Take the "Orthodont" dataset from "nlme" for an example. Let's say we want to fit a linear mixed effect model "distance ~ age + random intercept + random slope for age". It seems to me that the following two specifications are equivalent. However, they produce different SE and variance components estimates.
library(nlme)
data("Orthodont")
m.reml1 <- lmer(distance ~ age + (age | Subject), data = Orthodont, REML = T)
m.reml2 <- lmer(distance ~ age + (1 | Subject) + (0 + age | Subject), data = Orthodont, REML = T)
summary(m.reml1)
summary(m.reml2)
From m.reml1
, we get SE 0.77525 and 0.07125 for (Intercept)
and age
.
From m.reml2
, we get SE 0.71380 and 0.06561 for (Intercept)
and age
.
The variance components are also different.
So why the difference? Are they really specifying different models?