Mixed effects models with lme4

This vignette replicates some of the analyses in this excellent blog post by Solomon Kurz: Use emmeans() to include 95% CIs around your lme4-based fitted lines

Load libraries and fit two models of chick weights:

library(lme4)
library(tidyverse)
library(patchwork)
library(marginaleffects)

# unconditional linear growth model
fit1 <- lmer(
  weight ~ 1 + Time + (1 + Time | Chick),
  data = ChickWeight)

# conditional quadratic growth model
fit2 <- lmer(
  weight ~ 1 + Time + I(Time^2) + Diet + Time:Diet + I(Time^2):Diet + (1 + Time + I(Time^2) | Chick),
  data = ChickWeight)

Unit-level predictions

Predict weight of each chick over time:

pred1 <- predictions(fit1,
                     newdata = datagrid(Chick = ChickWeight$Chick,
                                        Time = 0:21))

p1 <- ggplot(pred1, aes(Time, predicted, level = Chick)) +
      geom_line() +
      labs(y = "Predicted weight", x = "Time", title = "Linear growth model")

pred2 <- predictions(fit2,
                     newdata = datagrid(Chick = ChickWeight$Chick,
                                        Time = 0:21))

p2 <- ggplot(pred2, aes(Time, predicted, level = Chick)) +
      geom_line() +
      labs(y = "Predicted weight", x = "Time", title = "Quadratic growth model")

p1 + p2

Predictions for each chick, in the 4 counterfactual worlds with different values for the Diet variable:

pred <- predictions(fit2)

ggplot(pred, aes(Time, predicted, level = Chick)) +
    geom_line() +
    ylab("Predicted Weight") +
    facet_wrap(~ Diet, labeller = label_both)

Population-level predictions

To make population-level predictions, we set the Chick variable to NA, and set include_ranom=FALSE. This last argument is offered by the insight::get_predicted function which is used behind the scenes to compute predictions:

pred <- predictions(
    fit2,
    newdata = datagrid(Chick = NA,
                       Diet = 1:4,
                       Time = 0:21),
    include_random = FALSE)

ggplot(pred, aes(x = Time, y = predicted, ymin = conf.low, ymax = conf.high)) +
    geom_ribbon(alpha = .1, fill = "red") +
    geom_line() +
    facet_wrap(~ Diet, labeller = label_both) +
    labs(title = "Population-level trajectories")