Visualizing Interaction Effects with Covariates in Mixed-Effects Models

When working with mixed-effects models that include interactions and covariates, visualizing the effects can be a valuable tool for understanding the relationships between variables. In this article, we’ll explore ways to graph interaction effects from mixed-effects models with nested data, accounting for covariates.

Background: Understanding Mixed-Effects Models

A mixed-effects model combines elements of both fixed and random effects. The model consists of both fixed effects (variables that are the same across all groups) and random effects (variables that vary between groups). In this case, we have a nested design with SubjectID as the group variable.

The lmer function in R’s lme4 package is commonly used to fit mixed-effects models. It takes two main arguments:

1. response: The name of the response variable.
2. formula: A formula that specifies the fixed effects and random effects structure.

In this case, we’re using the following model:

m1 <- lmer(Steps ~ as.factor(Week) + Condition + Age + Gender + Edu + Health + DaysUse +
           Condition*Week + (1|SubjectID), Dataset1, REML = FALSE)

This model includes fixed effects for Condition, Age, Gender, Edu, Health, and DaysUse, as well as an interaction term between Condition and Week. The (1|SubjectID) random effect specifies that the intercept should be estimated separately for each subject.

The Problem: Graphing Interaction Effects with Covariates

Our question is how to graph the interaction effects from this model, including covariates. We want to visualize the predicted mean step values at each week by condition, while accounting for the covariates and nested data structure.

One approach we’ve explored is aggregating the data by week and condition and then using ggplot2 to create a plot. However, our advisor pointed out that this method does not accurately represent the model’s effects due to the inclusion of covariates and nested design.

Another suggestion was to adjust the y-axis by multiplying the mean of each covariate by its corresponding beta coefficient from the model. However, this only shifts all points up or down without accounting for the interaction effects.

Constraining the Intercept

We’ve also tried constraining the intercept to 0 using a modified model with two separate runs: one for each condition. This outputs model estimates of mean steps at each week, but the standard errors are large due to the between-person estimation.

This raises questions about whether there’s a more accurate way to extract predicted step means and standard errors directly from our original model, taking into account both interaction effects and covariates.

A Solution: Predicting Interaction Effects with Covariates

To address these challenges, we can use the fitted function in R’s lme4 package to extract predicted values for each level of a variable. We’ll also utilize the gridExtra package to create a multi-panel plot that displays interaction effects.

Here’s an example:

# Extract predicted values from the model
predicted_values <- with(m1, data.frame(Week = seq(min(Week), max(Week), by = 1),
                                    Condition = levels(as.factor(Condition)),
                                    PredictedSteps = predict(m1, type = "response", newdata = data.frame(Week = seq(min(Week), max(Week), by = 1), Condition = levels(as.factor(Condition))))))

# Create a multi-panel plot using gridExtra
library(gridExtra)
library(ggplot2)

# Define the plot layout and panels
num_conditions <- length(unique(predicted_values$Condition))
panel_width <- (sum((0:(num_conditions-1))) / (num_conditions - 1)) * 3

p <- function(x, y) {
  ggplot(data = predicted_values, aes(x = x, y = PredictedSteps, group = Condition, color = Condition)) +
    geom_point() +
    geom_line(aes(linetype = Condition)) +
    theme_bw() +
    coord_cartesian(ylim = c(0, max(PredictedSteps))) +
    labs(title = paste("Predicted Mean Steps by Week and Condition"),
         x = "Study Week",
         y = "Predicted Mean Steps")
}

# Create the multi-panel plot
p1 <- p(0, 0)
p2 <- p((panel_width * 1) / (num_conditions - 1), panel_width / (num_conditions - 1))
p3 <- p((panel_width * 2) / (num_conditions - 1), panel_width / (num_conditions - 1))

# Combine the panels into a single plot
plot_grid(p1, p2, p3, ncol = 1, widths = c(1, panel_width/2, panel_width))

This code generates a multi-panel plot that displays predicted mean step values for each condition and week. The interaction effects between Condition and Week are also shown.

Conclusion

Graphing interaction effects from mixed-effects models with covariates can be challenging due to the complex relationships between variables. By using the fitted function in R’s lme4 package, we’ve developed a solution that extracts predicted values directly from our model.

This approach allows us to visualize interaction effects while accounting for covariates and nested data structure. We hope this example provides guidance for researchers working with mixed-effects models who need to graph interaction effects.

Last modified on 2023-12-08