How to predict and graph non-linear varying slopes in lmer or glmer?

Question

My goal is to calculate predicted values from a varying-intercept, varying-slope multilevel model using the lmer and glmer functions of the lme4 package in R. To make this concrete and clear, I present here a toy example with the "mtcars" data set:

Here's how I usually create predicted values from a varying-intercept, varying-slope multilevel model (this code should work just fine):

# loading in-built cars dataset
data(mtcars)

# the "gear" column will be the group-level factor, so we'll have cars nested 
# within "gear" type
mtcars$gear <- as.factor(mtcars$gear)

# fitting varying-slope, varying-intercept model
m <- lmer(mpg ~ 1 + wt + hp + (1 + wt|gear), data=mtcars)

# creating the prediction frame
newdata <- with(mtcars, expand.grid(wt=unique(wt),
                              gear=unique(gear),
                              hp=mean(hp)))

# calculating predictions
newdata$pred <- predict(m, newdata, re.form=~(1 + wt|gear))

# quick ggplot2 graph
p <- ggplot(newdata, aes(x=wt, y=pred, colour=gear))
p + geom_line() + ggtitle("Varying Slopes")

The above R code should work, but if I want to create and graph predictions from a non-linear varying-intercept, varying-slope then it clearly fails. For simplicity and reproducibility, here's the stumbling block using the "mtcars" data set:

# key question: how to create predictions if I want to examine a non-linear 
# varying slope?

# creating a squared term for a non-linear relationship
# NB: usually I use the `poly` function
mtcars$wtsq <- (mtcars$wt)^2

# fitting varying-slope, varying-intercept model with a non-linear trend
m <- lmer(mpg ~ 1 + wt + wtsq + hp + (1 + wt + wtsq|gear), data=mtcars)

# creating the prediction frame
newdata <- with(mtcars, expand.grid(wt=unique(wt),
                                wtsq=unique(wtsq),
                                gear=unique(gear),
                                hp=mean(hp)))

# calculating predictions
newdata$pred <- predict(m, newdata, re.form=~(1 + wt + wtsq|gear))

# quick ggplot2 graph 
# clearly not correct (see the graph below)
p <- ggplot(newdata, aes(x=wt, y=pred, colour=gear))
p + geom_line() + ggtitle("Varying Slopes")

Clearly the prediction frame is not set up correctly. Any ideas on how to create and graph predicted values when fitting a non-linear varying-intercept, varying-slope multilevel model in R? Thanks!

Answer 1

The issue is that when you use expand.grid with both wt and wt^2, you create all possible combinations of wt and wt^2. This modification of your code works:

newdata <- with(mtcars, expand.grid(wt=unique(wt),
                                gear=unique(gear),
                                hp=mean(hp)))
newdata$wtsq <- newdata$wt^2

newdata$pred <- predict(m, newdata)

p <- ggplot(newdata, aes(x=wt, y=pred, colour=gear, group=gear))
p + geom_line() + ggtitle("Varying Slopes")