This note was prepared for Conjointly researchers, but it would be a shame to hide it inside internal documentation. It is very technical. You do not need to know any of this to use the tools. 😊
Understanding random effects models starts with Jared Knowles’ article Getting Started with Mixed Effect Models in R. Now, let’s get our hands dirty and generate some random data:
library(lme4)
library(data.table)
N=300
# Assign real coefficients
real_coefficients=list(
blue=10,
yellow=-10,
green=5,
speed=5,
intercept=50
)
# Colour is a property of the object
data=data.table(
colour=sample(c("blue","yellow","green"),N,replace=T),
speed=runif(N,1,50)
)
# And assigning innate preference for each colour
for(i in names(real_coefficients)){
data[colour==i, innate_preference:= real_coefficients[[i]]]
}
# Actual preference is sum of innate preference for colour, innate preference for speed and error
data[,preference:=
real_coefficients[["intercept"]]+
innate_preference+
(real_coefficients[["speed"]]*speed)+
rnorm(N)
]
# Review what we have
data
Let’s estimate a simple model
summary(lm(preference~colour+speed,data=data))
Compare its coefficients to real_coefficients.
Let’s add random effect: measurement instrument (an intercept)
data$instrument=sample(c(-10,0,10),N,replace=T)
data[, new_preference:=preference+instrument]
# Explore results of model
model=lmer(new_preference~colour+speed + (1 | instrument), data = data)
summary(model)
coef(model)$instrument
Let’s add random effect: speed of measurement instrument (a slope)
data$instrument_speed=sample(c(-10,0,10),N,replace=T)
data[, new_preference:=preference+speed*instrument_speed+rnorm(N)]
# Explore results of model
model=lmer(new_preference~colour+speed + (speed | instrument_speed), data = data)
summary(model)
coef(model)$instrument_speed
That’s the end! Now we understand mixed effect models!
