Understanding the Fixed Effects Correlation in lmer Output

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In multilevel modeling, it’s common to encounter large matrices of correlations, particularly when dealing with fixed effects. These matrices can be challenging to interpret and visualize, especially for those unfamiliar with statistical analysis.

In this post, we’ll delve into the world of mixed models, focusing on extracting the correlation of fixed effects from lmer output. We’ll explore various approaches and discuss the benefits of using built-in functions in R, such as cov2cor(vcov(mod)).

Background: Mixed Models and Fixed Effects

Mixed models are an extension of traditional linear regression models, allowing for the incorporation of random effects to account for variability between groups or levels. The fixed effects, on the other hand, represent the main predictors in a model.

In lmer (linear mixed effects) output, there’s a section labeled “Fixed Effects.” This section displays the coefficients for the fixed effects terms, along with their standard errors and p-values. However, beneath this section lies a matrix of correlations between these fixed effects, which can be challenging to visualize.

Approaches to Extracting Fixed Effects Correlation

1. Using symbolic.cor=T in print method

As mentioned in the question, using the symbolic.cor=T parameter in the print method can provide a clearer representation of the summary output, including the correlation matrix for fixed effects.

print(mod <- lmer(activate ~ region * treatment + (0 + treatment | animal), ratbrain), symbolic.cor = T)

This approach is useful when dealing with smaller matrices, but it may not be ideal for larger datasets.

2. Creating a custom function: fixeff.plotcorr

The provided function, fixeff.plotcorr, offers an alternative method to visualize the correlation matrix of fixed effects. This function relies on another correlation plot library called GGally (Generalized Graphs).

fixeff.plotcorr <- function(mod, ...)
{
  # require(GGally)
  require(lme4)

  fixNames <- names(fixef(mod))

  df <- as.matrix(cov2cor(vcov(mod)))
  rownames(df) <- fixNames
  colnames(df) <- abbreviate(fixNames, minlength = 11)

  # ...
}

This approach provides more control over the visualization but requires additional libraries (GGally and RColorBrewer).

3. Utilizing cov2cor(vcov(mod))

The most straightforward method for extracting the correlation matrix of fixed effects is by using the built-in function cov2cor(vcov(mod)). This approach is efficient and doesn’t require any external libraries.

df <- as.matrix(cov2cor(vcov(mod)))
rownames(df) <- fixNames
colnames(df) <- abbreviate(fixNames, minlength = 11)

Choosing the Best Approach

When deciding which approach to use, consider the following factors:

• Dataset size: If you’re working with smaller datasets, symbolic.cor=T might be sufficient. For larger matrices, cov2cor(vcov(mod)) is a more efficient and straightforward solution.
• Visualization preferences: If you want more control over the visualization or prefer a different style, fixeff.plotcorr could be a better choice. However, this approach requires additional libraries and setup.

Example Use Case

Let’s create an example dataset and fit a simple mixed model to demonstrate how to extract the correlation matrix of fixed effects using cov2cor(vcov(mod)).

# Load required libraries
library(lme4)

# Create example dataset
set.seed(123)
treatment <- factor(rep(c("Basal", "Carbachol"), each = 10))
region <- factor(rep(c("BST", "LS", "VDB"), 3))
animal <- rep(1:30, 3)
activate <- rnorm(30)

# Fit mixed model
model <- lmer(activate ~ region * treatment + (0 + treatment | animal))

# Extract correlation matrix of fixed effects
df <- as.matrix(cov2cor(vcov(model)))
rownames(df) <- fixNames(fixef(model))
colnames(df) <- abbreviate(fixNames, minlength = 11)

# Print the correlation matrix
print(df)

This example showcases how to extract the correlation matrix of fixed effects from an lmer model using cov2cor(vcov(mod)). The resulting correlation matrix can be used for further analysis or visualization.

In conclusion, extracting the correlation matrix of fixed effects from lmer output is a crucial step in statistical analysis. By understanding the different approaches available and choosing the most suitable method, researchers can gain insights into the relationships between fixed effects terms.

Last modified on 2024-08-29