','C','D','A','B','C','D','A','B','C','D','E','G','E','G','A','H','J','K','L','Q','W','E','R','Y','U','I','O','P','Y','U','I','O','P', 'Z'))

 #Load libraries
 library(emmeans)
 library(lme4)

 #Set up break point manually
 bp = 365
 b1 <- function(x, bp) ifelse(x < bp, bp - x, 0)
 b2 <- function(x, bp) ifelse(x < bp, 0, x - bp)
 
 #Fit linear mixed effect model using piecewise regression
 m1 <- lmer(cond~b1(tsr, bp) + b2(tsr,bp) + b1(tsr, bp):release_type 
       + b2(tsr,bp):release_type + release_type + (1|notch), data = df)

 #Obtain slopes
 emtrends(m1, params = "bp", var = "tsr", pairwise ~ release_type)

I am only getting estimates for one slope of each release type. What am I doing wrong?

Note: I cannot use the summary() function to obtain slopes because it uses the function above to generate those estimates. So it is not the pure slopes.

Solution

You have to add at = list(tsr = c(10, 400)) to the emtrends() call to specify representative times before and after the breakpoint. Otherwise, it just uses the average value of tsr since it is a quantitative predictor.

Update

You need to specify tsr also. Otherwise it will average over the two values of tsr.

> emtrends(m1, params = "bp", var = "tsr", ~ release_type*tsr, at = list(tsr=c(10,400)))
NOTE: Results may be misleading due to involvement in interactions
 release_type tsr tsr.trend     SE   df lower.CL upper.CL
 H             10   -0.0170 0.0932 30.0 -0.20743   0.1734
 S             10   -0.0894 0.0759 25.5 -0.24569   0.0668
 H            400    0.0343 0.0215 30.0 -0.00970   0.0782
 S            400    0.0341 0.0214 29.3 -0.00963   0.0778

Degrees-of-freedom method: kenward-roger 
Confidence level used: 0.95

If you had read the annotations below the output when tsr was omitted, this would have been evident.