alternative interaction representations
On Sun, 22 Aug 2010 08:47:47 +0200,
Reinhold Kliegl <reinhold.kliegl-Re5JQEeQqe8AvxtiuMwx3w at public.gmane.org> wrote:
# This representation fits two linear slopes, one below and one after conc = 300, splicing them at 0: CO2new$conc1 <- ifelse(CO2new$conc < 300, CO2new$conc - 300, 0) CO2new$conc2 <- ifelse(CO2new$conc > 300, CO2new$conc - 300, 0)
# Basic LMM print(LMM <- lmer(uptake ~ conc1 + conc2 + (1 | Plant), data=CO2new), cor=FALSE) # ... the linear uptake is significant below 300, no longer significant after 300 # ... the intercept estimates the upake at conc=300
# To test whether there is significant between-plant variance in slopes below and above conc: # Varying-slopes LMM print(LMM.conc.1 <- lmer(uptake ~ conc1 + conc2 + (1 | Plant) + (0+conc1 | Plant), data=CO2new), cor=FALSE) print(LMM.conc.2 <- lmer(uptake ~ conc1 + conc2 + (1 | Plant) + (0+conc2 | Plant), data=CO2new), cor=FALSE) #print(LMM.conc.1.2 <- lmer(uptake ~ conc1 + conc2 + (1 | Plant) + (0+conc1 | Plant) + (0+conc2 | Plant), data=CO2new), cor=FALSE) #print(LMM.conc.12 <- lmer(uptake ~ conc1 + conc2 + (1 + conc1 + conc2 | Plant), data=CO2new), cor=FALSE)
anova(LMM, LMM.conc.1) anova(LMM, LMM.conc.2) # Apparently there is not enough information in the data to test the between-slope variance.
Thanks Reinhold, it seems as if these piecewise linear splines with one or two knots are easier to fit and interpret than using a factor. Cheers,
Seb